2022-23 LMF Seminar Series
Spring term
Date: Thursday, January 19, 2023
Time: 16:00-17:00
Location: LSE, 32L.LG.04
Speaker: Jan Palczewski
Title: A non-zero sum game of exit from a stochastic market with private information
Abstract: The timing of a strategic exit is one of the most important business decisions particularly under competition. Motivated by this problem, we examine a stochastic game of exit in which players are do not know their competitor's exit payoff. It is a non-zero sum stopping game with asymmetric information. The market uncertainty, observed by both players, is represented by a general one-dimensional diffusion. Under the condition that a single player exit problem has a solution of a threshold type, we construct a symmetric equilibrium in pure strategies. This equilibrium is further shown to be unique in a wide subclass of symmetric perfect Bayesian equilibria. Our arguments are mainly probabilistic with an occasional use of PDE methods.
Date: Thursday, January 19, 2023
Time: 17:00-18:00
Location: LSE, 32L.LG.04
Speaker: Stephan Eckstein
Title: Model uncertainty, neural networks, and convergence rates of regularized optimal transport
Abstract: First, this talk introduces the robust pricing problem in the context of model uncertainty and a numerical solution method based on neural networks. For the goal of obtaining approximation guarantees, we identify a crucial question, which is to quantify the error introduced by a certain regularization of the robust pricing problem. While this question is open in the general case, the main part of the talk will focus on an important special case, which is the multi-marginal optimal transport problem. In this regard, the talk showcases a method to obtain sharp convergence rates using a novel methodology based on quantization of probability measures and martingale couplings. The main benefits of the method are its general applicability (multi-marginal problems, general cost functions and regularization divergences), while even in the most frequently studied case of entropically regularized 2-Wasserstein distance, our results extend known results from the literature by allowing for non-compactly supported marginals. Based on joint work together with Michael Kupper and Marcel Nutz.
Date: Thursday, February 02, 2023
Time: 16:00-17:00
Location: LSE, 32L.LG.04
Speaker: Gechun Liang
Title: Robust limit theorem for nonlinear Levy processes under sublinear expectation
Abstract: We introduce a universal robust limit theorem under a sublinear expectation framework. It covers both Peng's robust CLT and Bayraktar-Munk's robust limit theorem for alpha-stable distribution. To prove the convergence, we develop a novel weak convergence approach based on the notion of tightness and weak compactness on a sublinear expectation space. We further prove a new type of Levy-Khintchine representation formula to characterise the limiting nonlinear Levy process. To establish the convergence rate, we use and extend techniques introduced by Krylov and Barles-Jakobsen for the monotone schemes for viscosity solutions. Based on a series of joint works with Mingshang Hu, Shuo Huang, Lianzi Jiang and Shige Peng.
Date: Thursday, February 02, 2023
Time: 17:00-18:00
Location: LSE, 32L.LG.04
Speaker: Eyal Neumann
Title: Optimal Liquidation with Signals: the General Propagator Case
Abstract: We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as minimization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we characterize the value function in terms of a solution to a free-boundary $L^2$-valued backward stochastic differential equation and an operator-valued Riccati equation. We then derive analytic solutions to these equations which yields an explicit expression for the optimal trading strategy. We show that our formulas can be implemented in a straightforward and efficient way for a large class of price impact kernels with possible singularities such as the power-law kernel. This is a joint work with Eduardo Abi-Jaber.
Date: Thursday, February 16, 2023
Time: 16:00-17:00
Location: LSE, 32L.LG.04
Speaker: Paolo Guasoni
Title: Rogue Traders
Abstract: Investing on behalf of a firm, a trader can feign personal skill by committing fraud that with high probability remains undetected and generates small gains, but that with low probability bankrupts the firm, offsetting ostensible gains. Honesty requires enough skin in the game: if two traders with isoelastic preferences operate in continuous-time and one of them is honest, the other is honest as long as the respective fraction of capital is above an endogenous fraud threshold that depends on the trader’s preferences and skill. If both traders can cheat, they reach a Nash equilibrium in which the fraud threshold of each of them is lower than if the other one were honest. More skill, higher risk aversion, longer horizons, and greater volatility all lead to honesty on a wider range of capital allocations between the traders.
Date: Thursday, February 16, 2023
Time: 17:00-18:00
Location: LSE, 32L.LG.04
Speaker: Yan Dolinsky
Title: Utility Indifference Pricing with High Risk Aversion and Small Linear Price Impact
Abstract: We consider the Bachelier model with linear price impact. Exponential utility
indifference prices are studied for vanilla European options and we compute their non-trivial scaling
limit for a vanishing price impact which is inversely proportional to the risk aversion. Moreover, we
find explicitly a family of portfolios which are asymptotically optimal.
Date: Thursday, March 02, 2023
Time: 16:00-17:00
Location: LSE, 32L.LG.04
Speaker: Huyen Pham
Title: Generative modeling for time series via Schrödinger bridge
Abstract: We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We can estimate the drift function from data samples either by kernel regression methods or with LSTM neural networks, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. We start with toy autoregressive and fat-tailed distribution models, and measure the accuracy of our algorithm with marginal and temporal dependencies metrics. A second series of tests deals with the example of fractional Brownian motion, and we finally illustrate our method for the application to deep hedging on real-data sets. (Based on joint work with Mohamed Hamdouche and Pierre-Henry Labordère.)
Date: Thursday, March 02, 2023
Time: 17:00-18:00
Location: LSE, 32L.LG.04
Speaker: Kees Oosterlee
Title: AIDA: an Analytic Isolation and Distance-based Anomaly detection algorithm
Abstract: In this presentation, we'll talk about anomaly detection and anomaly explanation, which is an important topic in anti-money laundering and also in fraud detection. Many unsupervised anomaly detection algorithms rely on the concept of nearest neighbours to compute the anomaly scores. Such algorithms are popular because there are no assumptions on the data, making them a robust choice for unstructured datasets. Unfortunately, the number (k) of nearest neighbours, which critically affects the model performance, cannot be tuned in an unsupervised setting. Hence, we propose a new and parameter-free Analytic Isolation and Distance-based Anomaly (AIDA) detection algorithm, that combines the metrics of distance with isolation. Based on AIDA, we also introduce the Tempered Isolation-based eXplanation (TIX) algorithm, which identifies the most relevant features characterizing an outlier, even in large multi-dimensional datasets, improving the overall explainability of the detection mechanism. Both AIDA and TIX are thoroughly tested and compared with state-of-the-art alternatives, proving to be useful additions to the existing set of tools in anomaly detection.
Date: Thursday, March 16, 2023
Time: 16:00-17:00
Location: LSE, 32L.LG.04
Speaker: Zachary Feinstein
Title: Axioms for Automated Market Makers: A Mathematical Framework in Decentralized Finance
Abstract: Within this talk, we introduce an axiomatic framework for Automated Market Makers (AMMs). By imposing reasonable axioms on the underlying utility function, we are able to characterize the properties of the swap size of the assets and of the resulting pricing oracle. We will analyze many existing AMMs and show that the vast majority of them satisfy our axioms. We will also consider the question of fees and divergence loss. In doing so, we will propose a new fee structure so as to make the AMM indifferent to transaction splitting. Finally, we will propose a novel AMM that has nice analytical properties and provides a large range over which there is no divergence loss.
Date: Thursday, March 16, 2023
Time: 17:00-18:00
Location: LSE, 32L.LG.04
Speaker: Kasper Larsen
Title: Equilibria with trading targets
Abstract: We will present various equilibrium models (Kyle, Radner, and Nash) populated by traders with different trading motives. Some traders can have an informational advantage (such as an insider) whereas other traders can face trading targets (soft or hard). We are interested in existence of equilibria and its properties.
2021-22 LMF Seminar Series
Spring term
Date: Thursday, January 20, 2022
Time: 16:00-17:00
Zoom registration:
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Date: Thursday, February 03, 2021
Time: 17:00-18:00
Zoom registration:
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Speaker: Agostino Capponi (Columbia University)
Title:
Robo-Advising: Personalization and Goals-Based Investing.
Abstract: Robo-advising encompasses any form of algorithmic advice offered to clients. We begin by presenting a dynamic optimization framework based on human-machine interactions, where robo-advisors personalize their portfolios to the clients they serve. We characterize the interaction frequency which strikes the optimal balance between frequent interactions to learn clients' risk attitudes and mitigation of behavior biases in clients' responses. We then discuss goal-based robo-advising which, rather than optimizing portfolio Sharpe ratios, aims at maximizing satisfaction of investors' goals by the specified deadlines. We introduce a stochastic control framework for goals based investing, and study the tradeoff between funding the current goal versus saving to meet higher priority future goals.
Date: Thursday, February 17, 2022
Time: 16:00-17:00
Zoom registration:
https://lse.zoom.us/meeting/register/tZwrfuigrj0rGtUvfSqhy4oNTUt7Y_m3ajjn
Speaker: Ludovic Tangpi (Princeton University)
Title: Optimal investment in a large population of competitive and heterogeneous agents
Abstract: We consider a large crowd of exponential utility maximizers acting competitively in the sense that each agent is concerned with the relative performance of their peers. In contrast to the growing literature on the question, we allow agents to weigh the performance of each of their peers differently. This leads to a game among heterogeneous agents set on a graph. We show that if the underlying graph stems from a step graphon then the finite population game converges to a so-called graphon game whose well-posedness is studied. This is a game played by a continuum of interacting players generalizing the mean field game (which corresponds to the constant graphon case). The analysis is based on purely probabilistic arguments, allows for trading constraints and a “not so dense graph”. The talk is based on a join work with Louise Zhou.
Date: Thursday, March 3, 2022
Time: 16:00-17:00
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Date: Thursday, March 17, 2022
Time: 16:00-17:00
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Date: Thursday, March 31, 2022
Time: 16:00-17:00
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Autumn term
Date: Thursday, September 30, 2021
Time: 16:00-17:00
Zoom registration: https://lse.zoom.us/meeting/register/tZwrfuigrj0rGtUvfSqhy4oNTUt7Y_m3ajjn
Speaker:
Semyon Malamud (Ecole Polytechnique Fédérale de Lausanne)
Title:
Persuasion by Dimension Reduction
Abstract: How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent (the receiver) to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by projecting the state onto a lower-dimensional object that we call the "optimal information manifold". We characterize geometric properties of this manifold and link them to the sender's preferences. The policy splits information into "good" and "bad" components. When the sender's marginal utility is linear, it is always optimal to reveal the full magnitude of good information. By contrast, with concave marginal utility, optimal information design conceals extreme realizations of good information and only reveals its direction (sign). We illustrate these effects by explicitly solving several multi-dimensional Bayesian persuasion problems.
Date: Thursday, October 14, 2021
Time: 16:00-17:00
Zoom registration: https://lse.zoom.us/meeting/register/tZwrfuigrj0rGtUvfSqhy4oNTUt7Y_m3ajjn
Speaker:
Dylan Possamai (ETH Zürich)
Title:
Non-asymptotic convergence rates for mean-field games: weak formulation and McKean–Vlasov BSDEs
Abstract: This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker [23], we consider a fully non-Markovian setting allowing for drift control, and interactions through the joint distribution of players’ states and controls. We provide first a new characterisation of mean-field equilibria as arising from solutions to a novel kind of McKean–Vlasov backward stochastic differential equations, for which we provide a well-posedness theory. We incidentally obtain there unusual existence and uniqueness results for mean-field equilibria, which do not require short-time horizon, separability assumptions on the coefficients, nor Lasry and Lions’s monotonicity conditions, but rather smallness conditions on the terminal reward. We then take advantage of this characterisation to provide non-asymptotic rates of convergence for the value functions and the Nash-equilibria of the N-player version to their mean-field counterparts, for general open-loop equilibria. This relies on new backward propagation of chaos results, which are of independent interest. This is a joint work with Ludovic Tangpi.
Date: Thursday, October 28, 2021
Time: 16:00-17:00
Zoom registration: https://lse.zoom.us/meeting/register/tZwrfuigrj0rGtUvfSqhy4oNTUt7Y_m3ajjn
Speaker:
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Date: Thursday, November 11, 2021
Time: 16:00-17:00
Zoom registration: https://lse.zoom.us/meeting/register/tZwrfuigrj0rGtUvfSqhy4oNTUt7Y_m3ajjn
Speaker:
Stephen Roberts (Oxford)
Title: Strength in Depth? Deep Learning for Finance.
Abstract: Love it or loathe it, there is no denying that Deep Learning helped to kickstart the AI frenzy of recent years. From high-profile game playing algorithms, to deeply impressive vision, language and text applications, it seems that Deep Learning offers a subtle twist on the way algorithms learn and reason. In this talk we will look at some of the concepts underpinning these advances and highlight our recent work using Deep Learning for limit order books, momentum trading, portfolios and execution strategies. (along with a few other things along the way).
Date: Thursday, November 25, 2021
Time: 16:00-17:00
Zoom registration: https://lse.zoom.us/meeting/register/tZwrfuigrj0rGtUvfSqhy4oNTUt7Y_m3ajjn
Speaker:
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Date: Thursday, December 9, 2021
Time: 16:00-17:00
Zoom registration: https://lse.zoom.us/meeting/register/tZwrfuigrj0rGtUvfSqhy4oNTUt7Y_m3ajjn
Speaker:
Sasha Rakhlin (MIT)
Title:
A new approach to contextual bandits
Abstract:
Contextual bandits, a generalization of the classical multi-armed bandit problem, is a basic decision-making setting where the reward
distribution depends on the side-information (covariates) presented to the statistician before each decision. A fundamental challenge in
contextual bandits is to develop flexible, general-purpose algorithms with computational requirements no worse than classical supervised
learning tasks. In this talk, we will describe a universal and minimax optimal reduction from contextual bandits to online and offline
regression. We characterize the minimax rates for contextual bandits with general, potentially nonparametric function classes, and show
that our algorithm is minimax optimal whenever the online regression method is optimal. We then turn to the case of iid data and present an
adaptive method that attains fast instance-dependent rates, whenever certain disagreement-based notions of problem complexity are bounded.
We discuss extensions to combinatorial settings with submodular rewards, as well as reinforcement learning.
2019-20 LMF Seminar Series
Spring term
Date: Thursday 23 January 2020
Speaker #1: Juan-Pablo Ortega (University of St. Gallen (Switzerland) and CNRS (France))
Time: 17:00-18:00 (registration starts at 16h30)
Place: Goldman Sachs Offices, Plumtree Court, 2 Stonecutter Street, London EC4A 4AH
Title: Reservoir Computing with Applications to Realized Volatility Forecasting
Abstract: The last years have seen the emergence of significant interplays between machine learning, dynamical systems, and stochastic processes with interesting applications in time series analysis and forecasting. The resulting techniques have revolutionized the way in which we learn and path-continue complex and high-dimensional deterministic dynamical systems and preliminary results show that the hope for similar success is justified in the stochastic context.
In this seminar, I will present how these techniques are built and will analyse their connections with classical results in systems and approximation theories, control, filtering, and dynamical systems. In order to adopt a point of view as close as possible to the applications, we will work in semi-infinite discrete-time input/output setups. This allows us to adequately model the non-markovianity associated to the observations and the subsystems of large dimensional systems and, additionally, provides us with the necessary tools for the development of both finite-sample and asymptotic results in estimation theory.
Some time will be dedicated to explaining the implementation of these techniques in the identification and path continuation of deterministic systems (learning of chaotic attractors) and forecasting of stochastic processes (realized financial covariances). We shall see how these novel techniques outperform all the benchmarks available in the literature to accomplish those tasks.
Speaker #2: Andreas Joseph (Bank of England)
Time: 18:00-19:00
Place: Goldman Sachs Offices, Plumtree Court, 2 Stonecutter Street, London EC4A 4AH
Title: Parametric inference on universal approximators and the case of financial crisis prediction using ML
Abstract: The class of universal approximators sits at the heart of modern machine learning advances, including artificial neural networks and tree-ensembles among others. These models are often critiqued as being black boxes: There is no transparent input-output relation from a fitted model. In this talk, I show how the Shapley value framework from cooperative game theory can be used to devise a rigorous - but also easy-to-use - statistical inference framework on general machine learning models. This opens the black box and allows for well-defined hypothesis testing. I apply this approach to the problem of predicting major financial crisis in the last 140 years. Model inference uncovers strong and important nonlinearities in the data generating process with credit growth and the yield curve slope, domestically and globally, being the most important predictors. A flat or inverted yield curve is of most concern when nominal interest rates are low and credit growth is high, suggesting search-for-yield behaviour as one of the causes of financial crises.
Date: Thursday 6 February 2020
Speaker #1: Mathias Beiglböck (University of Wien)
Time: 16:00-16:45
Place: King's College London, Strand Building, room S3.30
Title: Adapted Wasserstein distances and stability in mathematical finance
Abstract:Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize
some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility that Q
does not provide an exact description of reality. This leads us the following question: will the hedge still be somewhat meaningful for
models in the proximity of Q? If we measure proximity with the usual Wasserstein distance (say), the answer is NO. Models which are similar wrt Wasserstein distance may provide dramatically different information on which to base a hedging strategy. Remarkably, this can be overcome by considering a suitable adapted version of the Wasserstein distance which takes the temporal structure of pricing models into account. This adapted Wasserstein distance is most closely related to the nested distance as pioneered by Pflug and Pichler. It allows us to establish Lipschitz properties of hedging strategies for semimartingale models in discrete and continuous time. Notably, these abstract results are sharp already for Brownian motion and European call options.
Speaker #2: Josef Teichmann (ETH Zürich)
Time: 17:00-17:45
Place: King's College London, Strand Building, room S3.30
Title: Randomness in training neural networks and applications to
portfolio selection
Abstract: Several features of randomness enter successful training procedures in machine learning: random initialization or random feature selection, to mention just two. Some of them have interesting interpretations, and some of those interpretations are of interest in finance. We shall present recent work on controlled ordinary differential equations, which serve as a model for deep neural networks or recurrent neural networks depending on the respective input space, where expressiveness is explained by either random, hence generic, characteristics or random projections. Special random recurrent neural networks, called random signatures due to their reminiscence to signature from rough path theory, are then used to construct drift estimators in high dimensional market environments for the purposes of portfolio selection. We discuss the meaning of this procedure from a financial point of view. (joint work with Erdinc Akyildirim, Christa Cuchiero, Lukas Gonon,
Lyudmila Grigoryeva, Martin Larsson, Juan-Pablo Ortega)
Date: Thursday 20 February 2020
Speaker #1: Jaksa Cvitanic
Time: 16:00-16:45
Place: King's College London, Strand Building, room S3.30
Title: Optimal Fund Menus
Abstract:We study the optimal design of a menu of funds by a manager who is required to use linear pricing and does not observe the beliefs of investors regarding one of the risky assets. The optimal menu involves bundling of assets and can be explicitly constructed from the solution to a calculus of variations problem that optimizes over the indirect utility that each type of investor receives. We provide a complete characterization of the optimal menu and show that the need to maintain incentive compatibility leads the manager to offer funds that are inefficiently tilted towards the asset that is not subject to the information friction (joint with Julien Hugonnier).
Speaker #2: Philip Protter (Columbia University)
Time: 17:00-17:45
Place: King's College London, Strand Building, room S3.30
Title:New Results on Continuously Expanding a Filtration
Abstract:We "review" how one can expand a filtration by continuously adding a stochastic process. The new results (obtained with Léo Neufcourt) relate to the seimartingale decompositions after the expansion. We give some possible applications.
Date: Thursday 5 March 2020
Speaker #1: Mathieu Rosenbaum (Ecole Polytechnique)
Time: 16:00-16:45
Place: King's College London, Strand Building, room S3.30
Title: Super-Heston rough volatility, Zumbach effect and the Guyon's conjecture
Abstract:The rough Heston model is known to reproduce accurately the behavior of historical volatility time series as well as the dynamics of the implied volatility surface. However, some argue that actual volatility tails are even fatter than that generated in the rough Heston model. Furthermore, it fails to reproduce a very subtle property of historical data referred to as Zumbach effect. In this talk we address these two concerns introducing so-called super-Heston rough volatility models. It turns out that these models enable us to obtain joint calibration of both SPX and VIX implied volatility surfaces, hence providing a counter-example to a long-standing conjecture by Julien Guyon. This is joint work with Aditi Dandapani, Jim Gatheral and Paul Jusselin.
Speaker #2: Goncalo dos Reis (Edinburgh University)
Time: 17:00-17:45
Place: King's College London, Strand Building, room S3.30
Title:Ito type Chain rule for measure dependent random fields under full and conditional measure flows
Abstract:We present several Itô-Wentzell formulae on Wiener spaces for real-valued functionals random field of Itô type depending on measures. We distinguish the full- and marginal-measure flow cases. Derivatives with respect to the measure components are understood in the sense of Lions. This talk is based on joint work with V. Platonov (U. of Edinburgh), see https://arxiv.org/abs/1910.01892.
Date: Thursday 19 March 2020 (CANCELLED)
Speaker #1: Ioannis Karatzas (Columbia University)
Time: 16:00-16:45
Place: King's College London, Strand Building, room S3.30
Title:Consevarive diffusion as entropic gradient flux
Abstract:We provide a detailed, probabilistic interpretation, based on stochastic calculus, for the variational characterization of conservative diffusion as entropic gradient flux. Jordan, Kinderlehrer, and Otto showed in 1998 that, for diffusions of Langevin-Smoluchowski type, the Fokker-Planck probability density flow minimizes the rate of relative entropy dissipation, as measured by the distance traveled in terms of the quadratic Wasserstein metric in the ambient space of configurations. Using a very direct perturbation analysis we obtain novel, stochastic-process versions of such features. These are valid along almost every trajectory of the diffusive motion in both the forward and, most transparently, the backward, directions of time. The original results follow then simply by taking expectations. As a bonus, we obtain the HWI inequality of Otto and Villani relating relative entropy, Fisher information and Wasserstein distance; and from it, the log-Sobolev, Talagrand and Poincare inequalities of functional analysis. (Joint work with W. Schachermayer and B. Tschiderer, from the University of Vienna.)
Speaker #2: Erhan Bayraktar (Michigan University)
Time: 17:00-17:45
Place: King's College London, Strand Building, room S3.30
Title:
Abstract:
Date: Thursday 2 April 2020 (CANCELLED)
Speaker #1: Bernard de Meyer (Paris I University)
Time: 16:00-16:45
Place: King's College London, Strand Building, room S3.30
Title:
Abstract:
Speaker #2: Nick Westray (NYU/Courant)
Time: 17:00-17:45
Place: King's College London, Strand Building, room S3.30
Title:The Importance of Clean-Up Cost in Algorithmic Trading
Abstract:Given a set of fully and partially filled equity orders to be used in Transaction Cost Analysis (TCA) a common problem for practitioners is how to correctly account for unfilled shares. In this talk we first compare and contrast some of the common approaches used in practice today. Then we show how to formulate the problem in terms of stochastic control. Finally, by combining classical ideas from the control literature with modern machine learning methods we show how such problems can be efficiently solved numerically.
Joint work with Petter Kolm from NYU.
Autumn term
Date: Thursday 3 October 2019
Speaker #1: Martino Grasselli (Università di Padova)
Time: 18:15-19:00
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room 6001 (register in the lobby)
Title: Functional and recursive quantization for a class of non-Markovian processes
Abstract: We introduce a functional quantization approach for non-Markovian processes. Examples and applications to Finance reveal the great flexibility of the approach. Joint work with A. Sagna.
Speaker #2: Paolo Guasoni (Dublin City University)
Time: 19:00-19:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room 6001 (register in the lobby)
Title: Hedge Funds Flows and Risk Shifting
Abstract: When a hedge fund approaches its high-water mark, managers are paid performance fees and investors typically contribute new funds, while large drawdowns routinely lead to investors' redemptions and possibly liquidation. In a model where investors' flows depend on the current drawdown, we find in closed form the optimal investment policy of a manager who maximizes the expected present value of future fees and anticipates investors' response to performance. In contrast to models where outflows are performance-insensitive, a higher drawdown induces the manager to take more risk. Such risk-shifting incentive increases as flows' sensitivity to performance increase, and as managerial ability decreases. For typical parameters, the value of the high-water mark contract is comparable to the value of the fund.
Date: Thursday 17 October 2019
Speaker #1: Lisa McCrory (Pension Protection Fund)
Time: 18:15 - 19:00
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: The PPFs approach to funding and financial risk management
Abstract: The Pension Protection Fund is a unique and growing organisation, taking on the assets the liabilities of underfunded schemes following a sponsor insolvency. Our assets under management are currently over £30 billion and our strategy is to grow our reserves so that we are self-sufficient in the future. We achieve this by charging a levy payable by the universe of schemes we protect and targeting returns on our assets. The presentation aims to give an overview of who we are and what we do and provide practical examples of how we approach funding and manage the risks we face.
Speaker #2: Andrea Macrina (UCL)
Time: 19:00 - 19:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: Overnight and Term Interest Rate Benchmarks: a Dynamic Roll-Over Risk Approach
Abstract: The transition from interbank offer rates, e.g. LIBOR, to alternative benchmarks, such as risk-free rates (RFR), has sparked much debate and several consultations. In this talk, the development of an approach to term interest rate systems, based on dynamical models for roll-over risk, is presented. Due attention is reserved to the role played by secured and unsecured overnight benchmarks, e.g. SOFR and Fed Funds rates, respectively, and associated OIS rates. The proposed consistent and no-arbitrage models for term-dependent benchmark rates show how the funding/liquidity and the credit risk components may be discerned, thus allowing for the quantification of the funding/liquidity contribution to roll-over risk. The models generate different interest rate term structures for each tenor, that is, for each choice of the length of the interest rate accrual period, be it on an overnight (as for an OIS), three-month, six-month, etc., basis. Doubt emerges from this insight as to whether RFR benchmark systems are indeed suitable replacements for LIBOR and other term-based interest rate benchmarks. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3399680
Date: Thursday 31 October 2019
Speaker #1: Giulia Livieri (Scuola Normale Superiore, Pisa)
Time: 16:00-16:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: Statistical inferences for price staleness
Abstract: Asset transaction prices sampled at high frequency are stale, lacking frequently new updates and showing zero returns. In this paper, we define a continuous time stochastic process, called instantaneous (price) staleness, whose expected value, once integrated over a given time horizon, delivers the average probability of zero returns. A non-parametric theoretical framework, to study the intra-day dynamics of instantaneous staleness, is then proposed. In particular, we provide an inferential theory to estimate general integrated functionals of instantaneous staleness, and we develop tests for the constancy of instantaneous staleness and for establishing whether a deterministic diurnal pattern alone drives its dynamics. On ten representative stocks of the NYSE, we find that the null of constant instantaneous staleness is rejected and that a deterministic diurnal pattern is not always sufficient to explain the observed intra-day variability. Joint work with Aleksey Kolokolov (Alliance Manchester Business School) and Davide Pirino (Università Tor Vergata)
Speaker #2: Samuel Cohen (Mathematical Institute, Oxford)
Time: 17:00-17:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: Multi-armed bandits with uncertainty
Abstract: Making good decisions based on estimates is difficult, but of clear importance in many applications. This is particularly the case when the decisions made will affect the information available in the future. The interaction between our learning and control (or 'exploration and exploitation') leads to unusual mathematical questions; in particular, the filtration of our problem is not fixed in advance, but depends on the control used. We will consider the 'simplest' problem of this type, a multi-armed bandit problem, while taking account of uncertainty aversion. We will see that an extension of the classical Gittins' index approach describing optimal decisions is possible in this framework, despite many dynamic consistency issues.
Date: Thursday 14 November 2019
Speaker #1 : Laurence Carassus (Léonard de Vinci Pôle Universitaire Research Center and Université de Reims)
Time: 16:00-16:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: No-arbitrage with multiple-priors in discrete time.
Abstract : In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the so-called geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated.
Joint work with R. Blanchard.
Speaker #2 : Walter Schachermayer (University of Vienna)
Time: 17:00-17:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: From discrete to continuous time models — Some surprising news on an old topic
Abstract: We reconsider the approximation of the Black-Scholes model by discrete time models such as the binomial or the trinomial model.
We show that for continuous and bounded claims one may approximate the replication in the Black-Scholes model by trading in the discrete time models. The approximation holds true in measure as well as "with bounded risk", the latter assertion being the delicate issue. The remarkable aspect is that this result does not only apply to the well-known binomial model, but to a much wider class of discrete approximating models, including, e.g., the trinomial model. By an example we show that we cannot do the approximation with "vanishing risk".
We apply this result to portfolio optimization and show that, for utility functions with "reasonable asymptotic elasticity", the solutions to the discrete time portfolio optimization converge to their continuous limit, again in a wide class of discretizations including the trinomial model. In the absence of "reasonable asymptotic elasticity", however, surprising pathologies may occur.
Joint work with David Kreps (Stanford University).
Date: Thursday 28 November 2019
Speaker #1: Jan-Frederik Mai (TU Munich and XAIA Investments)
Time: 16:00-16:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: Static pricing-hedging duality for credit default swaps and the negative basis arbitrage
Abstract: Assuming the absence of arbitrage in a single-name credit risk model, it is shown how to replicate the risk-free bank account until a credit event by a static portfolio of a bond and infinitely many credit default swaps (CDS). From the viewpoint of classical arbitrage pricing theory this static portfolio can be viewed as the solution of a credit risk hedging problem whose dual problem is to price the bond consistently with the CDS. This duality is maintained when the risk-free rate is shifted parallel. In practice, there is a unique shift that is consistent with observed market prices for bond and credit default swaps. The resulting, risk-free trading strategy in case of a positive shift earns more than the risk-free rate, is referred to as negative basis arbitrage in the market, and the parallel shift defined in this way is a scientifically well-justified definition for what the market calls negative basis. In economic terms, it is a premium for taking the un-modeled residual risks of a bond investment after interest rate risk and credit risk have been eliminated. Chiefly, these are liquidity risk and legal risk.
Speaker #2: Peter Bank (TU Berlin)
Time: 17:00-17:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: Information flow modeling in stochastic control: Meyer sigma-fields and irreversible investment
Abstract: In stochastic control problems, it is of central importance to specify what information can be acted upon when by the controller. In Finance this is most obvious in high-frequency trading where no effort is spared to devise signals which allow one to preemptively trade on changes in order flow. For continuous-time models this leads to the need to differentiate information flow beyond the predictable case (where one can only react after a shock has hit the system) and the optional case (where one can "front-run" these shocks). Taking a general perspective on information flow modeling, we propose to use the theory of Meyer sigma-fields to systematically interpolate between these standard information flows. We illustrate some basic notions and tools of this theory in a simple linear toy model and we give an in-depth study of the stochastic singular control problem of irreversible investment with inventory risk to illustrate the effects that can be analyzed in this information modeling framework. Explicit solutions will be given in a compound Poisson process framework. We find optimality of ladlag controls whose jumps from the left are the agent's action on her signals and whose jumps from the right represent her reaction to the fully revealed shock.
Joint work with David Besslich (TU Berlin); see arxiv.org/abs/1810.08495 and arxiv.org/abs/1810.08491.
Date: Thursday 12 December 2019
Speaker #1: Carsten Chong (Ecole Politechnique Federale Lausanne)
Time: 16:00-16:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title: High-frequency analysis of SPDEs (and how it relates to rough volatility estimation)
Abstract: We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for power variations and related functionals to construct consistent nonparametric estimators and asymptotic confidence bounds for the integrated volatility process. As a byproduct of our analysis, we also obtain feasible estimators for the regularity of the spatial covariance function of the noise. We explain how the methods involved potentially relate to estimation of rough volatility.
Speaker #2: Enrico Scalas (University of Sussex)
Time: 17:00-17:45
Place: Cass Business School, 106 Bunhill Row, EC1Y 8TZ, Room LG002 (register in the lobby)
Title:Stochastic Modelling for High-Frequency Financial Data: A Survey of Results
Abstract: In the last decade, I worked on modelling high-frequency financial prices and returns for regulated stock exchanges. This includes papers on pricing intraday options (Politi et al. 2011 and Scalas and Politi 2013), on new models for non-stationary stochastic processes (Leonenko et al. 2017, Leonenko et al. 2019 and Ponta et al. 2019) and on testing information criteria for model selection (Chen et al. 2018, Ponta et al. 2019). I will present a survey of these results. This is joint work with several coauthors mentioned in the references below.
[1] Chen, J M, Hawkes, A G, Scalas, E and Trinh, M (2018) Performance of information criteria for selection of Hawkes process models of financial data. Quantitative Finance, 18 (2). pp. 225-235.
[2] Leonenko, N., Scalas, E. and Trinh, M. (2017) The fractional non-homogeneous Poisson process. Statistics and Probability Letters, 120. pp. 147-156.
[3] Leonenko, N., Scalas, E. and Trinh, M. (2019) Limit theorems for the fractional non-homogeneous Poisson process. Journal of Applied Probability, 56 (1). pp. 246-264.
[4] Politi, M., Kaizoji, T. and Scalas, E. (2011) Full characterization of the fractional Poisson process. Europhysics Letters, 96 (2). p. 20004.
[5] Ponta, L. Trinh, M., Raberto, M., Scalas, E. and Cincotti, S. (2019) Modeling non-stationarities in high-frequency financial time series. Physica A: Statistical Mechanics and its Applications, 521. pp. 173-196.
[6] Scalas, E. and Politi, M. (2013) A note on intraday option pricing. International Journal of Applied Nonlinear Science, 1 (1). pp. 76-86.
2018-19 LMF Seminar Series
Winter term
Date: Thursday 27 September 2018
Speaker #1: Martin Keller-Ressel, TU Dresden
Time: 16:00-17:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Affine forward variance models
Abstract: We introduce the class of affine forward variance (AFV) models which includes the Heston model and the rough Heston model. We show that such models are characterized by the affine form of their cumulant generating function, which can be obtained as solution of a convolution Riccati equation. We further introduce the class of affine forward order flow intensity (AFI) models, which are structurally similar to AFV models, but driven by jump processes. We show that a high-frequency limit of AFI models converges to the AFV model, which allows us to extend recent results by El Euch, Fukasawa and Rosenbaum on the micro-structural foundation of the leverage effect. This talk is based on joint work with Jim Gatheral.
Speaker #2: Alex Tse, Imperial College London
Time: 17:00-18:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Probability Weighting, Stop-Loss and the Disposition Effect
Abstract: Prospect theory (PT) has long been linked with the disposition effect. Despite significant progress towards rigorously modeling the trading behavior of PT investors, the literature has been largely silent on the effect of probability weighting. In this talk we incorporate probability weighting into a continuous-time model of an asset sale and find that investors follow strategies which are stop-loss, but not of threshold form on gains. The optimal prospect is skewed with a long right-tail. Moreover, probability weighting enables our PT model to match the magnitude of the disposition effect in Odean (1998). This is a joint work with Vicky Henderson (Warwick) and David Hobson (Warwick).
Date: Thursday 11 October 2018
Speaker #1: Ari-Pekka Perkkiö, Ludwig-Maximilians-Universität, München
Time: 16:15-17:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Convex duality in stochastic analysis and markets with frictions
Abstract: We extend classical results of Bismut, Dellacherie and Meyer by characterizing the topological duals of Frechet spaces of optional cadlag processes and of regular processes. We also derive expressions for conjugates of convex integral functionals on these spaces. The results have applications in optimal stopping, singular stochastic control and in financial models with nonlinear trading costs and portfolio constraints. The talk is based on joint works with Teemu Pennanen and with Erick Trevino.
Speaker #2: Victor DeMiguel, London Business School
Time: 17:15-18:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: A Transaction-Cost Perspective on the Multitude of Characteristics
Abstract: We investigate how transaction costs change the number of firm-specific characteristics that are jointly significant for explaining the cross section of stock returns. We find that transaction costs increase the number of significant characteristics from six to 15. The explanation is that, as we show theoretically and empirically, combining characteristics reduces transaction costs because the trades in the underlying stocks required to rebalance different characteristics often cancel out. Thus, transaction costs provide an economic rationale for considering a larger number of characteristics than that in prominent asset-pricing models.
Date: Thursday 25 October 2018
Speaker: Peter Bank, TU Berlin
Time: 17:15-18:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Liquidity in competitive dealer markets
Abstract: We consider competitive dealers whose business model is to service their clients' orders for some asset at competitive prices while managing their inventory risk through asset transfers to the end user market. In the end user market, asset prices are given exogenously, but transfers are subject to search costs that impede trading in this market. We formulate the dealers' inventory management problem by a quadratic tracking problem imposing quadratic costs on the transfer rate. This allows us to compute explicitly the equilibrium prices at which the clients' demand maximizes the dealers' risk adjusted expected proceeds. We also describe how the clients will optimize their quadratic expected utility and analyze when they benefit from the dealers' presence. Finally, we also look at the advantage of a large trader who internalizes her impact on asset pricing when devising her strategy. This offers a way to quantify the price of anarchy in our equilibrium model.
Date: Thursday 8 November 2018
Speaker #1: Christa Cuchiero, University of Vienna
Time: 16:15-17:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Rough affine covariance models
Abstract: We consider the rough volatility paradigm in a multivariate situation and present rough covariance models for more than one asset. We consider in particular a multivariate rough Heston type model based on a rough Wishart process. It arises from an underlying infinite dimensional affine process, whence we obtain an affine transform formula. We also present positive semidefinite Volterra processes of pure jump type which can serve as covariance processes as well.
Speaker #2: Johannes Muhle-Karbe, Carnegie Mellon University
Time: 17:15-18:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Inventory Management for High-Frequency Trading with Imperfect Competition
Abstract: We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large. In contrast, the HFTs' risk-adjusted profits and the equilibrium price impact converge to their risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.
Date: Thursday 22 November 2018
Speaker #1: Reimer Kühn, King's College London
Time: 16:15-17:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Of Brains and Markets
Abstract: In this talk I will describe a model of price fluctuations in financial markets. The general structure of the model can be derived from very generic considerations concerning projected dynamics. In its simplest form it takes the form of a model describing a network of analogue neurons. Such a system is expected to exhibit a large number of meta-stable states in a large part of its parameter space, and the salient features of market dynamics, such as fat-tailed return distributions and volatility clustering can be understood in terms of an interplay between the dynamics within meta-stable states and the dynamics of occasional transitions between them. I will also describe first tentative results about inference of parameters when the model is used to describe real market data.
Speaker #2: Patrick Cheridito, ETH Zürich
Time: 17:15-18:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Deep optimal stopping
Abstract: I present a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such it is broadly applicable in situations where the underlying randomness can efficiently be simulated. The approach is tested on two problems: the pricing of a Bermudan max-call option and the problem of optimally stopping a fractional Brownian motion. In both cases it produces very accurate results in high-dimensional situations with short computing times.
Date: Thursday 6 December 2018
Speaker #1: Zhenjie Ren, Université Paris-Dauphine
Time: 16:15-17:00
Place: University College London, Medical Sciences 131 AV Hill Lecture Theatre.
Title: Mean field game in Principal-Agent problem
Abstract: In this talk, we shall review the dynamic programming approach to solve the Principal-Agent (moral hazard) problem, and naturally observe that when the number of the agents or/and that of the principals goes to infinity and if their dynamics have mean-field interactions, it will lead to a mean field game. We shall mainly discuss a model connected to the mean field planning problem, and the other one where one agent can choose to work for different principals.
Speaker #2: Anthony Reveillac, INSA Toulouse
Time: 17:15-18:00
Spring term
Date: Thursday 24 January 2019
Speaker #1: Nadia Oudjane (EDF)
Time: 17:00-18:00
Place: Imperial College London, Blackett Building / Room 630
Title: McKean Feynman-Kac representations of nonlinear PDEs and related numerical approximations
Abstract: The presentation focuses on recent forward numerical schemes based on generalized Fokker-Planck representations for nonlinear PDEs in high space dimension. In the specific case of mass conservative PDEs, it is well known that the solution can be probabilistically represented as the marginal densities of a Markov diffusion nonlinear in the sense of Mckean. Then one can design forward interacting particle schemes to approximate numerically the PDEs solution. We present some extensions of this kind of representation and interacting particle schemes associated to a large class of PDEs including the case when they are non-conservative, with various kind of non-linearities. (joint work with Francesco Russo, (ENSTA ParisTech))
Speaker #2: Keita Owari (Ritsumeikan University)
Time: 18:00-19:00
Place: Imperial College London, Blackett Building / Room 630
Title: A Komlós type theorem and the Mackey topology on dual Orlicz spaces
Abstract: Our basic interest in this talk is to understand the Mackey topology of a dual Orlicz space in a probabilistic way; here by dual Orlicz space, we mean the dual of an Orlicz space that is itself an Orlicz space (e.g. the exponential Orlicz space). By means of a Komlós type theorem, we describe some aspects of the dual Orlicz space with the Mackey topology useful for convex duality and financial applications. Then we conclude with a few open questions.
Date: Thursday 7, February 2019
Speaker #1 : Idris Kharroubi (LPSM Sorbonne Université)
Time: 17:00-18:00
Place: Imperial College London, Blackett Building / Room 630
Title: Quenched mass transport of particles towards a target
Abstract: We consider the stochastic target problem of finding the collection of initial laws of a mean-field stochastic differential equation such that we can control its evolution to ensure that it reaches a prescribed set of terminal probability distributions, at a fixed time horizon. Here, laws are considered conditionally to the path of the Brownian motion that drives the system. We establish a version of the geometric dynamic programming principle for the associated reachability sets and prove that the corresponding value function is a viscosity solution of a geo- metric partial differential equation. This provides a characterization of the initial masses that can be almost-surely transported towards a given target, along the paths of a stochastic differential equation. This talk is based on a joint work with B. Bouchard (Paris Dauphine University) and B. Djehiche (KTH Stockholm).
Speaker #2 : John Armstrong (King's College London)
Time: 18:00-19:00
Place: Imperial College London, Blackett Building / Room 630
Title: Symmetries of Markets
Abstract: We will ask what it means for two markets to be isomorphic and discuss the classification of markets. It turns out classical markets such as Markowitz’ market, the Black-Scholes-Merton market and complete one period markets all have interesting classification theorems. A consequence is that all these markets have large symmetry groups: a symmetry of a market is an automorphism of the market. We’ll see that these market symmetries give rise to “mutual fund theorems” that generalize the classical two mutual fund theorem in the Markowitz model.
Date: Thursday 21 February 2019
Speaker #1: Sebastian Jaimungal (University of Toronto)
Time: 17:00-18:00
Place: Imperial College London, Blackett Building / Room 630
Title:Reinforcement Learning in Algorithmic Trading: Double Deep Q-learning and Reinforced Deep Kalman Filters
Abstract: Reinforcement learning aims to solve certain stochastic control problems without making explicit assumptions on the dynamics of the environment or on the effect that an agent’s actions has on its dynamics. In this talk, I will provide an overview of two approaches: (i) double deep Q-learning, and (ii) reinforced deep Kalman filters for algorithmic trading. Deep Q-learning approximates the action-value function with a neural net and aims to solve the Bellman equation through learning by acting in the environment and updating the network parameters. Reinforced Deep Kalman Filters on the other hand, takes a batch reinforcement learning perspective and aims to maximize the rewards directly by learning a latent model and updating that model as data arrives and the agent takes actions. Some sample results on real data will be shown.
Speaker #2: Niushan GAO (Ryerson University)
Time: 18:00-19:00
Place: Imperial College London, Blackett Building / Room 630
Title: Risk measures on Orlicz spaces
Abstract: For a coherent risk measure rho: L^infty to R, Delbaen (2002) proved that rho can be represented as the worst expectation over a class of probability measures whenever it has the Fatou property. Later, it has been asked whether Delbaen's representation theorem holds on more general model spaces containing unbounded positions. In this talk, we will present a comprehensive investigation on this problem for risk measures on Orlicz spaces. We first characterize the Orlicz spaces over which the representation holds. We also show that the representation holds on general Orlicz spaces if the risk measures possess additional properties, e.g., law-invariance or surplus-invariance.
Date: Thursday 7 March 2019
Speaker #1 : Oleksii Mostovyi (University of Connecticut)
Time: 17:00-18:00
Place: Imperial College London, Blackett Building / Room 630
Title: Sensitivity analysis of the utility maximization problem with respect to model perturbations
Abstract:We study the sensitivity of the expected utility maximization problem in a continuous semimartingale market with respect to small changes in the market price of risk. Assuming that the preferences of a rational economic agent are modeled with a general utility function, we obtain a second-order expansion of the value function, a first-order approximation of the terminal wealth, and construct trading strategies that match the indirect utility function up to the second order. If a risk-tolerance wealth process exists, using it as a numeraire and under an appropriate change of measure, we reduce the approximation problem to a Kunita-Watanabe decomposition. This talk is based on the joint work with Mihai Sirbu.
Speaker #2 : Charles-Albert Lehalle (Capital Fund Management)
Time: 18:00-19:00
Place: Imperial College London, Blackett Building / Room 630
Title: Optimal trading with signals
Abstract: Optimal liquidation mainly focused on risk control, providing tools and frameworks to make the balance between trading fast (to obtain a price as close as possible to the decision price) and trading slow (to avoid market impact). Usually the control of such problems is the trading speed. Nevertheless it is needed to interact in real-time with liquidity (for instance via limit order books) to really buy or sells shares and contracts. For few years academic papers started to document "execution predictors", like the order book imbalance, and practitioners try to use such predictors to drive their trading speed. In recent papers with Eyal Neuman, Othmane Mounjid, Hadrien De March and Mathieu Rosenbaum, I explored different ways to exploit such signals without giving up risk control. In this talk I will give some empirical evidence of the use of such signals by market participants and I will explain the main mechanisms allowing to safely use signals for optimal trading.
Date: Thursday 21 March 2019
Speaker #1: Christoph Kuhn (Johann Wolfgang Goethe-Universität)
Time: 17:00-18:00
Place: Imperial College London, Huxley Building, Room 145
Title: Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs
Abstract: In this talk, we discuss the arbitrage theory for finite discrete time market models with proportional transaction costs. In contrast to frictionless markets, the no-arbitrage property does not imply the existence of a separating probability measure since there can still exist an approximate arbitrage. To overcome this problem, Schachermayer (2004) introduced the robust no-arbitrage condition and showed that it is equivalent to the existence of a strictly consistent price system.
We introduce a slightly weaker condition called prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov, Rasonyi, and Stricker (2002). Like robust no-arbitrage, it implies that the set of attainable portfolios is closed in probability. This allows us to establish a version of the fundamental theorem of asset pricing with consistent price systems which are not necessarily strict, i.e., consistent frictionless prices may lie on the relative boundary of the bid-ask spread. Finally, we discuss some puzzling phenomena occurring in similar models with capital gains taxes and show how the prospective strict no-arbitrage property can be applied here. The talk is based on joint work with Alexander Molitor.
Speaker #2: Laurence Carassus (ESILV)
Time: 18:00-19:00
Place: Imperial College London, Huxley Building, Room 145
Title: Pricing without martingale measure
Abstract:For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. Here, we propose a new approach based on convex duality instead of martingale measures duality: our prices will be expressed using Fenchel conjugate and bi-conjugate. This naturally leads to a weak condition of (NA) called Absence of Immediate Profit (AIP). It asserts that the price of the zero claim should be zero or equivalently that the super-hedging cost of some call option should be non-negative. We propose several characterizations of the (AIP) condition and also study the relation with (NA) and a stronger notion of (AIP) linked to the no-free lunch condition. We show in a one step model that under (AIP) the super-hedging cost is just the payoff's concave envelop. In the multiple-period case, for a particular, but still general setup, we propose a recursive scheme for the computation of a the super-hedging cost of a convex option.We also give some promising numerical illustrations. (Joint work with Julien Baptiste and Emmanuel Lépinette).
Date: Thursday 4 April 2019
Speaker: Scott Robertson (Boston University)
Time: 18:00-19:00
Place: Imperial College London, ACEX Building Lecture Theatre 2
Title: Mortgage Contracts and Selective Default
Abstract: We analyze three recently proposed mortgage contracts, each of which aims to eliminate selective borrower default, and the associated costs, when the loan balance exceeds the house price (the “underwater" effect). In a model with diffusive interest rates and home prices, we identify the contract, default and prepayment option values with a free boundary problem. We provide explicit solutions in the perpetual case with constant interest rates, and numerically compute the prepayment and default boundaries in the general case. We show one contract (the "continuous workout mortgage" (CWM) of Shiller, et al (2011) does not remove the default incentive, but the other two (the "adjustable balance mortgage" (ABM) of Ambrose, et al (2012) and "shared responsibility mortgage" (SRM) of Mian and Sufi (2013) ) do. However, the ABM and SRM endogenously lead to home sales at low prices, if the borrower does not enjoy sufficient utility from living in the house. Furthermore, the capital gain sharing feature of the SRM does not compensate for the lower monthly payment, as it essentially eliminates prepayment when prices rise. In short, we find the ABM to be most effective at removing the default incentive while imposing the least losses to the bank, and the ABM becomes preferable to the traditional mortgage, should foreclosure costs exceed approximately 40% of the home value.
Joint work with Yerkin Kitapbayev (MIT).
2017-18 LMF Seminar Series
The October-December 2017 programme was hosted by King's College London.
Date: Thursday 5 October 2017
Speaker #1: Martin Haugh, Imperial College
Time: 16:15-17:00
Place: King's College London, Room K3.11
Title: Markov Decision Processes and Information Relaxations
High-dimensional Markov decision processes (MDPs) are ubiquitous in fields ranging from finance and economics to engineering and operations research. These problems are generally intractable due to the so-called "curse of dimensionality" and so we must make do with sub-optimal policies in practice. But how should we evaluate the quality of these policies? In recent years duality methods based on information relaxations have been developed to answer this question. These methods proceed by using the sub-optimal policy to construct lower and upper bounds on the unknown (and impossible to compute) optimal value function. Moreover a strong duality result implies that better sub-optimal policies should yield tighter bounds, thereby producing a ``certificate'' of near-optimality for policies that are close to optimal.
In this talk we discuss some recent developments and applications of this information relaxation approach. These applications include inventory control, multi-class queuing control and tax-aware dynamic portfolio optimization. On the methodological side, we discuss extensions to infinite horizon problems and the development of change-of-measure arguments to facilitate the solution of the dual control problems. We show that similar change-of-measure arguments can be used to extend the approach to partially observed Markov decision processes (POMDPs), an important extension that we will demonstrate with an application from robotic control.
The talk will be based on results from the following papers as well as ongoing research.
[1] Tax-Aware Dynamic Asset Allocation (2016), with Garud Iyengar and Chun Wang. Operations Research (2016). Available at http://www.columbia.edu/~mh2078/OR_TaxAssetAllocation_Published.pdf
[2] Information Relaxation Bounds for Infinite Horizon Markov Decision Processes (2015), with David Brown. Forthcoming in Operations Research. Available at http://www.columbia.edu/~mh2078/infinite_horizon_R3_final.pdf
[3] Information Relaxations Bounds for Partially Observed Markov Decision Processes (2017), with Octavio Ruiz Lacedelli. Working paper. Available at http://www.columbia.edu/~mh2078/POMDP_IR_paper.pdf
Speaker #2: Andreas Kyprianou, University of Bath
Time: 17:15-18:00
Place: King's College London, Room K3.11
Title: Sphere stepping algorithms for Dirichlet-type problems with the fractional Laplacian
We review the sphere-stepping algorithm for simulating the solution to the classical Dirichlet problem and consider whether the same can be done when the Laplacian can be changed to the fractional Laplacian. Whereas in the former case, we need knowledge about isotropic Brownian motion, in the latter case, we need information about isotropic stable Levy processes. We will show that the stable case offers a “faster” convergence than in the Brownian case thanks to the trajectory of stable processes having jumps.
Date: Thursday 19 October 2017
Speaker #1: Martin Herdegen,Warwick University
Time: 16:15-17:00
Place: King's College London, Room K3.11
Title: Equilibrium Returns with Transaction Costs
We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean-variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward-backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.
The talk is based on joint work with Bruno Bouchard, Masaaki Fukasawa and Johannes Muhle-Karbe.
Date: Thursday 2 November 2017
Speaker #1: Dirk Becherer, Humboldt University, Berlin, Germany
Time: 16:15-17:00
Place: King's College London, Room K3.11
Title: Good Deal Hedging and Valuation Under Combined Uncertainty About Drift and Volatility
We derive robust good-deal hedges and valuations under combined model ambiguity about the drift and volatility of asset prices for incomplete markets. Good-deal valuations are determined such that not just opportunities for arbitrage but also for overly attractive reward-to-risk ratios are excluded, by restricting instantaneous Sharpe ratios for any market extension by derivatives. From a finance point of view, this permits for hedges and valuation bounds than are less extreme (respectively expensive) than those from the more fundamental approach of almost-sure superhedging and its corresponding no-arbitrage bounds. In mathematical terms, it demands however that not just ambiguities about the volatility but also about the drift become relevant. For general measurable contingent claims, possibly path-dependent, the solutions are described by 2nd-order backward stochastic differential equations with non-convex drivers, building on recent research progress on non-linear kernels. Hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures, uniformly over all priors.
Speaker #2: Thorsten Rheinlaender,Vienna University of Technology
Time: 17:15-18:00
Place: King's College London, Room K3.11
Title: Brownian trading excursions
We study a parsimonious, but non-trivial model of the limit order book. In contrast to market orders which get executed instantaneously, limit orders are placed away from the current market price (which we will call mid-price), and get executed once the mid-price process hits the limit level. Hence the volume of orders in the limit order book constitutes a random field where the space parameter corresponds to the limit level relative to the mid-price. The volume field satisfies the stochastic heat equation with multiplicative noise. We will solve this equation in terms of a local time functional. Furthermore, we study different types of trades via excursion theory.
Date: Thursday 16 November 2017
Speaker #1: Clemence Alasseur, EDF Paris
Time: 16:15-17:00
Place: King's College London, Room K3.11
Title : An adverse selection approach to power pricing
We study the optimal design of electricity contracts among a population of consumers with different needs. This question is tackled within the framework of Principal-Agent problem in presence of adverse selection. The particular features of electricity induce an unusual structure on the production cost, with no decreasing return to scale. We are nevertheless able to provide an explicit solution for the problem at hand. The optimal contracts are either linear or polynomial with respect to the consumption. Whenever the outside options offered by competitors are not uniform among the different type of consumers, we exhibit situations where the electricity provider should contract with consumers with either low or high appetite for electricity. Joint work with Ivar Ekeland, Romuald Elie, Nicolás Hernández Santibáñez, Dylan Possamaï
Speaker #2: Eyal Neuman, Imperial College
Time: 17:15-18:00
Place: King's College London, Room K3.11
Title: Optimal Portfolio Liquidation in Target Zone Models
We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a di usion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider the optimal portfolio liquidation problem for an investor for whom prices are optimal at the barrier and who creates temporary price impact. This problem will be formulated as the minimization of a cost-risk functional over strategies that only trade when the price process is located at the barrier. We solve the corresponding singular stochastic control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess. In this setting the catalyst is a set of points which is given by the barriers of the price process. Later, we consider the case where the investors create an additional permanent impact. The central bank, who wishes to keep the currency exchange rate above a certain barrier, therefore needs to buy its own currency. The permeant price impact, which is created by the transactions of both sides, turns the optimal trading problems of the trader and the central bank into coupled singular control problems, where the common singularity arise from a local time along a random curve. We solve the central bank's control problem by means of the Skorokhod map and derive the trader's optimal strategy by solving a sequence of approximated control problems.
This is joint work with Alexander Schied.
Date: Thursday 30 November 2017
Speaker #1: David Skovmand
Time: 16:15-17:00
Place: King's College London, Room K3.11
Title : Rational Models for Inflation Linked Derivatives
We construct a model for the pricing and risk management of inflation derivatives. The model is rational in the sense that the real pricing kernel is a rational function of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that allows for closed form pricing of vanilla inflation products such a zero coupon swaps, caps and floors, year-in-year swaps, caps and floors as well as the exotic LPI swap. Furthermore the model retains the attractive features of a nominal multicurve interest rate model such as closed form pricing of nominal swaptions. Finally we study how the model can be calibrated to EUR data.
Speaker #2: Giulia di Nunno, University Oslo, Norway
Time: 17:15-18:00
Place: King's College London, Room K3.11
Title: Fully-dynamic risk-indifference pricing
We deal with dynamic pricing of financial products in an incomplete market and we focus on risk-indifference pricing. This can be seen as an alternative to the classical utility-indifference pricing in which the performance is written in terms of evaluation of risks instead of utility.
We propose a fully-dynamic risk-indifference criteria, in which a whole family of risk measures is considered. This is based on the concept of fully-dynamic risk measures which extends the one of dynamic risk measures by adding the actual possibility of changing the perspective on how to measure risk over time. Our framework fits well the study of both short and long term investments. Risk-indifference pricing has been studied from the point of view of how to find a solution under different assumptions on the underlying dynamics and information flows. Typically the price is also evaluated at the time of the initial investment t=0. We are interested in studying the risk-indifference pricing criterion in its time evolution in a setting free from specific choices of underlying dynamics. In the dynamic framework we analyse whether the risk-indifference criterion actually provides a proper convex price system. Furthermore, we consider the relationship of the fully-dynamic risk-indifference price with no-good-deal bounds. Recall that no-good-deal pricing guarantees that not only arbitrage opportunities are excluded, but also all deals that are “too good to be true”. We shall provide necessary and sufficient conditions on the fully-dynamic risk measure so that the corresponding risk-indifference prices satisfy the no-good-deal bounds. As it turns out, no-good-deal bounds also provide a method to select the risk measures that provide a proper fully-dynamic risk-indifference price system.
Date: Thursday 14 December 2017
Speaker #1: Umut Cetin,London School of Economics
Time: 16:15-17:00
Place: King's College London, Room K3.11
Title: Financial equilibrium with aymmetric information and random horizon
We study in detail and explicitly solve the version of Kyle's model introduced in a specific case by Back and Baruch, where the trading horizon is given by an exponentially distributed random time. We first focus on time-homogeneous equilibria using tools from the theory of one-dimensional diusions. It turns out that such an equilibrium is only possible if the final payoff is Bernoulli distributed. We shall show later that for a payoff with general distribution the equilibrium exists and is a time-changed version of the Bernoulli case. In both cases we characterise explicitly the equilibrium price process and the optimal strategy of the informed trader. Contrary to the original Kyle model it is found that the reciprocal of market's depth, i.e. Kyle's lambda, is a uniformly integrable supermartingale. While Kyle's lambda is a potential, i.e. converges to 0, for the Bernoulli distributed final payoff, its limit in general is different than 0.
Speaker #2: Alvaro Cartea, Oxford University
Time: 17:15-18:00
Place: King's College London, Room K3.11
Title: Maximizing Fill Ratios in Foreign Exchange Markets with Latency and Random Delays
We analyse how latency affects the strategies of foreign exchange (FX) traders that send liquidity taking orders to the FX electronic exchange. Latency is the time delay between a signal and a response as a result of the time it takes for the signal to travel inside the automated trading system of the Exchange and the hardware of the traders. Latency affects the prices and fill ratios obtained by traders -- by the time the exchange receives a trader's order, exchange rates could have moved, so trader may get a better or worse price or may not even get her order filled. In this paper we assume that traders send marketable orders with a price limit and targets a fill ratio (FR), defined as the number of orders that are filled divided by the total number of sent orders over a period of time (e.g. a trading day). We develop a model that maximizes FR whilst minimising how deep the marketable orders can walk the FX exchange's limit order book. We employ a proprietary data set with trader identifiers to categorise traders as: momentum or noise traders. We use traders' liquidity taking orders to show the performance of our proposed dynamic trading strategy.
The January-March 2018 programme was hosted by London School of Economics.
Date: Thursday 11 January 2018
Speaker #1: Paul Eisenberg, TU Wien
Time: 17:15-18:00
Place: London School of Economics, PAR.LG.03.
Title: Approximating flow commodity forward markets with finite dimensional future curve models without arbitrage.
The Heath-Jarrow-Morton type approach treats a family of securities -- written on an underlying -- as primary assets and models them directly. Originally, this reasonable approach has been used for the modelling of bond prices. We adopt this approach for modelling in electricity markets and model a curve valued process which has a straightforward relation to the prices of forwards with delivery periods. These forwards are the mainly traded securities in electricity markets. In this talk, we present a formula for the dynamics of the resulting forwards in a non-Gaussian setting and we present an approximation theorem for the forward prices with arbitrage free models which have a finite dimensional state space and affine-like dynamics.
Date: Thursday 25 January 2018
Speaker #1: Emmanuel Gobet, Ecole Polytechnique
Time: 17:15-18:00
Place: London School of Economics, OLD4.10
Title: Numerical Approximations of Mckean Anticipative Backward Stochastic Differential Equations Arising In Variation Margin Requirements
We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relaxed regularity assumptions on the parameters. We show that such stochastic equations arise within the modern paradigm of derivative pricing where a central counterparty (CCP) demands each member to deposit initial and variation margins to cover their exposure. In the case when the variation margin is proportional to the Conditional Value-at-Risk (CVaR) of the contract price, we apply our general result to obtain existence and uniqueness of the price as a solution of a MKABSDE. We also provide several linear and non-linear approximations, which we solve using different numerical methods (joint work A. Agarwal,, S. De Marco, J. G. Lopez-Salas, F. Noubiagain and A. Zhou).
Speaker #2: Kathrin Glau, Queen Mary University
Time: 18:15-19:00
Place: London School of Economics, OLD4.10
Title: Chebyshev interpolation for real-time problems in finance
Real-time methods for option pricing and the computation of risk quantities in multivariate settings are required in order to pave the way for innovation in a financial environment that adapts to digitalization and automatic trading. Technically and mathematically the development of such methods poses a serious challenge. We formulate Parametric Option Pricing (POP) as a generic instance of parametric conditional expectations and show that polynomial interpolation in the parameter space promises to considerably reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence and explicit error bounds. The method is most promising when the computation of the prices is most challenging. We therefore investigate its combination with Monte Carlo simulation. The Chebyshev method turns out to yield very promising results. We give an outlook to the application of the interpolation technique to stochastic dynamic programming problems, including a comparison with the Longstaff-Schwarz algorithm.
Date: Thursday 8 February 2018
Speaker #1: Christoph Reisinger, Oxford University
Time: 17:15-18:00
Place: London School of Economics, OLD4.10
Title: A forward equation for barrier options for efficient model calibration
In this talk, we present a novel and generic calibration framework for barrier options in a large class of continuous semi-martingale models. We derive a forward equation for arbitrage-free barrier option prices in terms of Markovian projections of the instantaneous variance. This gives a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted as the canonical extension of local volatility for barrier options. Alternatively, a forward partial-integro differential equation is deduced which yields up-and-out call prices for the complete set of strikes, barriers and maturities in one solution step. We apply this methodology to the calibration of a path-dependent volatility model (PDV) and a new Heston-type local stochastic volatility model with local vol-of-vol (LSV-LVV), using a two-dimensional particle method, for a set of EURUSD market data of vanilla and no-touch options. Finally, we conclude by extending the main Markovian projection formula to handle stochastic rates and discuss how the algorithms can be adapted at little extra computational cost. (Joint work with Alan Bain and Matthieu Mariapragassam.)
Speaker #2: Johannes Ruf, London School of Economics
Time: 18:15-19:00
Place: London School of Economics, OLD4.10
Title: Stochastic Portfolio Theory, Volatility and Arbitrage
The capitalization-weighted cumulative variation $\sum_{i=1}^d \int_0^\cdot \mu_i (t) \dx \langle \log \mu_i \rangle (t) $ in an
equity market consisting of a fixed number $d$ of assets with capitalization weights $\mu_i (\cdot) ,$ is an observable and a nondecreasing function of time. If this observable of the market is not just nondecreasing but actually grows at a rate bounded away from zero, then strong arbitrage can be constructed relative to the market over sufficiently long time horizons. It has been an open issue for more than ten years, whether such strong outperformance of the market is possible also over arbitrary time horizons under the stated condition. We show that this is not possible in general, thus settling this long-open question. We also show that, under appropriate additional conditions, outperformance over any time horizon indeed becomes possible, and exhibit investment strategies that effect it (Joint work with Bob Fernholz and Ioannis Karatzas).
Date: Thursday 22 February 2018
Speaker #1: Kevin Sheppard, Oxford University
Time: 17:15-18:00
Place: London School of Economics, OLD4.10
Title: Direct volatility modeling at multiple horizons
Volatility forecasts are often required across a range of horizons to manage risk. This paper studies the forecast performance over horizons
out to one month. Particular attention is paid to the choice between iterating a daily model and estimating a horizon-specific model.
Forecasts from the latter are often referred to direct forecasts. Direct forecasts may be preferable if the model used to produce iterative
forecasts is meaningfully misspecified. Both forecasting methods are compared using a panel of 25 financial asset return series covering the
major assets classes. Iterative models are found to out-perform direct forecasting methods across a wide range of horizons and assets. Direct
forecasts are only found to perform better than iterative forecasts when for a small subset of models when the estimation window is long.
Extensions to asymmetric models show that adding conditional asymmetries improves out-of-sample performance although the ranking between iterative and direct forecast is unaltered.
Speaker #2: Sascha Desmettre, Technische Universität Kaiserslautern
Time: 18:15-19:00
Place: London School of Economics, OLD4.10
Title: Worst-case optimal investment in incomplete markets
We study the worst-case optimal portfolio problem (compare [1]) of an investor facing the possibility of a Knightian market crash with stochastic market coefficients by adapting the martingale approach developed in [2]. With the help of a backward stochastic differential equations (BSDEs) we are able to characterise the resulting indifference optimal strategies in a fairly general setting. Under suitable conditions on the market price of risk, also optimality of the indifference strategies holds in the sense of [2]. We demonstrate our approach for the Heston stochastic volatility model, and solve the corresponding BSDEs via solving their asscociated PDEs, using a utility crash-exposure transformation.
Date: Thursday 8 March 2018
Speaker #1: Claudio Fontana, Université Paris-Diderot
Time: 17:15-18:00
Place: London School of Economics, OLD4.10
Title: The Value of Informational Arbitrage
In the context of a general complete semimartingale financial model, we aim at answering the following question: How much is an investor willing to pay for learning some private information that allows to achieve arbitrage profits? In particular, we are interested in the case where the private information can yield arbitrage opportunities but not arbitrages of the first kind. In the spirit of Amendinger, Becherer & Schweizer (2003, Finance Stoch.), we shall give an answer to this question by relying on an indifference pricing approach for general preferences over consumption and terminal wealth, relying on some recent results on initial enlargement of filtrations. We characterize when the indifference value of informational arbitrage is universal, in the sense that it does not depend on the preference structure. We illustrate our results by means of several explicit examples.
Speaker #2: Carole Bernard
Time: 18:15-19:00
Place: London School of Economics, OLD4.10
Title: Cost efficient strategies under model ambiguity
A strategy is cost-efficient if it is the cheapest way to achieve a given probability distribution of terminal wealth. The solution to the standard cost efficiency problem depends crucially on the fact that a single real-world measure P is available to the investor pursuing a cost-efficient approach. In most applications of interest however, a historical measure is neither given nor can it be estimated with accuracy from available data. To incorporate the uncertainty about the measure P in the cost efficiency approach we assume that, instead of a single measure, a class of plausible prior models is available. We define the notion of robust cost-efficiency and highlight its link with the maxmin expected utility setting of Gilboa and Schmeidler (1989) and more generally with robust preferences in a possibly non expected utility setting.
Date: Thursday 22 March 2018
Speaker #1 : Doyne Farmer, Oxford University
Time: 17:15-18:00
Place: London School of Economics, OLD4.10
Title: The computational approach to understanding systemic risk in financial markets
In contrast to the mainstream approach, which relies heavily on the rational expectations assumption and focuses on situations where it is possible to compute an equilibrium, the computational approach typically uses stylized behavioral assumptions and relies more on simulation. This makes it possible to include more actors and more realistic institutional constraints, and to explain phenomena that are driven by out of equilibrium behavior, such as clustered volatility and fat tails. I will argue that traditional equilibrium models and heterogeneous agent-based models are complements rather than substitutes, and review how the interaction between these two approaches has enriched our understanding of systemic financial risk. I will illustrate with several models of my own, including models of leverage cycles and interacting contagion networks, and present a vision of how systemic risk might be monitored and controlled in the future.
Speaker #2: Rüdiger Kiesel, Universität Duisburg Essen
Time: 18:15-19:00
Place: London School of Economics, OLD4.10
Title: Time-varying market order arrival rates and their impact on optimal intraday trading
We provide empirical analyses hinting towards time dependence of the rate at which buy and sell market orders arrive in the intraday power market for hourly deliveries in Germany. We then comment on how optimal intraday trading is impacted by this time dependence.
The results may be particularly useful for automated trading in the market under consideration.
2016-17 London Mathematical Finance Seminar Series
The October-December 2016 programme was hosted by University College London (UCL).
Date: Thursday 6 October 2016
Speaker: Lukasz Szpruch, University of Edinburgh
Time: 17:00-18:00
Place: University College London - Physics Building A1/3, Gower Place
Multilevel Monte Carlo for McKean-Vlasov SDEs
Stochastic Interacting Particle System (SIPS) and they limiting stochastic McKean-Vlasov equations offer a very rich and versatile modelling framework. On one hand, interactions allow to capture complex dependent structure, on the other provide a great challenge for Monte Carlo simulations. The non-linear dependence of the approximation bias on the statistical error renders classical variance reduction techniques not applicable. In this talk, we will propose a strategy to overcome this difficulty. In particular, we will establish Multilevel Monte Carlo estimator for SIPS and demonstrate its computational superiority over standard Monte Carlo techniques.
Speaker: Mikko Pakkanen, Imperial College London
Time: 18:00-19:00
Place: University College London - Physics Building A1/3, Gower Place
Modelling and forecasting rough volatility
In their recent, yet already seminal paper ("Volatility is rough", arXiv:1410.3394) Jim Gatheral, Thibault Jaisson, and Mathieu Rosenbaum argued that financial market volatility should be modelled by stochastic processes that are rougher than Brownian motion. In my talk, I will first present some new corroborative empirical evidence of the roughness of volatility, drawn from high-frequency data on more than five thousand assets. I will then introduce a new stochastic volatility model, building on the so-called Brownian semistationary (BSS) process, which is able to conveniently capture both the roughness and highly persistent long-term behaviour of volatility. Finally, I will discuss two parsimonious parameterisations of the BSS model and demonstrate their remarkable performance in volatility forecasting. Joint work with Mikkel Bennedsen and Asger Lunde.
Date: Thursday 20 October 2016
Speaker: Christoph Reisinger
Time: 17:00-18:00
Place: University College London - Physics Building A1/3, Gower Place
High-order filtered schemes for time-dependent second order HJB equations
In this talk, we present and analyse a class of “filtered” numerical schemes for second order Hamilton-Jacobi-Bellman (HJB) equations, with a focus on examples arising from stochastic control problems in financial engineering. We start by discussing more widely the difficulty in constructing compact and accurate approximations. The key obstacle is the requirement in the established convergence analysis of certain monotonicity properties of the schemes. We follow ideas in Oberman and Froese (2010) to introduce a suitable local modification of high order schemes, which are necessarily non-monotone, by "filtering" them with a monotone scheme. Thus, they can be proven to converge and still show an overall high order behaviour for smooth enough value functions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests.
This talk is based on joint work with Olivier Bokanowski and Athena Picarelli.
Speaker: Pietro Siorpaes, Mathematics, Imperial College London
Time: 18:00-19:00
Place: University College London - Physics Building A1/3, Gower Place
The martingale polar sets
Martingale optimal transport (MOT) is a variant of the classical optimal transport problem where a martingale constraint is imposed on the coupling. In a recent paper, Beiglböck, Nutz and Touzi show that in dimension one there is no duality gap and that the dual problem admits an optimizer. A key step towards this achievement is the characterization of the polar sets of the family of all martingale couplings. Here we extend this characterization to arbitrary finite dimension through a deeper study of the convex order.
Date: Thursday 3 November 2016
Speaker: Aleš Černý, Cass Business School
Time: 17:00-18:00
Place: University College London - Physics Building A1/3, Gower Place
Optimal trade execution under endogenous pressure to liquidate: theory and numerical solutions
We study optimal liquidation of a large trading position in a market with a temporary price impact. The novelty in our approach is that we endogenize the pressure to liquidate and hence allow the time horizon of liquidation to be determined endogenously, as part of the optimal strategy. The corresponding HJB equation leads to a severely singular initial value problem whose numerical solution we also study. In contrast to much of the existing literature spreading the liquidation strategy over a longer horizon is not necessarily beneficial to the trader.
Joint work with Pavol Brunovský and Ján Komadel.
Speaker: Antoine Jacquier, Mathematics, Imperial College London
Time: 18:00-19:00
Place: University College London - Physics Building A1/3, Gower Place
Some recent results on (asymptotics of) fractional stochastic volatility models
Date: Thursday 17 November 2016
Speaker: Chris Rogers, Statistical Laboratory, University of Cambridge
Time: 17:00-18:00
Place: University College London - Physics Building A1/3, Gower Place
High-frequency data: why are we looking at this?
High-frequency financial data is certainly a `big data' problem, with all of the associated issues: what are the stylized facts of the data? What are we trying to do with the data? What are appropriate models? Industry approaches get the first two of these questions, but do badly on the third. Most academic studies do badly on all three. For example, it is a fairy tale that we can propose a time-invariant model for the evolution of high-frequency data, estimate the parameters of this model, and then apply the conclusions of an analysis that assumes that the parameters were known with certainty. In this talk, I will try to identify what we might want to do with high-frequency data, critique some existing research agendas, and illustrate a possible way of trading in a high-frequency market.
Speaker: Umberto Cherubini, Statistical Sciences, Università di Bologna
Time: 18:00-19:00
Place: University College London - Physics Building A1/3, Gower Plac
No-Arbitrage Choquet Pricing with an Application to the Irrational Exercise Problem
In this paper we propose a pricing methodology that is based on the no-arbitrage assumption and that leads to option pricing formulas based on the Choquet integral, and interval based pricing. On one side, the Choquet pricing formula is typically derived from an approach based on non-additive expected utility theories, that is decision theory that take into account information ambiguity (such as the MMEU approach due to Gilboa and Schmeidler, 1989). On the other side, the no-arbitrage approach to interval based pricing is applied in the UVM pricing model based on interval-valued volatility due to Avellaneda, Levy and Paràs (1996). In our model we impose no-arbitrage applying the standard martingale probability model to the “basic probability assignment” (BPA) instead of the probability measure itself. The BPA is a probability measure applied to the power set instead of the set of events. The approach produces a pair of capacities (that is non-additive probability measures), one sub-additive and the other super-additive, linked by a duality relationship (the sub-additive measure on a subset plus the dual-superadditive measure of the complement set must add to 1). This no-arbitrage condition collapses to the standard equivalent martingale measure approach when the BPA is zero on all the elements of the power set that are not singletons. We show that the pricing formula generated by this model is a Choquet integral. For illustration purposes, we show how to apply the model to the problem of irrational exercise of options. Finally, we explore specific parametric forms of the Choquet pricing formulas, and their link with a stream of literature, developed in physics and known as q-calculus (Tsallis).
Based on joint work with Sabrina Mulinacci
Date: Thursday 1 December 2016
Speaker: Michael Tehranchi (University of Cambridge)TBA
Time: 17:00-18:00
Place: University College London - Physics Building A1/3, Gower Place
Black-Scholes inequalities: applications and generalisations
Various inequalities satisfied by the Black--Scholes call pricing formula and their applications to uniform bounds on implied volatility will be presented. To understand from where these inequalities arise, the family of call pricing functions is shown to be a noncommutative semigroup with involution with respect to a certain multiplication operator which is compatible with the convex order. A one-parameter sub-semigroup can be identified with a peacock, providing tractable call surface parametrisation in the spirit of the Gatheral-Jacquier SVI surface.
Speaker: Giorgia Callegaro, Università degli studi di Padova
Time: 18:00-19:00
Place: University College London - Physics Building A1/3, Gower Place
Optimal investment in markets with over and under-reaction to information
In this paper we introduce a jump-diffusion model of shot-noise type for stock prices, taking into account over and under-reaction of the market to incoming news. We work in a partial information setting, by supposing that standard investors do not have access to the market direction, the drift, (modelled via a random variable) after a jump. We focus on the expected (logarithmic) utility maximization problem by providing the optimal investment strategy in explicit form, both under full (i.e., from the insider point of view, aware of the right kind of market reaction at any time) and under partial information (i.e., from the standard investor viewpoint, who needs to infer the kind of market reaction from data). We test our results on market data relative to Enron and Ahold. The three main contributions of this paper are: the introduction of a new market model dealing with over and under-reaction to news, the explicit computation of the optimal filter dynamics using an original approach combining enlargement of filtrations with Innovation Theory and the application of the optimal portfolio allocation rule to market data.
Date: Thursday 15 December 2016
Speaker: Süleyman Başak, London Business School and CEPR
Time: 17:00-18:00
Place: University College London - Physics Building A1/3, Gower Place
Belief Dispersion in the Stock Market
We develop a dynamic model of belief dispersion which simultaneously explains the empirical regularities in a stock price, its mean return, volatility, and trading volume. Our model with a continuum of (possibly Bayesian) investors differing in beliefs is tractable and delivers exact closed-form solutions. Our model has the following implications. We find that the stock price is convex in cash-flow news, and it increases in belief dispersion while its mean return decreases when the view on the stock is optimistic, and vice versa when pessimistic. We also show that the presence of belief dispersion leads to a higher stock volatility, trading volume, and a positive relation between these two quantities. Furthermore, we demonstrate that the more familiar, otherwise identical, two-investor economies with heterogeneous beliefs do not necessarily generate our main results. Our quantitative analysis reveals that the effects of belief dispersion are economically significant and support the empirical evidence.
Speaker: Anes Dallagi, EDF France
Time: 18:00-19:00
Place: University College London - Physics Building A1/3, Gower Place
UK energy market: the trilemma
The UK energy system is facing unprecedented changes due to changing market conditions and regulatory constraints. The operation of the market and the generation assets are strongly related to the technological characteristics of the generation mix and to the behaviours of the consumers that shapes the load. This lead to a delicate balance that need to be maintained between three main objectives:
- Security of supply
- Affordability
- Low carbon energy mix
How to achieve this balance? And what are the tools and the methodologies that are used in order to simulate the operation of the UK energy systems and determine at which condition of regulation and market framework this balance may be achieved?
The January-March 2017 programme was hosted by Cass Business School, City, University of London.
Date: Thursday 26 January 2017
Speaker #1: Ivar Ekeland, CEREMADE and Institut de Finance, Université Paris-Dauphine
Time: 18:15-19:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Storers, processors and speculators: an equilibrium model for commodity markets
We present an infinite-horizon model of a commodity market. In each period t, two markets are open: a spot market for the commodity, and a futures market for financial contracts. Contracts traded at time t are settled at time t+1. Market participants are either storers, who have a capacity to store physical quantities, processors, who need the commodity to produce consumer goods, and speculators, who trade futures in order to turn a profit or to hedge other portfolios. Speculators do not trade on the physical market, but storers and processors trade on the futures market.
We seek an optimal Markov strategy for each participant, and we find it by solving a rational expectations equilibrium. We derive some insights concerning the impact of speculation on commodity markets, and we compare our findings with actual markets.
Joint work with Delphine Lautier, Bertrand Villeneuve and Edouard Jaeck.
Speaker #2: Mykhaylo Shkolnikov, ORFE, Princeton University
Time: 19:15-20:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
A random surface description of the capital distribution in large markets
We study the capital distribution in the context of the first-order models of Fernholz and Karatzas. We find that when the number of companies becomes large the capital distribution fluctuates around the solution of a porous medium PDE according to a linear parabolic SPDE with additive noise. Such a description opens the path to modelling the capital distribution surfaces in large markets by systems of a PDE and an SPDE and to understanding a variety of market characteristics and portfolio performances therein.
Joint work with Praveen Kolli.
Date: Thursday 9 February 2017
Speaker #1: Frank Riedel, Centre for Mathematical Economics, Bielefeld University
Time: 18:15-19:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Incompleteness of Financial Markets under Knightian Uncertainty
In diffusion models, few suitably chosen financial securities allow to complete the market. As a consequence, the efficienta llocations of static Arrow-Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow-Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow-Debreu equilibrium allocations are generically unattainable by dynamically trading few long-lived assets.
Date: Thursday 23 February 2017
Speaker #1: Scott Robertson, Questrom School of Business, Boston University
Time: 18:15-19:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Optimal Investment, Indifference Pricing, and Dynamic Default Insurance for Defaultable Assets
In this talk, we consider the optimal investment problem when the traded asset may default, causing a jump in its price. Upon default, the investor will lose her dollar position in the stock. For an investor with constant absolute risk aversion, our goal is to explicitly compute both the indifference price for a defaultable bond, and a fair price for dynamic protection against default. For the latter problem, our work complements Sircar and Zariphopoulou (2007), where it is implicitly assumed the investor is protected against default. We consider a factor model where asset returns, variances, correlations and default intensities are driven by a time homogeneous diffusion X taking values in an arbitrary region E of R^d. In addition to trading in the defaultable asset, the investor owns a non-traded asset whose terminal payoff depends upon the survival of the stock. Given X_t =x we identify the certainty equivalent with a semi-linear degenerate elliptic partial differential equation with quadratic growth in both the function and its gradient. Under a minimal exponential integrability assumption on the market price of risk, we show the certainty equivalent is a classical solution. In particular, our results cover when X is a one-dimensional affine diffusion, and when returns/variances are also affine.
Given the certainty equivalent we derive the indifference price for a defaultable bond as well as a fair price for dynamic protection against default. Numerical examples highlight the relationship between the factor process, and both the indifference price and default insurance. In fact, we show the insurance protection does not coincide with the default intensity under the dual optimal measure, as one may expect.
This is joint work with Tetsuya Ishikawa of Morgan Stanley.
Speaker #2: Peter Tankov, ENSAE ParisTech, Université Paris-Saclay
Time: 19:15-20:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Optimal forecast-based trading policies for a wind energy producer
We study the optimal trading policies for a wind energy producer who aims to sell the future production in the open electricity markets, and who has access to imperfect dynamically updated forecasts of the future production. We construct a stochastic model for the evolution of probabilistic forecasts and determine the optimal trading policies which are updated dynamically as new forecast information becomes available. Our results allow to quantify the expected future gain of the wind producer and to determine the economic value of the forecasts.
Date: Thursday 9 March 2017
Speaker #1: Mattheus Grasselli, Mathematics and Statistics, McMaster University
Time: 18:15-19:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Inequality in a monetary dynamic macroeconomic model
Thomas Piketty's influential book “Capital in the Twenty-First Century” documents the marked and unequivocal rise of income and wealth inequality observed across the developed world in the last three decades. His extrapolations into the distant future are much more controversial and have been subject to various criticisms from both mainstreams and heterodox economists. This motivates the search for an alternative standpoint incorporating heterodox insights such as endogenous money and the lessons from the Cambridge capital controversies. We argue that the Goodwin-Keen approach paves the road towards such an alternative.We first consider a modified Goodwin-Keen model driven by consumption by households, instead of investment by firms, leading to the same qualitative features of the original Keen 1995 model, namely the existence of an undesirable equilibrium characterized by infinite private debt ratio and zero employment, in addition to a desirable one with finite debt and non-zero employment. By further subdividing the household sector into workers and investors, we are able to investigate their relative income and wealth ratios for in the context of these two long-run equilibria, providing a testable link between asymptotic inequality and private debt accumulation
Speaker #2: Pretty Sagoo, Deutsche Bank
Time: 19:15-20:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
The Longevity Market according to Shrek
In 2009 the Life and Longevity Markets Association (‘The LLMA’) was set up, in anticipation of an explosion in derivatives linked to mortality rates, in particular to mortality improvement rates. The LLMA was formed by a collection of banks, insurers and reinsurers, all working towards standardization in mortality derivatives, especially those linked to aggregate and publicly available mortality data, such as E&W mortality data from the National Office of Statistics. In this talk we take a look at how that market developed and why it turned out very differently to that envisaged back in 2009.
Date: Thursday 23 March 2017
Speaker #1: Mathias Beiglböck, Mathematics, TU Vienna
Time: 18:15-19:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Brenier's Theorem, Martingale Optimal Transport and the Local Vol Model
A seminal result in optimal transport is Brenier's theorem on the structure of the optimal plan for squared distance costs. We briefly review related results on the martingale version of the transport problem and connections with robust finance. We then introduce a continuous time Brenier-type theorem for the martingale
transport problem which exhibits a particularly simple functional form. Finally, we explain a link of this result with the local vol model.
Speaker #2: Pierre Collin-Dufresne, École Polytechnique Fédérale de Lausanne
Time: 19:15-20:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Activism, Strategic Trading and Liquidity
We analyze dynamic trading in an anonymous market by an activist investor who can expend costly effort to affect firm value. We obtain the equilibrium in closed form for a general activism technology, including both binary and continuous outcomes. The optimal continuous trading strategy is independent of the activism technology. Activism, prices, and liquidity are jointly determined in equilibrium. Variation in noise trading volatility can produce either positive or negative effects on both efficiency and liquidity, depending on the activism technology and model parameters, because future effort depends on the realized amount of noise trading. The ‘lock in’ effect emphasized in previous literature (e.g., Coffee (1991), Bhide (1993) and Maug (1998)) holds only for special forms of the activism technology. Reducing the uncertainty about the activist’s position improves market liquidity, but the effect on efficiency depends on the specification of the effort cost function. Variation in the activist’s productivity produces a negative cross-sectional relation between efficiency and liquidity as the possibility of more activism exacerbates the risk of adverse selection.
Date: Thursday 6 April 2017
Speaker #1: Peter Takáč, Mathematics, Universität Rostock
Time: 18:15-19:00
Place: Cass Business School, 106 Bunhill Row, Room 6001 (6th floor)
Stochastic Volatility Models, Complete Markets, and Analyticity of Solutions to Ito’s Parabolic Problems
The problem of constant volatility, σ > 0, in the Black-Scholes option pricing model has sparked a number of new research directions on the nature of volatility. We first briefly recall the “most popular” volatility models based on mean reversion (the Ornstein-Uhlenbeck process): (i) Heston’s stochastic volatility model (1993); (ii) an alternative, mathematically much “easier” model due to Fouque, Papanicolaou, and Sircar (2000); and (iii) a more sophisticated model due to Dupire (1992) based on local implied volatility. We will discuss Dupire’s model and a possible generalization to volatility depending also on the asset (stock) price (as suggested by Lewis (2000)). This generalization does not cause any new mathematical difficulty (from an analytic or probabilistic point of view; numerical implementation might be harder).
Although Heston’s model for option pricing (i) is the simpliest model with stochastic volatility (SV), its rigorous analytical treatment is quite involved due to the degeneracies in Ito’s parabolic problem for very low and very high volatility levels (2016). This analysis is motivated by the analytical treatment of the alternative SV model (ii) due to Fouque, Papanicolaou, and Sircar which is much “easier” to handle. Ito’s parabolic problem for this model turns out to be uniformly parabolic with bounded analytic coefficients. Hence, it is not surprising that the solution is analytic in both, space and time variables, even if the initial data are only continuous. The “space” variable stands for the pair of the asset price and the volatility. We will prove the analyticity result for the option price by standard L2-methods in the Hardy space H2 of holomorphic functions that extend the real analytic functions to a suitable complex parabolic domain (2012).
We finish our lecture by applying well-known results on complete markets by M. H. A. Davis and J. Obloj (2008) to model (ii): Analyticity result for the option price implies that this option completes the market.
2015-16 London Mathematical Finance Seminar Series
The October-December 2015 programme was hosted by the Financial Mathematics and Risk and Stochastics groups at the London School of Economics and Political Science (LSE)
Date: Thursday 1 October 2015
Speaker #1: Markus Reiss, Humboldt University
Time: 16:00-17:00
Place: KCL - Strand Building, Room S0.13, Ground Floor
Improved volatility estimation under one-sided errors with applications to limit order books
Abstract: For a semi-martingale X, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation <X,X> is constructed. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive n^{−1/3} as optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with n observations (in mean). This considerably improves upon the classical n^{−1/4}-rate obtained for observations under centered noise. As an application estimating the integrated volatility of an efficient price process X from intra-day order book quotes is discussed.
Joint work with Markus Bibinger and Moritz Jirak
Speaker #2: Paolo Guasoni, Dublin City University (!!! note the change of time !!!)
Time: 17:30-18:30
Place: LSE - Thai Theatre, New Academic Building
Who should sell stocks?
Abstract: Never selling stocks is optimal for investors with a long horizon and a realistic range of preference and market parameters, if relative risk aversion, investment opportunities, proportional transaction costs, and dividend yields are constant. Such investors should buy stocks when their portfolio weight is too low, and otherwise hold them, letting dividends rebalance to cash over time rather than selling. With capital gain taxes, this policy outperforms both static buy-and-hold and dynamic rebalancing strategies that account for transaction costs. Selling stocks becomes optimal if either their target weight is low, or intermediate consumption is substantial.
(Joint work with Johannes Muhle-Karbe and Ren Liu)
Date: Thursday 15 October 2015
Speaker #1: Stéphane Villeneuve, University of Toulouse 1 Capitole
Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
Optimal exit under moral hazard
Abstract: We develop a model of optimal exit when a firm's asset owned by a risk-neutral principal is contracted out to a risk-neutral agent to manage. We characterize the optimal contract implementing effort at any time and prove that for a very profitable firm, it is optimal to let the agent shirk.
Speaker #2: Halil Mete Soner, ETH Zürich
Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
Stochastic target problems
Abstract: In a stochastic target problem, the controller tries to steer the state process into a prescribed target set with certainty. The state is assumed to follow stochastic dynamics while the target is deterministic and this miss-match renders the problem difficult. One exploits the degeneracies and/or the correlations of the noise process to determine the initial positions from which this goal is feasible. These problems appear naturally in several applications in quantitative finance providing robust hedging strategies. As a convenient solution technique, we use the geometric dynamic programming principle that we will describe in this talk. Then, this characterization of the reachability sets will be discussed in several examples.
Date: Thursday 29 October 2015
Speaker #1: Pierre Cardaliaguet, Université Paris-Dauphine
Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
Learning in mean-field games
Abstract: Mean field game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. The aim of this talk is to explain how such an equilibrium can appear: we introduce a learning procedure (similar to the fictitious play) and show its convergence when the mean field game is potential.
This is a joint work with S Hadikhanloo (Paris-Dauphine)
Speaker #2: Albina Danilova, LSE
Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
Markov bridges: SDE representation
Abstract:
Date: Thursday 12 November 2015
Speaker #1: Philipp Harms, ETH Zürich
Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
Affine representations of fractional processes with applications in mathematical finance
Abstract: Fractional processes have gained popularity in financial modelling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we show that a certain class of fractional processes can be represented as linear functionals of an infinite dimensional affine process. We demonstrate by means of several examples that the affine structure allows one to construct tractable financial models with fractional features.
Speaker #2: Marco Maggis, University of Milan
Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
Arbitrage theory without a reference probability: challenges of the model-free approach
Abstract: In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: is S reduces to a singleton, absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for S being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a Universal Aggregator of all arbitrage opportunities. Furthermore we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.
The talk is based on two papers joint with M Burzoni and M Frittelli.
Date: Thursday 26 November 2015
Speaker #1: Denis Belomestny, Duisburg Essen University
Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
Higher order variance reduction for discretised diffusions via regression
Abstract: In this talk we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows one to reduce the variance up to a certain power of discretisation error. In this way the complexity order of the plain MC algorithm can be reduced down to epsilon^{-2+delta} for any delta in [0,0.5) with epsilon being the precision to be achieved. These theoretical results are illustrated by several numerical examples.
Speaker #2: Ulrich Horst, Humboldt University
Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
Conditional analysis and a principal agent problem
Abstract: We analyse conditional optimization problems arising in discrete-time dynamic Principal-Agent models of delegated portfolio management. In these models, an investor (the Principal) outsources her portfolio selection to a manager (the Agent) whose investment decisions the investor cannot or does not want to monitor. We prove that if both parties' preferences are time-consistent and translation invariant and under suitable assumptions on the class of admissible contracts the problem of dynamic contract design can be reduced to a series of one-period conditional optimization problems of risk-sharing type under constraints, that the first-best solution is implementable if it exists and that optimal contracts must generally make use of derivatives. We fully solve the dynamic contracting problem for a class of optimized certainty equivalent (OCE) utilities including expected exponential utilities and Average Value at Risk. If information is generated by finitely many random walks, then our conditional optimization problems reduce to standard optimization problems in Euclidean spaces. In this case derivatives are not part of optimal compensation schemes and the contracting problem can be solved for all OCE utilities.
The talk is based on joint work with Julio Backhoff.
Date: Thursday 10 December 2015
Speaker #1: Peter Bank, TU Berlin
Time: 17:00-18:00
Place: LSE - Thai Theatre, New Academic Building
Optimal investment with price impact
Abstract: We consider a financial model with price impact where a large investor’s orders affect bid and ask prices. In a Brownian setting with exponential utility, this model allows for an explicit description of optimal investment strategies. In order to learn about indifference pricing and hedging of financial derivatives in such a frictional model, we consider a quadratic benchmark problem which emerges heuristically as the high-resilience limit of the original model. The benchmark problem also allows for a closed-form solution for very completely general options. It turns out that, rather than trading towards the currently optimal position from a frictionless reference model, it is optimal to trade towards a properly weighted average of this positions future expected values. This is joint work in progress with Mete Soner and Moritz Voss.
Speaker #2: Peter Tankov, Université Paris-Diderot (Paris 7)
Time: 18:15-19:15
Place: LSE - Thai Theatre, New Academic Building
Asymptotic lower bounds for optimal trading
Abstract: We consider the problem of tracking a target whose dynamics is modelled by a continuous Itô semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. We provide a comprehensive list of examples with explicit expressions for the lower bounds and discuss the application of our results to the problem of optimal trading in the presence of transaction costs.
The January-March 2016 programme was hosted by the King's College London.
Date: Thursday 21 January 2016
Speaker #1: Luciano Campi, LSE
Time: 16:15-17:00
Place: King's College London- Nash Lecture Theatre K2.31
On the support of extremal martingale measures with given marginals
After discussing some characterisations of extremal measures with given marginals available in the literature, going from functional analysis to combinatorics, we will turn to their martingale counter-parts whose study is related to robust pricing and hedging. In particular, we will give some sufficient and necessary conditions with a geometric and combinatorial flavour for a given set to be the support of an extremal martingale measure with pre-specified discrete marginals. Some open problems will be discussed as well. This is based on joint work with Claude Martini.
Speaker #2: Ying Hu Université de Rennes 1
Time: 17:15-18:00
Place: King's College London- Nash Lecture Theatre K2.31
An ergodic BSDE approach to large time behaviour of solution of semilinear parabolic partial differential equation
This talk is devoted to the study of the large time behaviour of solution of some semilinear parabolic partial differential equation (with Dirichlet or Neumann boundary condition). A probabilistic method (more precisely, an approach via an ergodic backward stochastic equation) is developped to show that the solution of a parabolic semilinear PDE at large time $T$ behaves like a linear term $\lambda T$ shifted with a function $v$, where $(v,\lambda)$ is the solution of the ergodic PDE associated to the parabolic PDE. The advantage of our method is that it gives an explicit rate of convergence. The result gives a perspective to give a precise estimate on the long run asymptotics for utility maximisation.
Date: Thursday 4 February 2016
Speaker #1: Jakša Cvitanić, Caltech
Time: 16:15-17:00
Place: King's College London- Nash Lecture Theatre K2.31
Dynamic Programming Approach to Principal-Agent Problems and Applications in Portfolio Management
We develop a new approach to solving a general finite horizon Principal-Agent problem from Contract Theory. We identify a family of admissible contracts for which the optimal agent's action is explicitly characterized; then, we show that we do not lose on generality when finding the optimal contract inside this family. Our argument relies on the Backward Stochastic Differential Equations approach to non-Markovian stochastic control, and more specifically, on the most recent extensions to the second order case. As a special case example, we apply the method to the problem of optimal compensation of a portfolio manager.
Joint with N. Touzi and D. Possamai
Speaker #2: Miklós Rásonyi, MTA Alfréd Rényi Institute of Mathematics
Time: 17:15-18:00
Place: King's College London- Nash Lecture Theatre K2.31
Find out more information about Miklós Rásonyi here
Sticky processes with jumps
We prove that sticky processes can be approximated arbitrarily well in L_p norm by processes that are martingales under an equivalent change of measure. The precise formulation of this result raises several issues which we will discuss. We also present some applications to the theory of illiquid markets.
Date: Thursday 18 February 2016
Speaker #1: Fabio Bellini, Università degli Studi di Milano-Bicocca
Time: 16:15-17:00
Place: King's College London- Nash Lecture Theatre K2.31
Elicitability, expectiles and backtesting with loss functions
We review the notion of elicitable statistical functional and discuss the characterisation of expectiles as the only elicitable coherent risk measures. We investigate the financial interpretation of expectiles and their possible use as risk measures for capital requirements, in comparison with the more established Value at Risk and Expected Shortfall. Finally, we discuss how consistent loss functions, whose existence is guaranteed by the elicitability property, may be used for testing and assessing the accuracy of a risk forecasting model.
Speaker #2: Jan Obloj, University of Oxford
Time: 17:15-18:00
Place: King's College London- Nash Lecture Theatre K2.31
Robust pricing-hedging duality with path constraints and applications to information quantification
We consider robust (pathwise) approach to pricing and hedging. Motivated by the notion of prediction set in Mykland (2003), we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. The framework interpolates between model--independent and model--specific settings. We establish a general pricing--hedging duality. The setup is parsimonious and includes the case of no traded options as well as the so-called martingale optimal transport duality of Dolinsky and Soner (2013) which we extend to multiple dimensions and multiple maturities. In presence of non-trivial beliefs, the equality is obtained between limiting values of perturbed problems indicating that the duality holds only if the market is stable under small perturbations of the inputs. Our framework allows to quantify the impact of making assumptions or gaining information. We focus in particular on the latter and study if the pricing-hedging duality is preserved under additional information.
Joint work with Zhaoxu Hou and Anna Aksamit.
Date: Thursday 3 March 2016
Speaker #1: Marco Fritelli, Università degli Studi di Milano
Time: 16:15-17:00
Place: King's College London- Nash Lecture Theatre K2.31
A Unified Approach to Systemic Risk Measures via Acceptance Sets
The purpose of this paper is to specify a general methodological framework that is flexible enough to cover a wide range of possibilities to design systemic risk measures via multi-dimensional acceptance sets and aggregation functions, and to study corresponding examples. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario-dependent allocation). We illustrate with several examples the advantages of this feature. We also provide conditions which ensure monotonicity, convexity, or quasi-convexity of our systemic risk measures.
Speaker #2: Matthias Scherer, Technische Universität München (TUM)
Time: 17:15-18:00
Place: King's College London- Nash Lecture Theatre K2.31
Exogenous shock models in high dimensions and a primer on model robustness
We review recent results on exogenous shock models and show how interesting subfamilies can be constructed in high dimensions. This is needed for applications in portfolio-credit risk and insurance. From a mathematical perspective, it bridges concepts from stochastic processes, self-similar distributions, and multivariate probability laws. Another-less obvious- application of the theory is the problem of model robustness in market risk management, for which we propose a new philosophy based on a distortion of the stochastic root of a risk model. The talk is based on joint work with Jan-Frederik Mai and Steffen Schenk.
Date: Thursday 17 March 2016
Speaker #1: Josef Teichmann, ETH Zürich
Time: 16:15-17:00
Place: King's College London- Nash Lecture Theatre K2.31
Rough Term structures
In the realm of Martin Hairer's regularity structures we introduce a Sobolev type norm on spaces of modelled distributions to enable the proper use of methods from stochastic analysis. We show several examples from term structure theory where regularity structures might be of importance in mathematical Finance.
(joint work with David Proemel, ETH)
Speaker #2: Philipp Keller, Deloitte
Time: 17:15-18:00
Place: King's College London- Nash Lecture Theatre K2.31
The foundations of the valuation of insurance liabilities
Valuation of liabilities is at the core of insurers’ risk management and determines the type of products that are being sold by insurers and their investment strategies. Accounting and regulatory valuation frameworks impact the entire financial market and society. Often insurers cover policyholders from a wide variety of risks over many decades, which makes the valuation of these covers highly complex and challenging.
We discuss the purposes of different valuation frameworks that are being used by insurance companies and put the different types of valuation standards into the context of replication with financial instruments to show their differences and commonalities. We focus on economic, market consistent valuation which is based on the cost of producing insurance liabilities with traded financial instruments and on consistency requirements between best estimates, the cost of capital and discount rates.
Finally, we give an overview over the connection between valuation, systemic risk and macroprudential policies and regulations of central banks.
Date: Thursday 31 March 2016
Speaker #1: Aleksandar Mijatovic, King's College London
Time: 16:15-17:00
Place: King's College London- Nash Lecture Theatre K2.31
A weak multilevel Monte Carlo scheme for multidimensional Lévy-type processes
Abstract: In this talk we describe a novel weak multilevel approximation scheme for time-changed Lévy processes and Lévy driven SDEs. The scheme is based on the state space discretisation of the driving Lévy process and is particularly well suited if the multidimensional driver is given by a Lévy copula.The multilevel version of the scheme is genuinely weak as it does not require strong convergence to control the level variances. The analysis of the level variances rests upon a new coupling between the approximating Markov chains of the consecutive levels, which is defined via a coupling of the corresponding Poisson Point Processes and is easy to simulate.
This is joint work with D. Belomestny.
Speaker #2: Martino Grasselli, Finance Lab at the Pôle Universitaire Léonard de Vinci / Università Degli Studi di Padova
Time: 17:15-18:00
Place: King's College London- Nash Lecture Theatre K2.31
Lie Symmetry Methods for Local Volatility Models
We investigate PDEs which are associated with the calculation of expectations for a large class of Local Volatility Models. We find nontrivial symmetry groups that can be used to obtain standard integral transforms of fundamental solutions of the PDE. We detail explicit computations in the separable volatility case when σ(t, x) = h(t)(α + βx + γx2), corresponding to the so called Quadratic Normal Volatility Model. We also consider choices for which exact fundamental solutions can be obtained.
Date: Thursday 23 June 2016
Speaker: Lan WU, Peking University
Time: 16:00-17:00
Place: King's College London- Strand Building, S4.23
Occupation Times of General Lévy Processes
Abstract: For a general Lévy process X which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of X and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of X. It is believed that our results would play an important role in financial applications.
2014-15 London Mathematical Finance Seminar Series
The October-December 2014 programme was hosted by King's College London
Date: 9 October 2014
Speaker: Sam Cohen, University of Oxford
Time: 16:30-17:30
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: Ergodic BSDEs with Lévy noise and time dependence
Abstract: In many control situations, particularly over the very long term, it is sensible to consider the ergodic value of some payoff. In this talk, we shall see how this can be studied in a weak formulation, using the theory of ergodic BSDEs. In particular, we shall consider the case where the underlying stochastic system is infinite dimensional, has Lévy-type jumps, and is not autonomous. We shall also see how this type of equation naturally arises in the valuation of a power plant.
Speaker: Sergei Levendorskiy, University of Leicester
Time: 17:45-18:45
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: Efficient Laplace and Fourier inversions and Wiener-Hopf factorization in financial applications
Abstract: A family of (quasi-) parabolic contour deformations increases the speed and accuracy of calculation of fairly complicated oscillatory integrals in option pricing formulas in many cases when standard approaches are either too slow or inaccurate or both. Variations: quasi-asymptotic formulas that are simple and much faster than general formulas, and which, for typical parameter values, are fairly accurate starting from relatively small distances from the barrier and maturities more than a year. When several Laplace and Fourier inversions are needed, it is necessary to use a family of contour transformations more flexible than Talbot's deformation of the contour in the Bromwich integral. Further step in a general program of study of the efficiency of combinations of one-dimensional inverse transforms for high-dimensional inversions [Abate-Whitt, Abate-Valko and others].
Calculations of Greeks and pdf can be made much more accurate; the latter can be used for fast Monte-Carlo simulations (faster than Madan-Yor method). Examples when insufficiently accurate pricing procedures may prevent one to see a good model (“sundial calibration”) or to see a local minimum of the calibration error when there is none, and the model may be unsuitable (“ghost calibration”) will be presented.
Date: 23 October 2014
Speaker: Jan Kallsen, University of Kiel
Time: 16:30-17:30
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: On portfolio optimization and indifference pricing with small transaction costs
Abstract: Portfolio Optimization problems with frictions as e.g. transaction costs are hard to solve explicitly. In the limit of small friction, solutions are often of much simpler structure. In the last twenty years, considerable progress has been made both in order to derive formal asymptotics as well as rigorous proofs. However, the latter usually rely on rather strong regularity conditions, which are hard to verify in concrete models. Some effort is still needed to make the results really applicable in practice. This talk is about a step in this direction. More specifically, we discuss portfolio optimization for exponential utility under small proportional transaction costs. As an example, we reconsider the Whalley-Willmott results of utility-based pricing and hedging in the Black-Scholes model. We relax the conditions required by Bichuch who gave a rigorous proof for smooth payoffs under sufficiently small risk aversion.
Speaker: Martijn Pistorius, Imperial College London
Time: 17:45-18:45
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: Optimal time to sell a stock with a jump to default
Abstract: We consider the problem of identifying the optimal time to sell a defaultable asset in the sense of minimizing the "prophet's drawdown" which is the ratio of the ultimate maximum (up to a random default time) and the value of the asset price at the moment of sale. We assume that default occurs at a constant rate, and that at the moment of default there is a random recovery value of $\rho(100)\%$. This problem is transformed to an optimal stopping problem, which we solve explicitly in the case that the asset price before default is modelled by a spectrally negative exponential Levy process. This is joint work with A. Mijiatovic.
Date: 6 November 2014
Speaker: Martin Schweizer, ETH Zurich
Time: 16:30-17:30
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: A new approach for stochastic Fubini theorems
Abstract: We prove a new stochastic Fubini theorem in a setting where we stochastically integrate a mixture of parametrised integrands, with the mixture taken with respect to a stochastic kernel instead of a fixed measure on the parameter space. To that end, we introduce a notion of measure-valued stochastic integration with respect to a multidimensional semimartingale. As an application, we show how one can handle a class of quite general stochastic Volterra semimartingales. The original question for this work came from a problem in mathematical finance, and we also briefly comment on that. The talk is based on joint work with Tahir Choulli (University of Alberta, Edmonton).
Speaker: Knut Aase, Norwegian School of Economics
Time: 17:45-18:45
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: Beyond the local mean-variance analysis in dynamic economics: Recursive utility etc
Abstract: I derive the equilibrium interest rate and risk premiums using recursive utility for jump-diffusions. Compared to to the continuous version, including jumps allows for a separate risk aversion related to jump size risk in addition to risk aversion related to the continuous part. We consider the version of recursive utility which gives the most unambiguous separation of risk preference from time substitution, and use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations. The model with jumps is shown to have a potential to give better explanation of empirical regularities than the recursive models based on merely continuous dynamics. Deviations from normality in the conventional model are also treated.
Date: 20 November 2014
Speaker: Gordan Zitkovic, University of Texas at Austin
Time: 16:30-17:30
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: On the dynamic programming principle for problems posed over martingale measures
Abstract: After an overview of the existing results on dynamic programming in continuous time, a simple abstract framework in which it holds will be described, and then used to analyze a class of problems posed over the "set of martingale measures". As an application, the super-replication and utility-maximization problems in a rather general family of incomplete Markovian financial market models will be treated.
Speaker: Sergio Pulido, Swiss Finance Institute
Time: 17:45-18:45
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: Existence and uniqueness results for multi-dimensional quadratic BSDEs arising from a price impact model with exponential utility
Abstract: In this work we study multi-dimensional systems of quadratic BSDEs arising from a price impact model where an influential investor trades illiquid assets with a representative market maker with exponential preferences. The impact of the strategy of the investor on the prices of the illiquid assets is derived endogenously through an equilibrium mechanism. We show that a relationship exists between this equilibrium mechanism and a multi-dimensional system of quadratic BSDEs. We also specify conditions on the parameters of the model that guarantee that the system of BSDEs has a unique solution, which corresponds to a family of unique equilibrium prices for the illiquid assets. The proof relies on estimates that exploit the structure of the equilibrium problem. Finally, we provide examples of parameters for which the corresponding system of BSDEs in not well-posed.
Joint work with Dmitry Kramkov.
Date: 4 December 2014
Speaker: Ragnar Norberg, University Lyon 1
Time: 16:30-17:30
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: On Marked Point Processes: Modelling, Stochastic Calculus, and Computational Issues
Abstract: The talk starts with a friendly introduction to marked point processes and their associated counting processes and martingales. Then it proceeds to three distinct, still intertwined, aspects of the theory: Modelling is a matter of specifying the intensities, which are the fundamental model entities with a clear interpretation as instantaneous transition probabilities; Prediction is a matter of calculating conditional expected values of functionals of the process, which involves stochastic calculus (can be made simple); Computation is a matter of solving Ordinary or Partial Integral-Differential Equations, looking for shortcuts (ODEs replacing PDEs) and looking out for pitfalls (non-smoothness points that cannot be detected by inspection of the equations). The unifying powers and the versatility of the model framework are demonstrated with examples from risk theory, life insurance, and non-life insurance.
Speaker: Michael Kupper, University of Konstanz
Time: 17:45-18:45
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: Robust Pricing Dualities
Abstract: We focus on representation results for monotone convex functionals with countably additive measures. As an application we consider a continuous-time financial market model under a family of probability measures and show that there exists no free lunch with disappearing risk if and only if there exists an equivalent family of martingale measures. Moreover, we discuss a generalized version of the transport duality with applications to model-free pricing. The talk is based on joint works with Patrick Cheridito and Ludovic Tangpi.
Date: 11 December 2014
Speaker: Peter Imkeller, Humboldt University Berlin
Time: 16:30-17:30
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: Cross hedging, (F)BSDE of quadratic growth and convex duality
Abstract: A financial market model is considered on which agents (e.g. insurers) are subject to an exogenous financial risk, which they trade by issuing a risk bond. They are able to invest in a market asset correlated with the exogenous risk. We investigate their utility maximization problem, and calculate bond prices using utility indifference. In the case of exponential utility, this hedging concept is interpreted by means of martingale optimality, and solved - even for non-convex constraints - with BSDE with drivers of quadratic growth. For more general utility functions defined on the whole or nonnegative real linewe show that if an optimal strategy exists then it is given in terms of the solution (X; Y;Z) of a fully coupled FBSDE. Conversely if the FBSDE admits a solution (X; Y;Z) then an optimal strategy can be obtained.
On a general stochastic basis, and with liability 0, we finally combine this FBSDE approach with the duality approach by Kramkov-Schachermayer who provide an abstract existence and uniqueness result for the optimal hedging strategy. Under some regularity conditions on the utility functions we associate to their solution a constructive one given by a numerically accessible FBSDE system describing the optimal investment process as the forward component, and a functional of the dual optimizer as the backward one. This is joint work with U.Horst, Y. Hu, V. Nzengang, A. Reveillac, and J. Zhang.
Speaker: Dylan Possamaï, Université Paris Dauphine
Time: 17:45-18:45
Place: Strand Campus, S-1.27 (1st basement, Strand Building)
Title: BSDEs, existence of densities and Malliavin calculus
Abstract: In recent years the field of Backward Stochastic Differential Equations (BSDEs) has been a subject of growing interest in stochastic calculus as these equations naturally arise in stochastic control problems in Finance, and as they provide Feynman-Kac type formulae for semi-linear PDEs. Since it is not generally possible to provide an explicit solution to these equations, one of the main issues especially regarding the applications is to provide a numerical analysis for the solution of a BSDE. This calls for a deep understanding of the regularity of the solution processes Y and Z. Here, we focus on the marginal laws of the random variables Yt, Zt at a given time t in (0,T). More precisely, we are interested in providing sufficient conditions ensuring the existence of a density (with respect to the Lebesgue measure) for these marginals on the one hand, and in deriving some estimates on these densities on the other hand. This type of information on the solution is of theoretical and of practical interest since the description of the tails of the (possible) density of Zt would provide more accurate estimates on the convergence rates of numerical schemes for quadratic growth BSDEs. This issue has been pretty few studied in the literature, since up to our knowledge only references [2, 1] address this question. The first results about this problem have been derived in [2], where the authors provide existence of densities for the marginals of the Y component only and when the driver h is Lipschitz continuous in (y,z), and some smoothness properties of this density. Concerning the Z component, much less is known since existence of a density for Z has been established in [1] only under the condition that the driver is linear in z. We revisit and extend the results of [2, 1] by providing sufficient conditions for the existence of densities for the marginal laws of the solution Yt,Zt (with t an arbitrary time in (0,T)) of a qgBSDE with a terminal condition ξ in (1) given as a deterministic mapping of the value at time T of the solution to a one- dimensional SDE, together with estimates on these densities. En route to these results, we provide new conditions for the Malliavin differentiability of solutions of Lipschitz or quadratic BSDEs. These results rely on the interpretation of the Malliavin derivative as a Gâteaux derivative in the directions of the Cameron-Martin space. Incidentally, we provide a new formulation for the characterization of the Malliavin-Sobolev type spaces D1,p.
The talk is based on joint works with Peter Imkeller, Thibaut Mastrollia and Anthony Reveillac.
The January-March 2015 programme is hosted by University College London (UCL).
Date: 15 January 2015
Speaker: Andrew Papanicolaou, University of Sydney
Time: 16:30-17:30
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions
Abstract: We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions. We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns.The results are an extension of the partially-informed investment strategies obtained by the Black-Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.
Speaker: Christoph Kuehn, J.W. Goethe-Universität, Frankfurt
Time: 17:45-18:45
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Modeling capital gains taxes in continuous time
Abstract: In most countries, trading gains have to be taxed. The modeling is complicated by the rule that gains on assets are taxed when assets are sold and not when gains actually occur. This means that an investor can influence the timing of her tax payments, i.e., she holds a timing option. In this talk, it is shown how the tax payment stream can be constructed beyond trading strategies of finite variation. We give an example for tax-efficient strategies for which the tax payment stream can be computed explicitly and show for which trading strategies the tax payment process is of (in)finite variation. Finally, we solve an optimal stopping problem that illustrates the basic effect of taxes on optimal investment decisions. This confirms the conjecture that the value of the tax-timing option is increasing in the volatility of the asset the investor holds. (The talk is based on joint work with Björn Ulbricht and partly with Budhi Arta Surya)
Date: 29 January 2015
Speaker: Damiano Brigo, Imperial College London
Time: 16:30-17:20
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Nonlinear valuation under credit gap risk, collateral margins, funding costs and multiple curves
Abstract: Following a quick introduction to derivatives markets and the classic theory of valuation, we describe the changes triggered by post 2007 events. We re-discuss the valuation theory assumptions and introduce valuation under counterparty credit risk, collateral posting, initial and variation margins, and funding costs. A number of these aspects had been investigated well before 2007. We explain model dependence induced by credit effects, hybrid features, contagion, payout uncertainty, and nonlinear effects due to replacement closeout at default and possibly asymmetric borrowing and lending rates in the margin interest and in the funding strategy for the hedge of the relevant portfolio. Nonlinearity manifests itself in the valuation equations taking the form of semi-linear PDEs or Backward SDEs. We discuss existence and uniqueness of solutions for these equations. We present an invariance theorem showing that the final valuation equations do not depend on unobservable risk free rates, that become purely instrumental variables. Valuation is thus based only on real market rates and processes. We also present a high level analysis of the consequences of nonlinearities, both from the point of view of methodology and from an operational angle, including deal/entity/aggregation dependent valuation probability measures and the role of banks treasuries. Finally, we hint at how one may connect these developments to interest rate theory under multiple discount curves, thus building a consistent valuation framework encompassing most post-2007 effects.
Speaker: Claude Martini, Zeliade Systems
Time: 17:45-18:35
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Investigating the extremal martingale measures with pre-specified marginals
Abstract: The extremal points in the set of all measures with pre-specified marginals, without the martingale constraint, have been extensively studied by many authors in the past (e.g. Denny, Douglas, Letac, Klopotowski to cite only a few). In this talk, we will focus on the characterization provided by Denny in the countable case: a key property is that the support of the probability Q has no “cycle”, otherwise a perturbation of Q can be constructed so that Q can not be extremal. In the context of the 2 marginals martingale problem studied by Beiglböck-Juillet, with special cases provided by Henry-Labordère and Touzi, Hobson and Klimmeck, Hobson and Neuberger, and Laachir, we give examples of extremal and non-extremal points, and give partial results towards a characterization theorem. (Joint work with L. Campi, LSE)
Date: 12 February 2015
Speaker: Julien Hugonnier, EPFL
Time: 16:30-17:20
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Heterogeneity in Decentralized Asset Markets
Abstract: We study a search and bargaining model of an asset market, where investors’ heterogeneous valuations for the asset are drawn from an arbitrary distribution. Our solution technique renders the analysis fully tractable and allows us to provide a full characterization of the equilibrium, in closed form, both in and out of steady state. We use this characterization for two purposes. First, we establish that the model can naturally account for a number of stylized facts that have been documented in empirical studies of over-the-counter asset markets. In particular, we show that heterogeneity among market participants implies that assets are reallocated through “intermediation chains,” ultimately producing a core-periphery trading network and non-trivial distributions of prices and trading times. Second, we show that the model generates a number of novel results that underscore the importance of heterogeneity in decentralized markets. We highlight two: first, heterogeneity magnifies the price impact of search frictions; and second, search frictions have larger effects on price levels than on price dispersion. Hence, quantifying the price discount or premium created by search frictions based on observed price dispersion can be misleading.
Speaker: Matthieu Rosenbaum, Université Pierre et Marie Curie
Time: 17:45-18:35
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Volatility is rough
Abstract: Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H<1/2. We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not long memory in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact. Finally, we provide a quantitative market microstructure-based foundation for our findings, relating the roughness of volatility to high frequency trading and order splitting. This is joint work with Jim Gatheral and Thibault Jaisson.
Date: 26 February 2015
Speaker: Stefan Ankirchner, Universität Jena
Time: 16:30-17:20
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: A generalized Donsker theorem and approximating SDEs with irregular coefficients
Abstract: We provide a new method for approximating the law of a diffusion M solving a stochastic differential equation with coefficients satisfying the Engelbert-Schmidt conditions. To this end we construct Markov chains whose law can be embedded into the diffusion M with a sequence of stopping times that have expectation 1/N, where N is a discretization parameter.
The transition probabilities of the Markov chains are determined by a reference probability measure, scaled with a factor depending on N and the state. We show that the Markov chains converge in distribution to the diffusion M, thus refining the Donsker-Prokhorov invariance principle. For some cases we provide a convergence rate. Finally, we illustrate our results with several examples. The talk is based on joint work with Thomas Kruse and Mikhail Uruso
Speaker: Bruno Bouchard, Université Paris-Dauphine
Time: 17:45-18:35
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Almost-sure hedging with permanent price impact
Abstract: We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging strategy.
Date: 12 March 2015
Speaker: Ulrich Horst, Humboldt-Universität, Berlin
Time: This talk has been cancelled.
Title: Weak law of large numbers for a limit order book model with fully state dependet order dynamics
Abstract: We study a one-sided limit order book (LOB) model, in which the order dynamics depend on both, the current best bid price and the current volume density function. For the joint dynamics of the best bid price and the standing buy volume density we derive a weak law of large numbers, which states that the LOB model converges to a continuous-time limit when the size of an individual order as well as the tick size tend to zero and the order arrival rate tends to infinity. In the scaling limit the standing buy volume density follows a non-linear PDE coupled with a non-linear ODE that describes the best bid price. The talk is based on joint work with Doerte Kreher.
Speaker: Huyên Pham, Université Paris-Diderot
Time: 17:45-18:35
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: An optimal trading problem in intraday electricity markets
Abstract:
We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intraday market and thermal power generation, and exhibit some remarkable properties of the trading rate. Furthermore, we study the case when there are jumps on the demand forecast and on the intraday price, typically due to error in the prediction of wind power generation. Finally, we solve the problem when taking into account delay constraints in thermal power production.
Based on joint work with René Aid (EDF) and Pierre Gruet (Paris Diderot).
Date: 19 March 2015
Speaker: Thaleia Zariphopoulou, University of Texas at Austin
Time: 16:30-17:20
Place: NASH LECTURE THEATRE (K2.31), Strand Campus, KING'S COLLEGE
Title: Forward investment performance processes: review and open problems
Abstract: In this talk, I will discuss the concept of forward investment performance process and will present results on discrete and continuous time. The latter are related to a fully-non linear SPDE, and to ergodic and infinite horizon BSDE. I will also state some open problems in asset allocation under these alternative criteria.
Date: 26 March 2015
Speaker: Tomasz Bielecki, Illinois Institute of Technology
Time: This talk has been cancelled.
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Market making via sub-scale invariant Dynamic Acceptability Indices
Abstract: The main goal of this study is to develop a general theoretical pricing framework that will capture some practically relevant properties, such as: the prices are not homogeneous in number of shares traded; the underlying securities bear transaction costs; the securities pay dividends; the dividends may be different for a long or short position. To achieve this goal, we use sub-scale invariant Dynamic Acceptability Indices (DAIs) as the main tool in developing thepricing methodology, and consequently, we present a representation of proposed prices in terms of a class of Backward Stochastic Difference Equations and g-Expectations. Besides the above mentioned properties, we also prove that: considered market models do not admit arbitrage; bid and ask prices do shrink the super hedging pricing interval; the prices are time consistent in some appropriate sense; if the drivers are linear we recover the classical martingale pricing theory. Finally, we provide some practical examples.
Speaker: Ernst Eberlein, University of Freiburg
Time: 17:45-18:35
Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF
Title: Lévy driven two price valuation with applications to long-dated contracts
Abstract:
In the classical valuation theory the law of one price prevails and market participants trade freely in both directions at the same price. This approach is appropriate for highly liquid markets. In the absence of perfect liquidity the law of one price should be replaced by a two price valuation theory where market participants continue to trade freely with the market but the terms of trade now depend on the direction of the trade. We develop here a static as well as a continuous time theory for two price economies. The two prices are termed bid and ask or lower and upper price but they should not be confused with the literature relating bid-ask spreads to transaction costs or other frictions involved in modeling financial markets. The bid price arises as the infimum of test valuations whereas the ask price is the supremum of such valuations. The two prices are related to nonlinear expectations. Probability as well as measure distortions are used to make this approach operational. We consider specific models where the uncertainty is given by purely discontinuous Lévy processes. The approach is illustrated to price stochastic perpetuities, i.e. contracts with no apparent maturity, and to value compound Poisson processes of insurance loss liabilities.
This is joint work with Dilip Madan, Martijn Pistorius, Wim Schoutens and Marc Yor.
The May-June 2015 programme was hosted by the Finance Faculty at Cass Business School, City University London
Date: 21 May 2015
Speaker: Giovanni Puccetti, University of Milan
Time: 18:10 - 19:00
Place: CASS BUSINESS SCHOOL, 106 BUNHILL ROW, EC 8TZ
Title: Reducing model risk via additional (in)dependence assumptions
Abstract: We derive lower and upper bounds for the Value-at-Risk of a portfolio of losses when the marginal distributions are known and an additional (in)dependence structure is assumed. We provide several actuarial examples showing that the newly proposed bounds strongly improve those available in the literature that are based on the sole knowledge of the marginal distributions. This talk is based on joint works with Valeria Bignozzi, Daniel Small, Ludger Rüschendorf and Steven Vanduffel.
Date: 18 June 2015
Speaker: Steven Kou, National University of Singapore
Time: 17:00 - 17:50
Place: CASS BUSINESS SCHOOL, 106 BUNHILL ROW, EC 8TZ
Title: Separating Skilled and Unskilled Fund Managers by Contract Design
Abstract: Foster and Young (2010, Quarterly Journal of Economics) shows that it is very difficult to design performance fee contracts rewarding skilled fund managers while screening out unskilled fund managers. In particular, none of the standard practices, such as postponing bonuses and claw-back provisions, can separate skilled and unskilled managers. We show that if (1) there is a liquidation boundary, meaning that the fund investors will close the fund immediately if the fund return is bad enough to hit the boundary, and (2) the fund manager has to use his/her own money to set up a deposit to offset the potential losses from the fund investors, then the skilled and unskilled fund managers can be separated. The deposit can be a combination of cash or an equity stake in the fund. A particular version of this type of contracts, called the first-loss scheme, is quite popular in China, and is emerging in U.S. This is joint work with Xuedong He and Sang Hu.
Speaker: David P. Newton, Nottingham University Business School
Time: 18:10 - 19:00
Place: CASS BUSINESS SCHOOL, 106 BUNHILL ROW, EC 8TZ
Title: Advancing the universality of numerical integration methods to any underlying process for option pricing
Exceptional accuracy and speed for option pricing are available via quadrature (Andricopoulos et al., JFE, 2003), extending into multiple dimensions with complex path-dependency and early exercise (Andricopoulos et al., JFE, 2007). However, the technique was incomplete, leaving many modelling processes outside the Black-Scholes-Merton framework unattainable. In this seminar paper (following Chen, Harkonen and Newton, JFE, 2014), I discuss how to remove the remaining major block to universal application. Although this had appeared highly problematic, the solution turns out to be conceptually simple and implementation is straightforward. Crucially, the method retains its speed and flexibility across complex combinations of option features but is now applicable across other underlying processes.
2013-14 London Mathematical Finance Seminar Series
3 October 2013
Speaker: Mike Tehranchi, Cambridge University
Title: An HJM approach to equity derivatives
There has been recent interest in applying the Heath-Jarrow-Morton interest rate framework to other areas of financial modelling. Unfortunately, there are serious technical challenges in implementing the approach for modelling the dynamics of the implied volatility surface of a given stock. We provide a partial solution to these difficulties by giving an existence result for associated HJM equation for the evolution of symmetric surfaces. The proof relies on a suitable change of parametrisation of the surface.
17 October 2013
Speaker: Mark Davis, Imperial College London
Title: Foundations of Probability Forecasting and Risk Management
Recently there has been renewed debate about the relative merits of VaR and CVaR as measures of financial risk. VaR is not coherent and does not qantify the risk beyond VaR, while CVaR shows some computational instabilities and is not "elicitable" (Gneiting 2010, Zwiebel 2013).
It is argued in this talk that such questions are best addressed from the point of view of probability forecasting or Dawid's "prequential statistics". We introduce a concept of "consistency" of a risk measure, which is close to Dawid's "strong prequential principle", and show that VaR indeed has special properties not shared by any other risk measure.
Speaker: Gechun Liang, Kings College London
Title: Optimal Switching at Poisson Random Intervention Times
In this talk, we consider a class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward stochastic differential equation system. The value function and the optimal switching strategy are characterized by the solution of the underlying switching system. In a Markovian setting, we give a complete description of the structure of switching regions by means of the comparison principle.
31 October 2013
Speaker: Stephane Loisel, Université Lyon 1
Title: Ruin probability for some particular correlated claims, for worsening risks, and risks with infinite mean
We first give explicit formulas for the infinite time ruin probability for some particular correlated claim amounts or interarrival times. We then investigate asymptotics of ruin probabilities when claim distribution is worsening over time, due to phenomena like sectorial inflation or global warming. We end up with some results in the case where claim amounts have infinite mean.
Speaker: Jocelyne Bion-Nadal, Ecole Polytechnique
Title: Martingale problem for path dependent diffusion processes application to robust pricing
Diffusion processes are characterized by their generator. In this talk I present the study of the martingale problem for path dependent generators with possibly a jump term. I introduce a new topological point of view for progressive functions on the canonical space of cadlag paths. The existence and uniqueness of solutions to the martingale problem is proved under the assumption that the coefficients of the diffusion are progressive functions with some continuity properties. This result generalizes to the path dependent case the Stroock's results for diffusions with Levy generators.
The financial market information is usually compatible with many classes of models. This leads to the problem of robust pricing under a possibly non dominated set of probability measures on the space of cadlag paths. I propose the construction of a robust time consistent dynamic pricing procedure making use of the martingale problem approach.
14 November 2013
Speaker: Andrea Pascucci, University of Bologna
Title: Approximate Implied vol for any local-stochastic vol model
Abstract: We consider an asset whose risk-neutral dynamics is described by a general local-stochastic volatility model. In this setting, we derive a family of asymptotic expansions for the transition density of the underlying as well as for European-style option prices and for implied volatilities. Our expansions are numerically efficient. Approximate transition densities and implied volatilities are explicit; they do not require any special functions nor do they require numerical integration. Approximate option prices require only a Normal CDF (as is the case of the Black-Scholes setting). Additionally, we establish rigorous error bounds for our transition density expansion. To illustrate the accuracy and versatility of our implied volatility expansion, we implement this expansion under different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility and 3/2 stochastic volatility.
Our implied volatility expansion is found to perform favorably compared to other well-known expansions for these models.
Speaker: Mario Wuthrich, ETH Zürich
Title: From Ruin Theory to Solvency in Non-Life Insurance
Abstract: We start from ruin theory considerations in the classical Cramer-Lundberg process. These considerations will be modified step by step so that we arrive at today's modern solvency assessments for non-life insurance companies. These modifications include discussions about time horizons, risk measures, claims development processes, financial returns and valuation of insurance liabilities.
28 November 2013
Speaker: Antonis Papapantoleon, TU Berlin
Title: Affine LIBOR models with multiple curves: theory, examples and calibration
Abstract: In this talk, we present an extension of the LIBOR market model with stochastic basis spreads, in the spirit of the affine LIBOR models. This multiple-curve model satisfies the main no-arbitrage and market requirements (such as nonnegative LIBOR-OIS spreads) by construction. The use of multidimensional affine processes as driving motions ensures the analytical tractability of the model. We provide pricing formulas for caps, swaptions and basis swaptions and discuss an efficient numerical implementation. Furthermore, the connection between the affine LIBOR setup and the 'classical' LIBOR market models is clarified. We present also some new examples of affine processes on $\mathbb{R}^2_+$ which admit explicit solutions of the Riccati equations. We conclude this talk by presenting calibration results to market data. This is joint work with Z. Grbac, J. Schoenmakers and D. Skovmand.
Speaker: Damir Filipovic, École Polytechnique Fédérale de Lausanne
Title: Linear-Rational Term Structure Models
Abstract: We introduce the class of linear-rational term structure models, where the state price density is modeled such that bond prices become linear-rational functions of the current state. This class is highly tractable with several distinct advantages: i) ensures non-negative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk premia, and iii) admits analytical solutions to swaptions. For comparison, affine term structure models can match either i) or ii), but not both simultaneously, and never iii). A parsimonious specification of the model with three term structure factors and one, or possibly two, unspanned factors has a very good fit to both interest rate swaps and swaptions since 1997. In particular, the model captures well the dynamics of the term structure and volatility during the recent period of near-zero interest rates.
12 December 2013
Speaker: Riccardo Rebonato, Pimco
Title: Affine Models for the Buy Side: Another Look at Convexity, Risk Premia and Reversion Levels
Abstract: There have been exciting new developments in affine modelling, which have pursued the increasingly converging paths of using principal components as mean-reverting factors, and imputing risk premia from the latter. These novel approaches offer exciting avenues, but also open up unexpected problems. The talk tries to explain what can and what cannot be done with an affine treatment of principal components, and highlights some unexpected 'impossibilities'. The risk premium beast remains elusive...
16 January 2014
Speaker: Bernt Oksendal, University of Oslo
Title: Model Uncertainty and Robust Duality in Finance
Abstract: A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities:
(i) The optimal terminal wealth X*(T):= X_{\phi*}{T} of the classical problem to maximise the expected U-utility of the terminal wealth X_{\phi}{T} generated by admissible \phi(t); 0\leq t\leq T in a market with the risky asset price process modlled as a semimartingale.
(ii) The optimal scenario dQ*/dP of the dual problem to minimise the expected V-value of dQ/dP over a family of equivalent locl martingale measures Q.
Here V is the convex dual function of the concave function U.
1) In the first part of this talk we consider markets modelled by Ito-Levy processes, and we present a new approach to the above result in this setting, based on the maximum principle in stochstic control theory. An advantage with our approach is that it also gives an explicit relation between the optimal portfolio \phi* and the optimal scenario Q*, in terms of backward stochastic differential equations. This can be used to obtain a general formula for the optimal portfolio \phi*(t) by means of the Malliavin derivative.
2) In the second part we extend our study to a robust portfolio problem and its dual. More specifically, we study the portfolio problem and its dual under model uncertainty, and we prove a corresponding duality equivalence in that setting. Our approach allows us to obtain explicit relations between the solutions of the robust primal and robust dual problem.
We illustrate the results with explicit examples.
The presentation is based on joint work with Agnes Sulem, INRIA-Rocquencourt, France.
30 January 2014
Speaker: Julien Hok, Markit
Title: Forward implied volatility expansion in time-dependent local volatility models (Cancelled)
Abstract: We introduce an analytical approximation to efficiently price forward start options on equity in time-dependent local volatility models as the forward start date, the maturity or the volatility coefficient are small. We use a conditional argument to represent the price as an expectation of a Black-Scholes formula computed with a stochastic implied volatility depending on the value of the equity at the forward date. Then we perform a volatility expansion to derive an analytical approximation of the forward implied volatility with a precise error estimate. We also illustrate the accuracy of the formula with some numerical experiment.
Speaker: Luca Capriotti, Credit Suisse
Title: Real time counterparty credit risk management with adjoint algorithmic differentiation (AAD)
Abstract: One the most active areas of risk management today is counterparty credit risk management (CCRM). Managing counterparty risk is particularly challenging because it requires the simultaneous evaluation of all the trades facing a given counterparty. For multi-asset portfolios this typically with extradordinary computational challenges.
We show how Adjoint Algorithm Differentiation (AAD) can be used to reduce the computational cost by hundreds of times. As a result, AAD allows one to perform in minutes risk runs that would take otherwise several hours or could not even be performed overnight without large parallel computers. AAD makes therefore possible risk time risk management in Monte Carlo, allowing investment firms to hedge their positions more effectively, actively manage their capital allocation, reduce their infrastructure costs, and ultimately attract more business.
13 February 2014
Speaker: Pierre Collin-Dufresne, École Polytechnique Fédérale de Lausanne
Title: Insider trading, stochastic liquidity and equilibrium prices
Abstract: We extend Kyle's (1985) model of insider trading to the case where liquidity provided by noise traders follows a general stochastic process. Even though the level of noise trading volatility is observable, in equilibrium, measured price impact is stochastic. If noise trading volatility is mean-reverting, then the equilibrium price follows a multivariate stochastic volatility 'bridge' process. More private information is recealed when volatility is higher. This is because insiders choose to optimally wait to trade more aggressively when noise trading volatility is higher. In equilibrium, market makers anticipate this, and adjust prices accordingly. In time series, insiders trade more aggressively, when measured price impact is lower. Therefore, aggregate execution costs to uninformed traders can be higher when price impact is lower.
Speaker: Yan Dolinsky, Hebrew University
Title: Robust hedging with proportional transaction
Abstract: Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Trading of both the options and the stock are subject to proportional transaction costs. The main theorem is duality between hedging and a Monge-Kantorovich type optimization problem. In this dual transport problem the optimization is over all the probability measures which satisfy an approximate martingale condition realted to consistent price systems in addition to an approximate marginal constraints. (Joint work with Mete Soner)
27 February 2014
Speaker: Anis Matoussi, University of Maine
Title: American and game options under uncertainty via Reflected second-order BSDEs
Abstract: We study the existence and uniqueness of second-order reflected 2BSDEs with one and two obstacles. For the later one, under some regularity assumptions on one of the barriers, we provide a complete wellposedness theory for doubly reflected second-order BSDEs. We also show that tjese pbjects are related to non-standard optimal stopping games, thus generalizing the connection between DRBSDEs and Dynkin games first proved by Cvitanic and Karatzas (1996). More precisely, we show that the second order DRBSDEs provide solutions of what we call uncertain Dynkin games that they also allow us to obtain super and subhedging prices for American game options (also called Israeli options) in financial markets with volatility uncertainty.
This is based on several joint work with D. Possamai, C. Zhou, and L. Piozin.
Speaker: Monique Jeanblanc, Universite D'Evry
Title: Arbitrages in a progressive enlargement of filtration
Abstract: In a first part, we present some models where the no arbitrage condition in the reference filtration implies that there are no arbitrages in the progressively enlarged filtration. Then, we study the case of honest times. Under the hypothesis that the financial market is complete in the reference filtration, we show that there exists arbitrages in the enlarged filtration, before and after the random time used to enlarged the filtration.
In a third part, we pay attention to arbitrages to the first kind. We give criteria such that this condition remains valud in the enlarged filtration (before and after the random time), and we give some examples corresponding to logarithm wealth optimization.
Joint work with A. Aksamit, T. Choulli, J. Deng.
13 March 2014
Speaker: Giulia Iori, City University
Title: The Impact of Reduced Pre-Trade Transparency Regimes on Market Quality
Abstract: The paper studies the effects of pre-trade quote transparency on spread, price discovery and liquidity in an artificial limit order market with heterogeneous trading rules. Our numerical experiments suggest that full quote transparency incurs to substantial transaction costs to traders and dampens trading activity in an order-driven market. Ecogenous restriction of displayed depth, up to several best quotes, does not benefit market performance. On the contrary, endogenous restriction of displayed quote depth, by means of iceberg orders, improved market quality in multiple dimensions: it alleviates the problem of adverse selection to patient limit order traders, relieves average transaction costs, maintains higher liquidity and moderate olatility, balances the limit order book and enhances price discovery.
Speaker: Frank Riedel, Bielefeld University
Title: Finance under Knightian Uncertainty
Abstract: We develop some basic results of finance under Knightian, or model uncertainty. In a first step, we investigate how one can formulate the basic hedging and asset pricing results without working with a probability space. In this case, topological considerations play a role.
In a second step, we consider the new framework of stochastic calculus based on Peng's theory of uncertainty. We consider (super)hedging prices and duality results and present some fist results on financial equilibria. We will also solve the usual Merton portfolio problem when interest rate and volatility are ambiguous. A surprising result says that the investor optimally puts all wealth into stocks when interest rate ambiguity is too large.
27 March 2014
Speaker: Christa Cuchiero, Vienna University of Technology
Title: A convergence result for the Emery topology and insights in the proof of the fundamental theorem of asset pricing
Speaker: Torsten Schoeneborn, Deutsche Bank
Title: Adaptive basket liquidation
Abstract: We consider the infinite time-horizon optimal basket portfolio liquidation problem fr a von Neumann-Morgenstern investor in a multi-asset extension of the liquidity model of Almgren (2003) with cross-asset impact. Using a stochastic control approach, we establish a "separation theorem'': the sequence of portfolios held during an optimal liquidation depends only on the (co-)variance and (cross-asset) market impact of the assets, while the speed with which these portfolios are attained depends only on the utility function of the trader. We derive partial differential equations for both the sequence of attained portfolios and the trading speed.
22 May 2014
Speaker: Francois Delarue, Universite Nice
Title: Large population stochastic control with a common noise
Abstract: We discuss the optimal control of mean-field interacting financial agents subjected to the influence of two noises: a noise that is specific to each agent and a noise that is common to all of them. Assuming that the agents obey similar dynamics, we investigate asymptotic equilibriums inside the population when the number of players tends to the infinity. We show that asymptotic McKean-Vlasov type. We also show that the decoupling field o this forward-backward system satisfies a 'master equation' according to the terminology introduced by Lasry and Lions in the theory of mean-field games.
Speaker: Luca Capriotti, Credit Suisse
Title: Real time counterparty credit risk management with adjoint algorithmic differentiation (AAD)
Abstract: One the most active areas of risk management today is counterparty credit risk management (CCRM). Managing counterparty risk is particularly challenging because it requires the simultaneous evaluation of all the trades facing a given counterparty. For multi-asset portfolios this typically with extradordinary computational challenges.
We show how Adjoint Algorithm Differentiation (AAD) can be used to reduce the computational cost by hundreds of times. As a result, AAD allows one to perform in minutes risk runs that would take otherwise several hours or could not even be performed overnight without large parallel computers. AAD makes therefore possible risk time risk management in Monte Carlo, allowing investment firms to hedge their positions more effectively, actively manage their capital allocation, reduce their infrastructure costs, and ultimately attract more business.
29 May 2014
Speaker: Min Dai, National University of Singapore
Title: Asymptotics for Merton problem with capital gain taxes and small interest rate
Abstract: We consider the continuous time optimal investment and consumption decision of a constant relative risk aversion investor who faces capital gain taxes. We provide asymptotic expansions with small interest rate. Our expansions offer a good approximation of the optimal buy and sell boundaries for small interest rate. Moreover, we obtain an estimate of the equivalent wealth loss due to capital gain taxes. In addition, we present an estimate of the optimal weight in the risky asset after realizing capital gain losses. Numerical results are presented to demonstrate our theoretical analysis. This work is jointly with Xinfu Chen.
2012-13 London Mathematical Finance Seminar Series
25 October 2012
Speaker: Nizar Touzi, Centre de Mathématiques Appliquées, Ecole Polytechnique
Title: Viscosity solutions of fully nonlinear part-dependent PDEs
Abstract: We propose a notion of viscosity solutions for path dependent fully nonlinear parabolic PDEs. This can be viewed as an alternative approach to backward stochastic differential equations and their second order extension. One typical example is the path dependent HJB equations, which can also be viewed as viscosity solutions of second order Backward SDEs and G-martingales. The definition is based on a nonlinear optimal stopping problem, and is consistent with the notion of classical solution in the sense of Dupire's functional It\^o calculus. We prove the existence, uniqueness, stability, and comparison principle for the viscosity solutions.
Speaker: Alexander Schied, Department of Mathematics, University of Mannheim
Title: Trading under transient price impact
Abstract: Based on an idealized model of a limit order book with resilience, Obizhaeva & Wang (2005) were the first to analyse optimal portfolio liquidation trajectories under transient price impact. Their original model has been generalised in several ways, e.g., so as to include nonlinear price impact, non-exponential resilience, multiple assets, or additional drift. In this talk, we will review some of these extensions and discuss the optimisation problems arising in the corresponding portfolio liquidation problems. Particular emphasis will be given to the role played by a drift in asset prices.
1 November 2012
Speaker: Ying Hu, Universite de Rennes 1, Institut de recherche mathematique de Rennes
Title: Ergodic BSDEs and Applications
Abstract: In this talk, we first introduce the notion of ergodic BSDE which arises naturally in the study of ergodic control. The ergodic BSDE is a class of infinite-horizon BSDEs where the unknown is the triple $(Y, Z, \lambda)$: $Y, Z$ are adapted processes and $\lambda$ is a real number. We review the existence and uniqueness result for ergodic BSDE under strict dissipative assumption. Then we study ergodic BSDEs under weak dissipative assumptions. We show the existence and uniqueness of solution to the ergodic BSDE by use of uniform coupling estimates for perturbed forward stochastic differential equations. Furthermore, we give some recent results on ergodic BSDEs with quadratic generators and ergodic BSDEs driven by Markov chains. Finally, applications are given to the optimal ergodic control of stochastic differential equations to illustrate our results. We give also connections with ergodic PDEs.
Speaker: Chris Rogers, University of Cambridge, Quantitative Finance Group, Statistical Laboratory
Title: Extremal martingales
Abstract: Availability of market prices of call options of all strikes determines the risk neutral distribution of the underlying asset at the terminal time. Finding the maximum and minimum price of various derivatives whose prices depend on the maximal value and the terminal value (such as barrier options) has been studied in the last 15 years or so by Hobson, Cox, Obloj, Brown, and others, and some quite complete results are known. This talk takes as its starting point some older work characterizing the possible joint laws of the maximum and terminal value of a martingale; this converts the problem of finding the extremal martingale into a linear programming problem, an observation which allows effective numerical solution. More recent work with Moritz Duembgen characterizes the possible joint distributions of the maximum, minimum, and terminal value of a continuous martingale.
15 November 2012
Speaker: Nick Bingham, Imperial College London, Department of Mathematics
The Worshipful Company of Actuaries annual lecture
Title: Risk for actuaries and risk for everyone
Speaker: Juan Carlos Pardo, Centro de Investigacion en Matematicas
Title: Occupation times for refracted Levy Processes
29 November 2012
Speaker: Michael Monoyios, University of Oxford, Department of Mathematics
Title: Malliavin calculus method for asymptotic expansion of dual control problems
Abstract: We develop a technique based on Malliavin calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of functional in which the control features quadratically, while in the state dynamics it appears as a drift perturbation to Brownian paths on Wiener space. This drift is interpreted as a measure change using the Girsanov theorem, leading to a form of the integration by parts formula in which a directional derivative on Wiener space is computed. Applications to incimplete Ito process markets are given, in which indifference prices are approximated in the low risk aversion limit. We also give an application to identifying the minimal entropy martingale measure as a perturbation to the minimal martingale measure in stochastic volatility models.
13 December 2012
Speaker: Hans Föllmer, Humboldt Universitat zu Berlin
Title: Shifting martingale measures and the birth of a bubble
Abstract: We study a flow in the space of equivalent martingale measures. This will allow us to capture the birth of a perceived bubble and to describe it as an initial submartingale which then turns into a supermartingale and falls back to its initial value zero. The talk will be based on joint work with F. Biagini and S. Nedelcu
Speaker: Michel Dacorogna, SCOR
Title: Surviving the next crisis, a risk management perspective
Abstract: With the economic and financial crisis, the question of solvency has become increasingly discussed and challenged. This presentation addresses the current financial crisis, analyses its specific nature, its impact on the financial system and its consequences on the solvency requirements. It takes a fresh look at crises and their characteristics to draw lessons for risk management.
The pro-cyclicality of the current capital models for insurances is highlighted and its consequences on financial stability are discussed. It finally proposes to make the regulatory system more flexible to respond to future crises and suggests a way to do it without compromising the principles on which the whole valuation model is built.
31 January 2013
Speaker: David Hobson, University of Warwick
Title: Indivisible Asset Sales, Consumption and Undiversifiable Risks
Abstract: Consider an agent with a single unit of an indivisible asset to sell, the price of which fluctuates over time. The aim of the agent is to maximise utility of consumption over time. In addition to the indivisible asset the agent has outside wealth and she is free to invest this wealth on a financial market. When should the agent sell the indivisible asset? What should her investment and consumption strategies be, both before and after she sells the asset? We set up the problem as a stochastic control problem. The solution has some natural and expected features, but there are also some suprising consequences.
Speaker: Dilip Madan, University of Maryland at College Park
Title: Two Price Economies in Continuous Time
Abstract: Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro-differential equations that are solved numerically for the three valuations of bid, ask and expectation. The operators imply concave distortions by inducing a probability into the infinitesimal generator of a Hunt process. This probability is then distorted. Two nonlinear operators based on different approaches to truncating small jumps are developed and termed QV for quadratic variation and NL for normalized Levy. Examples illustrate the resulting valuations. A sample book of derivatives on a single underlier is employed to display the gap between the bid and ask values for the book and the sum of comparable values for the components of the book.
14 February 2013
Speaker: Kostas Kardaras, LSE
Title: A guide through market viability for frictionless markets
Abstract: In this talk, we elaborate on the notions of no-free-lunch that have proved essential in the theory of financial mathematics --- most notably, arbitage of the first kind. Focus will be given in most recent developments. The precise connections with the semimartingale property of asset-price processes, as well as existence of deflators, numeraires and pricing probabilities via use of Foellmer's exit measure are explained. Furthermore, the consequences that these notions have in the valuation of illquid assets in the market will be briefly explored.
Speaker: Giovanni Cesari, UBS
Title: CVA/FVA/RWA: A portfolio view to price derivatives
Abstract: Pricing and hedging derivatives is moving from using highly sophisticated models for single trades to a portfolio view, which enables firms to consider the cost of counterparty exposure, cost of collateral, and cost of funding. In this talk, starting from the computation of counterparty credit exposure, we examine the interaction between CVA, DVA, and FVA, and suggest how to build a framework to compute these quantities consistently.
28 February 2013
Speaker: Jean Jacod, Universite Paris VI
Title: New efficient estimators for integrated volatility in the presence of non-summable jumps
Abstract: Estimation of the integrated volatility for Ito semimartingales which are discretely observed at n points is well understood, when the underlying process is continuous, or has summable jumps, and in this case it is possible to achieve the standard sqrt(n) convergence rate. When jumps are not summable the minimax rate becomes smaller. However, if one assumes that the small jumps are sufficiently close to those of a stable process (or a stochastic integral with respect to a stable process), we will show that it is possible to construct estimators with rate sqrt{n} again, and even variance-efficient under a kind of symmetry assumption.
This is a joint work with Viktor Todorov.
Speaker: Bryan Joseph, PriceWaterhouseCoopers
Title: Insurance - A Practical Use of Mathematics and Statistics
Abstract: The insurance industry has long relied on mathematics and statistics to define its business. Actuaries, as the financial engineers of this industry, has long been at the heart of this business. The talk is aimed at providing a practical perspective of an actuary and showing how mathematics is being applied in a number of different circumstances within the industry and how current developments are beinging new problems and requiring new or different solutions from practioners.
14 March 2013
Speaker: Fred Espen Benth, University of Oslo
Title: Modelling energy forward markets
Abstract: We analuse various approaches to model forward prices in energy markets. Empirical findings suggest a high degree of isionsyncratic risk between contracts at different matruities, pointing towards infinite-dimensional models for the price dynamics. We introduce a class of infinite-dimensional Levy processes based on subordination, and apply these in an HJM-approach to forward price modelling. Explicit representations of the spot price dynamics are classified. We also investigate a different pricing approach based on Ambit fields. Here, one is modelling the dynamics of forward prices directly rather than as the solution of some stochastic partial differential equation. Applications will be studied, including numerical simulation and optimal investments.
Speaker: Andrew Cairns, Heriot-Watt University
Title: Robust hedging of longevity risk
Abstract: We will begin with a brief introduction to longevity risk and the types of contract that might be used to hedge it including q-forwards and longevity swaps. We consider situations where a pension plan has opted to hedge its longevity risk using an index-based longevity hedging instrument. The use of index-based hedges gives rise to basis risk, but benefits, potentially, from lower costs to the hedger and greater liquidity. We focus on quantification of optimal hedge ratios and hedge effectiveness and investigate how robust these quantities are relative to inclusion of recalibration risk, parameter uncertainty and Poisson risk. In contrast, single-instrument hedging strategies are found, in general, to lack robustness relative to the inclusion of recalibration risk at the future valuation date, although we also demonstrate that some hedging instruments are more robust than others. To address this problem, we develop multi-instrument hedging strategies that are robust relative to recalibration risk.
21 March 2013
Speaker: Andreas Kyprianou, University of Bath
Title: Censored stable processes
Abstract: We look at a general two-sided jumping strictly alpha-stable process where alpha is in (0,2). By censoring its path each time it enters the negative half line we show that the resulting process is a positive self-similar Markov process. Using Lamperti's transformation we uncover an underlying driving Levy process and, moreover, we are able to describe in surprisingly exlicit detail the Wiener-Hopf factorization of the latter. Using this Wiener-Hopf factorization together with a series of spatial path transformation, it is now possible to produce an explicit formula for the law of the original stable processes as it first ``enters" a finite interal, thereby generalizing a result of Blumenthal, Getoor and Ray fro symmetric stable processes from 1961.
This is joint work with Alex Watson(Bath) and JC Pardo(CIMAT).
27 March 2013
Speaker: Michail Anthropelos, University of Piraeus
Title: Agents' stategic behavior in optimal risk sharing
Abstract: We consider the market of n financial agents who aim to increase their utilities by efficiently sharing their random endowments. Given the endogenously derived optimal sharing rules, we address the situation where agents do not reveal their true endowments, but instead they report as endowments the random qantities that maximize their utilities when the sharing rules are applied. Under mean-variance preferences, it is shown that each agent should share only a fraction of his true endowment and report that he is exposed to some endowment he does not possess. Furthermore, if all agents follow similar strategic behavior, the market equilibrates at a Nash-type equilibrium which benefits the speculators and results in risk sharing inefficiency. This agents' strategic behavior, when applied to oligopoly markets of exogenously given financial securities, changes the effective market portfolio and implies a price pressure on the traded securities.
Speaker: Sara Biagini, Scuola Normale Superiore, Pisa
Title: Dynamic quasi-concave performance measures
Abstract: We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characterization of a CPM in terms of an induced family of conditional convex risk measures. In the case of indexes these risk measures are coherent. Then, Dynamic Performance Measures (DPMs) are introduced and the problem of time consistency is addresses. The definition of time consistency chosen here ensures that the positions which are considered good tomorrow are already considered good today. We prove the equivalence between time consistency for a DPM and weak acceptence consistency for the induced families of risk measures. Finally, we extend CPMs and DPMs to dividend processes.
Joint work with J. Bion-Nadal, Ecole Polytechnique and CNRS
9 May 2013
Speaker: Walter Schachermayer, University of Vienna
Title: Portfolio Optimisation under Transation Costs
Abstract: We give an overview of some old and some new results on portfolio optimiszation under transaction costs. The emphasis will be on an asymptotic point of view when proportional transaction costs tend to zero.
23 May 2013
Speaker: Stephane Villeneuve, Toulouse School of Economics
Title: Optimal liquidity management under partial information about the firm's profitability
Abstract:We revisit the classical problem of optimal dividend distribution by assuming that the profitability of the cash reserves process is not observable. This leads us to solve a defenerate bi-dimensional singular control problem where the two state variables are the cash reserves and the posteriori belief about the firm's profitability. We characterize the value function by means of viscosity solution and provide an explicit solution when the firm's profitability has a symmetric two points distribution.
Speaker: Jean-Philippe Bouchaud, Capital Fund Management
Title: Liquidity, market impact, HFT: the complex ecology of financial markets
Abstract: We will review recent empirical findings concerning the impact of trades on prices, which is related to bod-ask spreads at high frequencies, and to what we call "latent liquidity" on lower frequencies, for so-called "metaorders". We discuss in particular a) the relation between spreads and volatility and the profitability of market making strategies and b) the rather surprising square root impact law of metaorders. We will argue that financial markets are (and have always been) on the verge of instability. The role of High Frequency Trading in the complex ecology of financial markets will be addressed.
31 May 2013
Speaker: Scott Robertson, Carnegie Mellon University
Title: Static fund separation for long term investments
Abstract: In this talk we will prove a class of static fund separation theorems, valid for investors with a long horizon and constant relative risk aversion, and with stochastic investment opportunities. An optimal portfolio decomposes as a constant mix of a few preference-free funds, which are common to all investors. The weight in each fund is a constant that may depend on an investor's risk aversion, but not on the state variable, which changes over time. Vice versa, the composition of each fund may depend on the state, but not on the risk aversion, since a fund appears in the portfolios of different investors. We prove these results for two classes of models with a single state variable, and several assets with constant correlations with the state. In the linear class, the state is an Ornstein-Uhlenbeck process, risk premia are afine in the state, while volatilies and the interest rate are constant. In the square root class, the state follows a square root diffusion, expected returns and the interest rate are affine in the state, while volatilities are linear in the square root of state.
