The 2014-15 London Mathematical Finance Seminar Series will be hosted by University College London in the second term of the academic session.

To subscribe the seminar email list: https://mailman.ic.ac.uk/mailman/listinfo/mathfin-seminar

The seminar is partially supported by INTECH.


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 BieleckiIllinois 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 asthe 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.


Date: 21 May 2015

Speaker: Giovanni PuccettiUniversity 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.