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: 16:30-17:20

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: TBA

Abstract:TBA


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: TBA

Abstract:TBA


Date: 26 March 2015

Speaker: Tomasz Bielecki,Illinois Institute of Technology

Time: 16:30-17:20

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: TBA

Abstract:TBA


Speaker: Ernst Eberlein, University of Freiburg

Time: 17:45-18:355

Place: CHANDLER HOUSE, G10, 2 WAKEFIELD STREET, LONDON, WC1N 1PF

Title: Lévy driven two prcie 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.