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Seminars 2006-2007

Summer Term 2007

Wednesday 16 May 2007

Dirk Becherer (Imperial) Optimal liquidation in markets with finite resiliency
16:30-17:30, Room 413, Huxley Building, Mathematics Department
Abstract: If financial market is not infinitely liquid, a large trader who wants to liquidate an asset position faces an execution problem. His orders affect the market prices against which they are executed, hence the liquidation proceeds become a nonlinear function of the trading strategy. There is no standard model for illiquidity yet. In this talk we report on results from a research project with Prof P. Bank (Columbia University). We propose a new model for markets with finite resiliency and nonlinear market impact functions, and discuss the differences to previous modelling suggestion. For our model, we obtain explicit solutions for the optimal strategy that maximizes the discounted liquidation proceeds.

Wednesday 30 May 2007 (Joint Maths-Tanaka Series)

Jean-Paul Décamps (University of Toulouse)
14.30-15.30 Tanaka Business School 2nd Floor, Lecture Theatre 2

Wednesday 6 June 2007

Ralf Korn (Universität Kaiserslautern) Worst-Case Control for Optimal Portfolios: Basics and recent Aspects
16:30-17:30 Room 413 Huxley Building, Mathematics Department

Abstract: Due to insufficient ability to estimate parameters accurately it might in some situations be preferable to model stock price behaviour in a non-stochastic way and obtain worst-case bounds for their performance instead of optimal behaviour based on unreliable information. An example of such a situation is the worst-case approach to portfolio optimization in the presence of the threat of a crash. In the talk we motivate the approach, review basic applications to portfolio optimization and consider more recent aspects. Among them are the worst- case app roach in the presence of an additional insurance risk process, the situation of changing market coefficients and -as a very recent result - a verification theorem for a Hamilton-Jacobi-Bellman system of inequalities and a complementarity condition. Besides theoretical results explicit examples exhibiting closed form solutions will be presented.

Wednesday 20 June 2007 (Joint Maths-Tanaka Series)

Nizar Touzi (Imperial College and Ecole Polytechnique)
14.30-15.30 Tanaka Business School 2nd Floor, Lecture Theatre 2

Spring Term 2007

Wednesday 10 January 2007

Andreas Kyprianou (Bath) Distributional study of De Finetti's dividend problem for a general Levy model of insurance risk
17:00 – 18:00 Mathematics Department, Room 140 (Huxley Blg)

Wednesday 17 January 2007

Jan Obloj (IMS, Imperial) Skorokhod embedding and financial applications (abstract)
16:00 – 17:00 Mathematics Department, Room 140 (Huxley Blg)

Abstract: The talk is organised in two parts. In the first part, we describe how the Skorokhod embedding problem can be used to obtain price-range for exotics (and often also the hedging strategies). From the traded prices of calls we can read the terminal distribution of the stock price. The price process can be then seen as a time-changed Brownian motion with a fixed terminal distribution - that is a solution to the Skorokhod embedding problem (SEP). Determing a model-free price-range for an exotic option amounts to finding the range of values of a given functional among solutions to the SEP. Simple examples include the maximum (lookback option) and quadratic variation (variance or volatility swaps) which we solve giving the explicit constructions realising the lower and upper bounds.\par

In the second part of the talk we illustrate the approach with an example of an option paying a convex function of the terminal local time. We compute the price range and provide a model-free hedging strategy. This part is based on a joint work with A.M.G. Cox and David Hobson.

Wednesday 24 January 2007

Pavel Gapeev (Humboldt University, Berlin) Convertible bonds in structural and reduced form models
16:00 – 17:00 Mathematics Department, Room 140 (Huxley Blg)

Wednesday 31 January 2007

Semyon Malamud (ETH Zurich) A Unified Approach to Idiosyncratic Risk and General Market Incompleteness
16:00 – 17:00 Mathematics Department, Room 140 (Huxley Blg)

Abstract: We present a constructive method for analyzing optimal consumption, opt imal inve stment, and the equilibrium prices of a ssets and liabilities in incomplete markets. For example, w e explicitly construct (1) equilibria with trade for the Constantinides and Duffie (1996)models and sh ow that procyclical risk can increase equity premium, contrary to the Constantinides a nd Duffie "law", (2) the optimal consumption stream for a general diffusion driven incomplete market (e.g., He and Pearson) with general recursive utilities, (3) the optimal investment strategy for the benchmark macroeconomic model of Krusell and Smith and quantitatively analyze equilibria, and (4) a unified asset pricing / insurance premia model and its optimal market consistent insurance premia flow. [Joint work with Eugene Trubowitz]

Wednesday 14 February 2007

Martijn Pistorius (King’s College) On barrier options driven by Levy processes
16:00 – 17:00 Mathematics Department, Room 140 (Huxley Blg)

Wednesday 21 February 2007

Jiang Lun Wu (University of Wales Swansea) On the martingale property of empirical processes
16:00 – 17:00 Mathematics Department, Room 140 (Huxley Blg)
Abstract: Starting with Doob' measurability problem, we will give a brief account of the richness of Loeb product space of probability measure spaces (nonstandard). Then we will demonstrate that on such a nonstandard product measure space framework, a large collection of stochastic processes are martingale essentially if and only if so are the empirical processes. The talk is based on (1) J. Berger, H. Osswald, Y Sun, J-L Wu, Illinois J Math 46 (2002), 319-330, and (2) S Albeverio, Y Sun, J-L Wu, Trans Amer Math Soc 359 (2007), 517-527.

Wednesday 28 February 2007 (Joint Maths-Tanaka Series)

Raymond Brummelhuis (Birkbeck) Auto-tail dependence coefficients for financial time series
14:30 – 15:30 Tanaka Business School, 2nd Floor - Lecture Theatre 2
Abstract: We study dependence in non-linear time-series models like GARCH from the point of view of the lower tail dependence coefficient and certain generalizations thereoff. In risk management terms, these can be interpreted as the conditional probability of a value-at-risk violation taking place, conditional upon one already having occured. We also report on some results for empirical financial time-series.

Wednesday 07 March 2007

Goran Peskir (Manchester University)
16:00 – 17:00 Mathematics Department, Room 140 (Huxley Blg)

Wednesday 14 March 2007

Peter Friz (Cambridge University)
16:00 – 17:00 Mathematics Department, Room 140 (Huxley)

Autumn Term 2006

Wednesday 25 October 2006
Joint Maths-Tanaka Series

Dorje C. Brody (Imperial): Information-based asset pricing
14:30 – 15:30 2nd Floor – Lecture Theatre 2, Tanaka Business School

Abstract: A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the corresponding price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent market factors. With each such market factor we associate a market information process, the values of which we assume are accessible to market participants. Each market information process consists of a sum of two terms; one contains true information about the value of the associated market factor, and the other represents noise. The price of an asset is given by the expectation of the discounted cash flows in the risk neutral measure, conditional on the information provided by the market filtration. In the case where the cash flows are the random coupon/dividend payments, explicit models are obtained for the bond/share-price processes. Dividend growth is taken into account by in troducing appropriate struct ure on the market factors. The prices of options on coupon/dividend-paying assets are derived. The information-based framework has two other significant consequences: (i) it provides a stable hedging strategy for an option on credit-risky bond; and (ii) it generates a natural explanation for the origin of unhedgeable stochastic volatility in financial markets. (The talk is based on work carried out in collaboration with L.P. Hughston and A. Macrina.)

Wednesday 15 November 2006

Mike Tehranchi (Cambridge): No-arbitrage implied volatility dynamics
17:00 -18:00 Room 140 (Huxley) Mathematics Department

Abstract:We study the implications of a no-arbitrage assumption on the possible shapes and dynamics of the volatility surface implied by the Black-Scholes formula. In particular, we prove that the implied volatility surface flattens at long maturities in a rather precise manner. Furthermore, the long implied volatility cannot fall, in complete analogy with the Dybvig-Ingersoll-Ross theorem on long zero coupon rates. Finally, we show that a conjecture of Steve Ross on the impossibility of parallel movements of the implied volatility surface is true for a large class of models. This work is joint with Chris Rogers.

Wednesday 22 November 2006

Johannes Wissel (ETH Zurich): Term structure of implied volatilities: Absence of arbitrage and existence results
17:-18:00 Room 140 (Huxley) Mathematics Department

Abstract:In this talk we study modelling and existence issues for market models of stochastic implied volatility in a continuous-time framework with one stock, one bank account and a family of European options for all maturities with a fixed payoff function h. We first characterize absence of arbitrage in terms of drift conditions for the forward implied volatilities corresponding to a general convex h. For the resulting infinite system of SDEs for the stock and all the forward implied volatilities, we then study the question of solvability and provide sufficient conditions for existence and uniqueness of a solution. We do this for two examples of h, namely calls with a fixed strike and a fixed power of the terminal stock price, and we give explicit examples of volatility coefficients satisfying the required assumptions. This talk is based on a joint work with Martin Schweizer, "Term str uctures of implied volatilities: Absence of arbitrage and existence results" (to appear in Mathematical Finance).

Wednesday 29 November 2006

Joint Maths-Tanaka Series

Alexander Lipton (Merrill Lynch): Dynamic credit correlation models: jump diffusion of the market factor and its implications.
14:30 – 15:30 2nd Floor - Lecture Theatre 2, Tanaka Business School

Wednesday 06 December 2006

Christoph Reisinger (Oxford): Asymptotic expansions and numerical approaches for basket derivatives
17:00 – 18:00 Room 140 Huxley Building, Mathematics Department

Wednesday 13 December 2006

Ulrich Horst (University of British Columbia):On the Spanning Property of Risk Bonds Priced by Equilibrium
17:00 – 18:00 Room 140 Huxley Building, Mathematics Department

Abstract: We propose a method of pricing financial securities written on non-tradable underlyings such as temperature or precipitation levels. To this end, we analyze a financial market where agents are exposed to financial and non-financial risk factors. The agents hedge their financial risk in the stock market and trade a risk bond issued by an insurance company. From the issuer's point of view the bond's primary purpose is to shift insurance risks related to non-catastrophic weather events to financi al markets. As such its terminal payoff and yie l d curve depend on an underlying climate or temperature process whose dynamics is independent of the randomness driving stoc k prices. We prove that if the bon d's payoff function is monotone in the external risk process, it can be priced by an eq uilibrium approach. The equilibrium market price of climate risk and the equilibrium price process are characterized as solution of non-linear backward stochastic differential equations. Transferring the BSDEs into PDEs, we represent the bond prices as smooth functions of the underlying risk factors.