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Financial Mathematics and Applied Probability Seminars 2004-2005 Unless otherwise indicated, all seminars take place at Lecture Theatre 2C, King's College London, The Strand, London WC2R 2LS. Tuesday 12 Martin Johansson October, Imperial College and Citigroup, London 5:30 pm Malliavin Monte Carlo Greeks for Jump Diffusions Tuesday 19 October, 5:30 pm Room 3B20 Dr Ales Cerny Imperial College, London The Risk of Optimal, Continuously Rebalanced Hedging Strategies and Its Efficient Evaluation via Fourier Transform Abstract: It is well known that stock returns on short time horizons are highly non-normal, contrary to the assumptions in the Black--Scholes model. The present paper shows that non-normality of stock returns introduces a sizeable hedging error, even if one hedges optimally, continuously and in the absence of transaction costs. Our finding is in sharp contrast with the standard textbook knowledge claiming that continuous hedging is risk-free. This paper gives a theoretical description of optimal continuous-time mean-variance hedging strategies in a world with leptokurtic stock returns. We find closed form expressions for the optimal delta, the unconditional variance of the optimal hedging error and the dynamic Sharpe ratio of the entire hedging strategy, and suggest an efficient scheme for their evaluation using the fast Fourier transform. The analysis presented here extends the work of Cox, Ross and Rubinstein (1979) to the world of fat-tailed IID returns, and at the same time it adds an important time dimension to the optimal portfolio framework of Markowitz (1952) and Sharpe (1966). In much of the asset pricing literature (with the notable exception of Duffie and Richardson 1991, Toft 1996, Cochrane and Saa-Requejo 2000, and Khanna and Madan 2004) the hedging error is either not modelled by assuming market completeness, or it is effectively ignored by considering the so-called representative agent price, corresponding to the price at which a trader would not wish to buy or sell an option given her risk preferences. In practice traders sell large amounts of option contracts and, in the presence of hedging error, by doing so the traders enter into a risky position. To make the trading activity worthwhile the option price must therefore include a risk premium proportional to the hedging error, implying that option price can move in a bound around the Black-Scholes price. The width of the bound increases with the Sharpe ratio of the optimal hedging strategy. We find that a calibrated model of high frequency FT100 returns yields robust and nontrivial option price bounds. Tuesday 26 Dr Umut Cetin October, London School of Economics 5:30 pm Optimal Portfolios in Markets with Limited Depth Wednesday 3 Dr Massimo Bernaschi November, Istituto Applicazioni del Calcolo ---- IAC-CNR , Rome, Italy 5:30 pm Optimal Strategies for the Issuances of Public Debt Securities Room 17B Abstract: We describe a model for the optimization of the issuances of Public Debt securities developed for the Italian Ministry of Economy and Finance. The goal is to determine the composition of the portfolio issued every month which minimizes a specific cost function. Mathematically speaking, this is a stochastic optimal control problem with strong constraints imposed by national regulations and the Maastricht treaty. The main stochastic component of the problem is represented by the evolution of interest rates. We discuss the different optmization strategies we employ (from classic Linear Programming techniques to sophisticated Model Predictive Control strategies) and provide an estimate of the risk associated with any issuance policy. Tuesday 9 Dr Thorsten Rheinlander November, Department of Statistics, London School of Economics 5:30 pm Arbitrage opportunities in diverse markets via a non-equivalent measure change Tuesday 16 Dr Peter Tankov November, Centre de Mathematiques Appliquees, Ecole Polytechnique, France 5:30 pm Retrieving exponential Levy models from option prices using relative entropy Tuesday 23 Tim Johnson November, Department of Mathematics, King's College London 5:30 pm A discretionary stopping problem with applications to the optimal timing of investment decisions. Tuesday 30 Dr Matthias Winkel November, Department of Statistics, Oxford 5:30 pm Limit theorems for multipower variation in the presence of jumps in financial econometrics Tuesday 7 December, 5:30 pm Dr Ian Buckley Tanaka Business School, Imperial College, London Bias-free option calibration using Shannon and Renyi entropies Tuesday 25 Dr Alvaro Cartea January, School of Economics, Mathematics and Statistics, Birkbeck College, London 5:30 pm Generalised Fractional-Black-Scholes Equation: pricing and hedging Tuesday 1 February, 5:30 pm Dr Aytac Ilhan Mathematical Institute, Oxford Optimal Static-Dynamic Hedges for Exotic Options Thursday 3 Professor Fred Espen Benth February, Department of Mathematics, University of Oslo 3:30 pm Room 521 Stochastic volatility models, minimal entropy martingale measure and option pricing Tuesday 8 February, 5:30 pm Dr Sergei Fedotov School of Mathematics, The University of Manchester Adaptive method for valuing an option on assets with stochastic volatility Tuesday 15 Professor Giulia Iori February, City University, London 5:30 pm The impact of heterogeneous trading rules on the limit order book and order flows Monday 21 Professor Stathis Tompaidis February, University of Texas at Austin 2:30 - 4:00 pm Energy Finance: An introduction Room 28A Tuesday 22 Dr Henrik Rasmussen February, Mathematical Institute, Oxford 5:30 pm A family of markovian HJM models Tuesday 1 March, 5:30 pm Dr Michael Monoyios Department of Economics and Finance, Brunel University Esscher transforms, martingale measures and optimal hedging in incomplete diffusion models Tuesday 31 Professor Steven E. Shreve May, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh 5:30 pm Satisfying Convex Risk Limits by Trading Friday 3 June, Dr Jan Vecer 12:00 am Department of Statistics, Columbia University, New York Crash Options, Rally Options Tuesday 7 June, 5:30 pm Professor Eckhard Platen School of Finance and Economics, University of Technology, Sydney, Australia. A Benchmark Approach to Risk Management Tuesday 21 Dr Xin Guo June, School of Operations Research and Industrial Engineering, Cornell University, New York. 5:30 pm Information Reduction in Credit Risk Tuesday 28 Professor Florin Avram June, Department of Mathematics, Pau University, France. 5:30 pm On clustering, mixtures estimation and the method of moments