Download Abstract: It is well known that stock returns on short time horizons are

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