Nomura Seminar
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Fri, 25/05 14:15 |
Prof Dorje Brody (Brunel Univeristy) |
Nomura Seminar  |
DH 1st floor SR |
| The geometric Lévy model (GLM) is a natural generalisation of the geometric Brownian motion (GBM) model. The theory of such models simplifies considerably if one takes a pricing kernel approach. In one dimension, once the underlying Lévy process has been specified, the GLM has four parameters: the initial price, the interest rate, the volatility and the risk aversion. The pricing kernel is the product of a discount factor and a risk aversion martingale. For GBM, the risk aversion parameter is the market price of risk. In this talk I show that for a GLM, this interpretation is not valid: the excess rate of return above the interest rate is a nonlinear function of the volatility and the risk aversion such that it is positive, and is increasing with respect to these variables. In the case of foreign exchange, Siegel’s paradox implies that one can construct foreign exchange models for which the excess rate of return is positive for both the exchange rate and the inverse exchange rate. Examples are worked out for a range of Lévy processes. (The talk is based on a recent paper: Brody, Hughston & Mackie, Proceedings of the Royal Society London, to appear in May 2012). | |||
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Fri, 01/06 14:15 |
Prof Scott Robertosn (Pittsburgh) |
Nomura Seminar |
DH 1st floor SR |
| In this talk, approximations to utility indifference prices for a contingent claim in the large position size limit are provided. Results are valid for general utility functions and semi-martingale models. It is shown that as the position size approaches infinity, all utility functions with the same rate of decay for large negative wealths yield the same price. Practically, this means an investor should price like an exponential investor. In a sizeable class of diffusion models, the large position limit is seen to arise naturally in conjunction with the limit of a complete model and hence approximations are most appropriate in this setting. | |||
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Fri, 15/06 14:15 |
Dr Antoine Jacquier (Imperial College London) |
Nomura Seminar |
DH 1st floor SR |
| Given a diffusion in R^n, we prove a small-noise expansion for its density. Our proof relies on the Laplace method on Wiener space and stochastic Taylor expansions in the spirit of Benarous-Bismut. Our result applies (i) to small-time asymptotics and (ii) to the tails of the distribution and (iii) to small volatility of volatility. We shall study applications of this result to stochastic volatility models, recovering the Berestycki- Busca-Florent formula (using (i)), the Gulisashvili-Stein expansion (from (ii)) and Lewis' expansions (using (iii)). This is a joint work with J.D. Deuschel (TU Berlin), P. Friz (TU Berlin) and S. Violante (Imperial College London). | |||