Efficient Simulation of the Wishart Model

74 Pages Posted: 17 Sep 2009 Last revised: 25 Sep 2009

Multiple version iconThere are 2 versions of this paper

Date Written: September 17, 2009

Abstract

In financial mathematics, Wishart processes have emerged as an efficient tool to model stochastic covariance structures. Their numerical simulation may be quite challenging since they involve matrix processes. In this article, we propose an extensive study of financial applications of Wishart processes. First, we derive closed-form formulas for option prices in the single-asset case. Then, we show the relationship between Wishart processes and Wishart law. Finally, we review existing discretization schemes (Euler and Ornstein-Uhlenbeck) and propose a new scheme, adapted from Heston's QEM discretization scheme. Extensive numerical results support our comparison of these three schemes.

Keywords: Stochastic Volatility, Equity options, Multifactor model, Wishart model, Discretization scheme, Random Matrix, Heston model

JEL Classification: C15, G13

Suggested Citation

Gauthier, Pierre and Possamaï, Dylan, Efficient Simulation of the Wishart Model (September 17, 2009). Available at SSRN: https://ssrn.com/abstract=1474728 or http://dx.doi.org/10.2139/ssrn.1474728

Pierre Gauthier

Daiwa Capital Markets Europe ( email )

5 King William Street
London, EC4N 7DA
United Kingdom

Dylan Possamaï (Contact Author)

ETH Zürich ( email )

Raemistrasse 101
Raemistr. 101
Zurich, 8092
Switzerland

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