Efficient Simulation of the Wishart Model

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