Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model

In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model—a single asset model with a multidimensional Wishart variance process. Our method is based on analysis of the conditional characteristic function of the log-price given a terminal volatility level. In particular, we found an explicit expression for the conditional characteristic function for the Heston model. Numerical experiments demonstrate that our new method is much faster and reliable than the Euler discretization method.