In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. [14]. Our method is based on analysis of the conditional characteristic function of the logprice given volatility level. In particular, we found an explicit expression for the conditional characteristic function for the Heston model. We perform numerical experiments to demonstrate the performance and accuracy of our method. As a result of numerical experiments, it is shown that our new method is much faster and reliable than Euler discretization method.

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