A mixed PDE/Monte-Carlo method for stochastic volatility models

Abstract

We propose a pricing method for derivatives modeled by a set of stochastic differential equations with the objective of reducing the computing time. The speed up observed in our numerical implementation can be as large as 50. The method is based on a joint use of Monte-Carlo simulations and PDE or analytical formulas. The method is tested in the framework of the Heston stochastic volatility model with and without barriers. To cite this article: G. Loeper, O. Pironneau, C. R. Acad. Sci. Paris, Ser. I 347 (2009).