A mixed finite element method for pricing American options and Greeks in the Heston model

Abstract

In this paper, we propose a numerical algorithm for solving a complementarity system associated with pricing American options. More precisely, we consider the stochastic volatility Heston's model. Our method is based on a semi-Lagrangian approach that couples mixed finite elements with a discretization of the material derivative along the characteristics. A primal dual active set solver is developed to handle the complementarity saddle point system obtained at the discrete level. To demonstrate the precision and effectiveness of our method, numerical examples are provided.