Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

In this paper we introduce a new numerical method for the linear complementarity problems (LCPs) arising from two-asset Black–Scholes and Heston's stochastic volatility American options pricing. Based on barycenter dual mesh, class of finite volume (FVM) is proposed spatial discretization, coupled with backward Euler Crank–Nicolson schemes are employed time stepping partial differential equations (PDEs). Then, resulting time-dependent LCPs solved by using an efficient modulus-based successive overrelaxation (MSOR) iteration method. Numerical experiments carried out to verify efficiency usefulness