On the convergence of projected triangular decomposition methods for pricing American options with stochastic volatility

Abstract

Numerical pricing of American options with Heston stochastic volatility model is considered. The complementarity problem with a two-dimensional parabolic partial differential operator is discretized by the Craig–Sneyd alternative direction implicit scheme, and the resulted linear complementarity problems at each time step are solved by the projected triangular decomposition methods, which are constructed as an extension of the classical Brennan Schwartz algorithm. The convergence theorems are established when the system matrix is an M-matrix. Numerical experiments show that the proposed methods with alternative direction implicit schemes are efficient and outperform the classical PSOR method and operator splitting method.