An iterative method for pricing American options under jump-diffusion models

Abstract

We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is for-mulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou’s andMerton’s jump-diffusionmodels show that the resulting iteration converges rapidly.