A L-stable Numerical Scheme for Option Pricing under Jump-Diffusion Models

摘要

A L-stable and highly accurate method for option pricing under jump-diffusion models is developed in this paper. A semidiscretization scheme is performed on the partial integro-differential equation, and a numerical scheme is constructed based on Pade approximations of the matrix exponential. Due to the integral term, which cause the resulting system to be dense, an iteration to solve the equations in numerical scheme is present. Numerical examples for European option and barrier option with Merton's jump-diffusion model show that the algorithm is efficiently and avoid spurious oscillations.