A SECOND-ORDER FINITE DIFFERENCE METHOD FOR OPTION PRICING UNDER JUMP-DIFFUSION MODELS

We develop a finite difference method to solve partial integro-differential equations which describe the behavior of option prices under jump-diffusion models. With localization to a bounded domain of the spatial variable, these equations are discretized on uniform grid points over a finite domain of time and spatial variables. The proposed method is based on three time levels and leads to linear systems with tridiagonal matrices. In this paper the stability of the proposed method and the second-order convergence rate with respect to a discrete l(2)-norm are proved. Numerical results obtained with European put options under the Merton and Kou models show the behaviors of the stability and the second-order convergence rate.