Truncation of computational domains as an error control strategy for approximating option pricing involving PIDEs

Pricing of option contracts where the underlying asset follows a jump diffusion process leads to a partial integro-differential equation. Due to the integral term, an exact or closed form solution to the resulting equation is impossible in general. In this paper, we have investigated the localization error when the finite difference method is applied to approximate the solution of the resulting equation. The main focus of this paper is to reduce the complexity in implementation of the integral term by truncating of computational domain in which the localization error is controlled. The numerical results present the behavior of the localization error with respect to the computational domain.