An efficient numerical method for pricing option under jump diffusion model

Abstract

The aim of the present manuscript is to develop an efficient and accurate numerical method for pricing the option when underlying asset follows jump diffusion process. The governing equation is time semi discretized by using the implicit–explicit Crank-Nicolson Leap-Frog scheme followed by radial basis function based finite difference method. Numerical results are presented to show the efficiency of the methods for put and call option under Merton and Kou model. The stability of time semi discretized scheme is also proved.