Comparison of Finite Difference and Finite Element Methods to solve Merton's and Kou's Jump-diffusion models.

Abstract

In this paper, we discuss about PIDE for Kou’s and Merton’s Jump-diffusion models to calculate the European call option price. We will use two numerical method which are Finite Difference Method and Finite Element Method. In FDM case, we used finite difference which is similar to crank-nicholsen method to approximate the differenceterm, and in FEM case, we used hat function to use weak formulation. For integral term, both of them used trapezoidal rule. And by comparing the numerical results of two methods, we can confirm the accuracy of the result values.