Option Pricing in Jump Diffusion Models with Quadratic Spline Collocation

Abstract

In this paper, we develop a robust numerical method in pricing options, when the underlying asset follows a jump diffusion model. We demonstrate that, with the quadratic spline collocation method, the integral approximation in the pricing PIDE is intuitively simple, and comes down to the evaluation of the probabilistic moments of the jump density. When combined with a Picard iteration scheme, the pricing problem can be solved efficiently. We present the method and the numerical results from pricing European and American options with Merton's and Kou's models.