Wavelet-Galerkin Method for Option Pricing under a Double Exponential Jump-Diffusion Model

Abstract

The paper is concerned with pricing European options using a double exponential jump-diffusion model proposed by Kou in 2002. The Kou model is represented by nonstationary partial integro-differential equation. We use the Crank-Nicolson scheme for semidiscretization in time and the Galerkin method with cubic spline wavelets for solving integro-differential equation at each time level. We show the decay of elements of the matrices arising from discretization of the integral term of the equation. Due to this decay the discretization matrices can be truncated and represented by quasi-sparse matrices while the most standard methods suffer from the fact that the discretization matrices are full. Since the basis functions are piecewise cubic we obtain a high order convergence and the problem can be resolved with the small number of degrees of freedom. We present a numerical example for a European put option and we compare the results with other methods.