TY - JOUR T1 - A Computational Scheme for Options Under Jump Diffusion Processes JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 110 EP - 123 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/758.html KW - Jump diffusion processes, option pricing, finite volume method, integral partial differential equation, FFT. AB -

In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the discretization methods are unconditionally stable in time and the system matrices of the resulting linear systems are M-matrices. The resulting linear systems involve products of a dense matrix and vectors and an Fast Fourier Transformation (FFT) technique is used for the evaluation of these products. Furthermore, a splitting technique is proposed for the solution of the discretized system arising from the Crank-Nicolson scheme. Numerical results are presented to show the rates of convergence and the robustness of the numerical method.