In this paper we develop two novel numerical methods for thepartial integral differential equation arising from the valuation of an optionwhose underlying asset is governed by a jump diffusion process. These methodsare based on a fitted finite volume method for the spatial discretization, animplicit-explicit time stepping scheme and the Crank-Nicolson time steppingmethod. We show that the discretization methods are unconditionally stablein 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 andan Fast Fourier Transformation (FFT) technique is used for the evaluation ofthese products. Furthermore, a splitting technique is proposed for the solutionof the discretized system arising from the Crank-Nicolson scheme. Numericalresults are presented to show the rates of convergence and the robustness ofthe numerical method.
|Journal||International Journal of Numerical Analysis and Modeling|
|Publication status||Published - 2009|