SINC-GALERKIN METHOD FOR THE OPTION PRICING UNDER JUMP-DIFFUSION MODEL

摘要

In this paper, the sinc-Galerkin method is employed for discretizing the spatial direction of a partial integro-differential equation arising in option pricing with jump-diffusion model. The resulting dense matrix by the sinc-Galerkin method is Toeplitz-like. Hence the matrix-vector multiplication can he efficiently computed by the fast Fourier transform. However. the payoff functions for typical options or the initial conditions are non-smooth, which will reduce the accuracy of sinc approximation and make it not competitive even with first order finite difference method. Therefore we exploit the domain decomposition method to handle this issue. For the temporal direction, we prefer to use the implicit-explicit Euler time scheme. Numerical tests are performed to illustrate the effi-ciency of our method.