Fourth Order Compact Boundary Value Method for Option Pricing with Jumps

Abstract

We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation. Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations. For the temporal direction, we utilize the favorable boundary value methods owing to their advantageous stability properties. In addition, the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type preconditioner. Numerical results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.