Fourth Order Compact Boundary Value Method for Option Pricing with Jumps (Advances in Applied Mathematics and Mechanics, 2021)
We consider pricing options in a jump-diffusion model which requires solvinga partial integro-differential equation. Discretizing the spatial directionwith a fourth order compact scheme leads to a linear system of ordinarydifferential equations. For the temporal direction, we utilize the favorableboundary value methods owing to their advantageous stability properties. Inaddition, the resulting large sparse system can be solved rapidly by theGMRES method with a circulant Strang-type preconditioner. Numerical resultsdemonstrate the high order accuracy of our scheme and the efficiency of thepreconditioned GMRES method.