On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models

Abstract

In this paper, we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou's jump-diffusion model which is governed by a system of partial integro-differential equations (PIDEs). We show that this scheme is consistent, stable and monotone as the mesh sizes in space and time approach zero, hence it ensures the convergence to the solution of continuous problem. Finally, numerical experiments are performed to demonstrate the efficiency, accuracy and robustness of the proposed method.