On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, we construct and analyze a Crank-Nicolson fitted finitevolume 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 sizesin space and time approach zero, hence it ensures the convergence to the solution ofcontinuous problem. Finally, numerical experiments are performed to demonstrate theefficiency, accuracy and robustness of the proposed method.