A robust numerical method for pricing American options under Kou's jump-diffusion models based on penalty method

We develop a novel numerical method for pricing American options under Kou's jump-diffusion model which governed by a partial integro-differential complementarity problem (PIDCP). By using a penalty approach, the PIDCP results in a nonlinear partial integro-differential equation (PIDE). To numerically solve this nonlinear penalized PIDE, a fitted finite volume method is introduced for the spatial discretization and the Backward Euler and Crank-Nicolson schemes for the time discretization. We show that these schemes are consistent, stable and monotone, hence convergence to the solution of continuous problem. Numerical experiments are performed to verify the effectiveness of this new method.