Abstract: Firstly, we considered a Crank-Nicolson fitted finite volume method for solving American options under Kou’s jump-diffusion models, and gave the convergence analysis. Secondly,  an iterative algorithm for the nonlinear algebraic system was designed and its convergence was proved. Finally,  the convergence, robustness and effectiveness of the new method are verified by numerical experiments.

Key words: American options under Kou’s jump-diffusion model, Crank-Nicolson fitted finite volume method, convergence analysis