主要研究了一类状态转换下美式跳扩散期权定价模型的修正Crank-Nicolson 拟合有限体积法并且给出收敛性分析. 文章所构造的新方法是对[Gan X T, Yin J F, Li R, Fitted finite volume method for pricing American options under regime-switching jump-diffusion models based on penalty method. Adv. Appl. Math. Mech., 2020, 12(3): 748--773]中时间方向上Crank-Nicolson格式的改进. 同时, 还对求解非线性系统迭代方法的收敛性证明进行了补充. 最后, 数值实验验证了新方法的有效性.

In this paper, we study a modified Crank-Nicolson fitted finite volume method for American options under regime-switching jump-diffusion model and present the convergence analysis. The proposed new method is a modified of the Crank-Nicolson time-stepping scheme in (Gan, et al. 2020). Meanwhile, we supplement the proof of convergence of iterative solution method that has been designed to solve the nonlinear algebraic systems. Finally, numerical experiments are presented to illustrate the efficient of the modified method.