Chen Yingzi, Wang Wansheng, Xie Jiaquan
In this manuscript we proposed using the implicit-explicit splitting method to solve the linear complementarity problem satisfied by American options in financial option pricing problems. Although implicit-explicit methods have been widely used in jump-diffusion models, they are mostly applied in European options, and there is little stability analysis in numerical solutions for American options. In this paper, we proposed that in terms of time, we adopted three discretization methods: the implicit-explicit Backward differential formula of order two (BDF2), the implicit-explicit Crank-Nikolson Leap-Frog(CNLF), and the implicit-explicit Crank-Nikolson AdamBashforth(CNAB), and proved their stability. In space, finite difference discretization is presented, and due to the nonsmoothness of the initial value function, a local mesh refinement strategy is considered near the strike price to improve accuracy. To verify the theoretical results, numerical results for pricing American options under Merton type and Kou type jump-diffusion models were presented. The numerical experimental results show that our proposed method is stable and effective.
