A Power Penalty Approach to Numerical Solutions of Two-Asset American Options

作     者：K. Zhang S. Wang X. Q. Yang K. L. Teo 

作者机构：Department of Finance Business School Shenzhen University Shenzhen China School of Mathematics and Statistics University of Western Australia Australia Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong Department of Mathematics and Statistics Curtin University of Technology Australia 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2009年第2卷第2期

页      面：202-223页

核心收录：

学科分类：12[管理学] 02[经济学] 0202[经济学-应用经济学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 020204[经济学-金融学（含∶保险学）] 08[工学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：The authors would like to thank two anonymous referees for their helpful comments and suggestions toward the improvement of this paper 

主　　题：Complementarity problem option pricing penalty method finite volume method. 

摘      要：This paper aims to develop a power penalty method for a linear parabolic variational inequality （VI） in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant λ〉 1 and a power parameter k 〉 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O（λ^-k/2）. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.