FINITE DIFFERENCE APPROXIMATION FOR PRICING THE AMERICAN LOOKBACK OPTION

作     者：Tie Zhang Shuhua Zhang Danmei Zhu 

作者机构：Department of Mathematics School of Information Science and Engineering Northeastern University Shenyang 110003 China Research Center for Mathematics and Economies Tianjin University of Finance and Economics Tianjin 300222 China Department of Mathematics School of Information Science and Engineering Northeastern University Shenyang 110004 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2009年第27卷第4期

页      面：484-494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）] 07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported in part by the National Basic Research Program(2007CB814906) the National Natural Science Foundation of China(10771031,10471019,10471103,and 10771158) Social Science Foundation of the Ministry of Education of China(Numerical methods for convertible bonds,06JA630047) Tianjin Natural Science Foundation(07JCYBJC14300)and Tianjin University of Finance and Economics 

主　　题：American lookback options Finite difference approximation Stability andconvergence Error estimates. 

摘      要：In this paper we are concerned with the pricing of lookback options with American type constrains. Based on the differential linear complementary formula associated with the pricing problem, an implicit difference scheme is constructed and analyzed. We show that there exists a unique difference solution which is unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite difference solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the O（△t ＋ △x^2）-order error estimate is derived in the discrete L2-norm provided that the continuous problem is sufficiently regular. In addition, a numerical example is provided to illustrate the theoretical results.