基于Landau’s变换的求解美式期权的有限差分法  

Finite Difference Method for Solving American Option Based on Landau's Transformation

作　　者：赵文雯[1,2] 张琪[1] 吕显瑞[1] ZHAO Wenwen ZHANG Qi LU Xianrui(College of Mathematics, Jilin Universtiy, Changchun 130012, China Tianjin Vocational College of Mechanics and Electricity, Tianjin 300350, China)

机构地区：[1]吉林大学数学学院,长春130012 [2]天津机电职业技术学院,天津300350

出　　处：《吉林大学学报（理学版）》2017年第4期898-902,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11271157;U1530116)

摘　　要：针对标准美式看跌期权定价问题给出一种基于Landau’s变换的有限差分法.先利用Landau’s变换及截断技巧将美式期权问题转化为一个有界规则区域上的抛物问题,再利用有限差分法求解期权价格,并利用Newton迭代法同时求解出最佳实施边界.数值实验结果表明,该算法能快速有效地求解出较传统二叉树法更光滑的最佳实施边界,并能准确地模拟美式看跌期权价格.We proposed a finite difference method based on Landau＇s transformation for the standard American put option pricing problem.Firstly,the Landau＇s transformation and truncation technique was used to transform the American option problem into a parabolic problem on a regular bounded domain,and then we used the finite difference method to solve the option price and used the Newton iteration method to solve the optimal exercise boundary at the same time.The numerical results show that the algorithm can effectively solve the optimal exercise boundary more smoothly than traditional binomial tree method,and can accurately simulate the American put option price.

关 键 词：美式看跌期权 Landau’s变换 有限差分法 

分 类 号：O241.8[理学—计算数学]