基于Landau's变换的求解美式期权的有限差分法

摘要

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.%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.