美式看跌期权定价的一种混合数值方法

本文对美式看跌期权的定价提供了一种新的混合数值方法,即快速傅里叶变换法加龙格-库塔法.首先将美式看跌期权价格所满足的Black-Scholes微分方程定解问题转化为一个标准的抛物型初、边值问题,然后通过傅里叶变换,使之转换为一个不带股价变量的常微分方程初值问题,再利用龙格-库塔法对其进行数值求解.数值实验表明,本文算法是一种快速的高精度的算法.

A KIND OF MIXED COMPUTATIONAL PRICING METHOD FOR AMERICAN PUT OPTIONS

This paper offers a new kind of mixed computational pricing method,i.e.the"FFT-RK"method,for American put options.It is a very fast and highly accurate numerical pricing method.Firestly,the solving problem of Black-Scholes differential equation for the American put option is transformed into a standard initial and boundary value problem of Parabolic type.Afterwards,it is transformed into an initial value problem of ordinary differential equation without stock price through Fourier transform and solved with the "FFT-RK"method again.The numerical experiment shows that the "FFT-RK"method is a fast and highly accurate algorithm.