广义Black-Scholes方程数值方法分析

摘要

Black- Scholes equation is one of the most effective equation describing option pricing, and the solving problem is always the focus of people's attention.Since the 1970s, emerged a large number of methods for solving the differential equation of flops. Abraham J.Arenas and others have used nonstandard fi-nite difference scheme to solve the generalized Black-Scholes equation. On this basis, we use the precision linear difference format and spatial derivative approximation to get the approximate solution of the general-ized Black-Scholes equation. At the same time, this method has been generalized to find the numerical solu-tion of the nonhomogeneous Black-Scholes equation, and we get the approximate solution which is similar to that of the generalized Black-Scholes equation.%Black-Scholes方程作为描述期权定价最有效的方程之一，其求解问题一直是人们关注的焦点。自20世纪70年代以来，涌现出了大量求解这一偏微分方程的方法。Abraham J.Arenas等人就利用非标准的有限差分格式求解出了广义Black-Scholes方程，在此基础上，利用精确的线性差分格式和空间导数的近似，得到了广义Black-Scholes方程的近似解。同时，又将该方法推广到了求解非齐次的Black-Scholes方程的数值解问题，并得到与广义Black-Scholes方程类似的近似解。