非线性Black-Scholes模型下算术平均亚式期权定价问题

Arithmetic Average Asian Option Pricing Problem Under the Nonlinear Black-Scholes Model

在非线性Black-Scholes模型下,研究了算术平均亚式期权定价问题.首先利用单参数摄动方法,将亚式期权适合的偏微分方程分解成一系列常系数抛物方程.其次通过计算这些常系数抛物型方程的解,给出了算术平均亚式期权的近似定价公式.最后分析了近似结论的误差估计,并通过数值算例验证了所得近似结论的合理性.

Arithmetic average Asian options are studied under nonlinear Black-Scholes model.First,the partial differential equations for the arithmetic average Asian options are transformed into a series of parabolic equations with constant coefficients by the perturbation method of single-parameter.Second,the approximate pricing formulae of the arithmetic average Asian options are given by solving those parabolic equations with constant coefficients.Final,the error estimates of the approximate solutions are analyzed,and numerical results are presented to demonstrate those error estimates.