摄动法求亚式期权的近似解

Obtain an Approximate Solution of Asian Option by Perturbation Method

阐述了连续样本的算术亚式期权定价模型。首先证明了该定价模型中的偏微分方程不能转化为常系数的热传导方程。因此,不能通过一般的方法来求解。接下来,采用摄动法求解经过变换的偏微分方程,得到了一个序列形式的近似解析解。随后,本文给出了该序列近似解析解的图像,从而判断出该序列具有很好的收敛性。

The price model of continuously sampled arithmetic Asian options is identified. First the partial differential equation （PDE） of the model can not be transformed into a heat equation with constant coefficients,which means that it can not be solved in an ordinary way. Then the transformed PDE with a perturbation method is solved and got a series formed analytical solution. A picture of the series shows that the series formed solution convergents perfectly.