汇率变动的分数阶福克——普朗克方程

The Application of Inverse-stable Subordinate in Foreign Exchange Market

该文主要运用拉普拉斯变换、拉普拉斯逆变换,以R.Friench模型为基础,推导出随机过程{ΔX(Sα(t))}的概率密度函数所满足的分数阶福克—普朗克方程。并且指出,所得到的分数阶福克—普朗克方程要比古典的福克—普朗克方程优越,更适合描述外汇市场中外汇的变化规律,从而为下一步推导非古典的期权定价方程奠定了理论基础。

In this paper,we mainly use the method of Laplace transform,Laplace inverse transform.Based on the model（1）,we give the fractional Fokker-Planck equation which satisfies the probability density function of the stochastic process {ΔX（Sα（t））}.Pointing out,the fractional Fokker-Planck equation is more excellent than the classical Fokker-Planck equation,for it describes the change of foreign exchange rate more rationally.Just based on this,we can derive the option price equation which is not classical.