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杨丽玲,陈文婷 (江南大学 商学院,江苏 无锡 214122) 
中文关键词:CGMY模型  外汇期权  Lévy过程  分数阶偏微分方程
Analytically Pricing Foreign Exchange Options under the CGMY Model
Abstract:Modifying the traditional effective market hypothesis (EMH) and assuming that the foreign exchange rate exists jumps and spreads, the fractional partial differential equation (FPDE) of the European foreign exchange option price under the CGMY model is derived by using Fourier transform method. Although the “globalness” caused by fractional partial derivatives is difficult to handle, the explicit closed-form analytical solution and the put-call parity of European foreign exchange options under the CGMY model are still derived. In addition, to effectively overcome the computational difficulties caused by the integrand decay, a new scaling parameter m is introduced to control the growth rate of the exponential function, so that it can achieve a balance with the attenuation of the Lévy density function. Finally, the influence of key parameter changes on the price of European foreign exchange options is analyzed from the perspective of mathematics and finance.
keywords:CGMY model  foreign exchange options  Lévy process  FPDE
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