基于期权价格的Lévy过程参数估计研究

The research of parameter estimation under the Lévy process based on option pricing

Lévy过程可准确描述某些复杂的分布特征,如:尖峰、厚尾及有偏等,也可将标的资产运动过程中所展现的非连续性体现出来,因此在金融过程中得到了广泛而有效的运用.本研究基于期权的定价公式,运用极大似然法以及快速傅里叶变换对方差伽马(Variance-Gamma,VG)模型、Carr-Geman-MadanYor(CGMY)模型及VGSA模型(VG和Cox-Ingersoll-Ross模型的复合指数模型)等几种典型Lévy过程的参数进行有效估计,并且通过香港恒生指数期权数据对该方法进行验证.

The Lévy process can accurately describe the complex features of distribution,such as spikes,fat tails,and the discontinuity of the underlying asset reflected in the movement.Thus,the application of the Lévy processes in financial engineering becomes extensive and effective.However,estimation of the Lévy process parameters is difficult.Based on the option pricing formula,we used the maximum likelihood method and the fast Fourier transforms to make valid estimation on several typical Lévy process parameters,including the Variance-Gamma（VG） model,Carr-Geman-Madan-Yor（CGMY） model and VGSA（the exponential form for combining VG with Cox-IngersollRoss） model.The method is tested by the Hong Kong Hang Sheng Index Options data,which is important to promote the achievements of previous results which focus on the Lévy parameter estimation.