Levy Tempered Stable金融资产收益分布及其CF-CGMM估计方法研究

本文在对经典的和修正的Levy tempered stable分布进行研究的基础上,结合现实中金融资产收益分布的实际特征,分析Levy tempered stable分布在构建模拟金融资产价格过程的Levy Jump模型的优势。由于这类分布的概率密度函数不存在解析式,直接应用传统MLE方法进行参数估计存在困难。为此,根据特征函数与概率密度函数的等价关系,本文建立基于特征函数(CF)具有连续矩条件的GMM(简称CF-CGMM)的Levy tempered Stable分布参数估计方法。同时,利用恒生指数、上证指数、标准普尔500指数数据对以上分布和参数估计方法进行实证研究,并根据参数计算结果和统计假设检验,对不同Levy tempered Stable分布的拟和优度进行检验和比较。本文也在参数估计和统计检验工作的基础上,根据Levy tempered Stable分布模型中不同参数的含义,结合实证计算的结果,对恒生指数、上证指数、标准普尔500指数价格运动特征给出符合现实的解释。

Levy Tempered Stable Distributions for Financial Assets Return and Its Method of Estimation by Characteristic Function Based on GMM with a Continuum of Moment Conditions

This paper introduces a type of Levy tempered stable distributions for financial assets return,and some properties of those distributions along with the advatages in applying them to finance assets prices process modeling will be discussed. Direct maximum likelihood estimation is usually impossible for most of continuous-time models in finance except some special cases since it is hard for these models to have analytical form for probility density function. Because characteristic function is equivalent to probility density function,estimation conducted by characteristic function based on GMM with a continuum of moment conditions(CF-CGMM) is developed in this paper. According to the data of HANG SENG INDEX,SSE Composite Index and S &;P500 Index,emperical research on these Levy tempered stable distributions are done with the estimations by the CF-CGMM methods,and then statistics measuring and goodness of fit for the models are completed. Moreover the paper also gives some realistic interpretations about the price process of HANG SENG INDEX、SSE Composite Index and S &;P500 Index based on the different parameters in Levy tempered stable distribution and emperical results.