无限活动纯跳跃Levy金融资产价格模型及其CF-CGMM参数估计与应用

发布时间：2018-05-21 10:21

本文选题：无限活动纯跳跃 + Levy过程　；参考：《系统管理学报》2010年04期

【摘要】：根据Levy过程的相关定理,结合现实中金融资产价格过程的实际特征,分析无限活动纯跳跃Levy过程在构建金融资产价格模型的优势。由于具有跳跃的Levy过程概率密度函数一般不存在解析式,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,建立了基于特征函数(CF)具有连续矩条件的GMM(简称CF-CGMM)的Levy过程参数估计方法,并利用恒生指数、上证综指、标准普尔500指数数据,对不同Levy过程和参数估计方法进行实证研究,根据参数计算结果和统计检验,对无限活动纯跳跃Levy金融资产价格模型的拟和优度进行检验和比较。最后,结合Levy金融资产价格模型中不同参数的含义,根据实证计算的结果,对恒生指数、上证综指、标准普尔500指数变动特征给出符合现实的解释。
[Abstract]:According to the relevant theorems of the Levy process and the actual characteristics of the real financial asset price process, this paper analyzes the advantages of the infinite activity pure jump Levy process in the construction of the financial asset price model. Because the probability density function of Levy process with jump does not usually have analytic formula, it is difficult to directly use traditional MLE method to estimate parameters. Therefore, according to the equivalent relation between the characteristic function and the probability density function, a Levy process parameter estimation method based on the continuous moment condition of the characteristic function (CF-CGMMM) is established, and the Hang Seng Index and the Shanghai Composite Index are used to estimate the parameters of the GMMs (CF-CGMMM). Based on the data of Standard & Poor's 500 Index, this paper makes an empirical study on different Levy processes and parameter estimation methods. According to the result of parameter calculation and statistical test, the paper tests and compares the fitting and superiority of infinite activity pure jump Levy financial asset price model. Finally, combining the meaning of different parameters in the Levy financial asset price model, according to the results of empirical calculation, this paper gives a realistic explanation of the change characteristics of Hang Seng Index, Shanghai Composite Index and Standard & Poor's 500 Index.
【作者单位】：中央财经大学;联想集团;
【基金】：国家自然科学基金资助项目(70603034,70971145) 教育部人文社科项目(08JC790107) 中央财经大学“211工程”三期项目
【分类号】：F830;F224

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