Correlation Research And Empirical Analysis On Stock Returns Ratio Based On Copula Methods

There are many correlation analyses in the financial market, and most of them are using linear correlation coefficient. However, the related structures are not always linear. They might be non-normal and asymmetrical. Copula function has its unique superiority in financial market correlation analysis. It can be directly used for establishing models, describing non-normal and asymmetrical distribution information in the tail part, which is very significant for practically describing the related structure.This article first introduced some basic types and related properties of Copula function, and then studied on some primary correlation analysis methods. This paper described the correlation by replacing Pearson correlation coefficient with Copula function in correlation analysis. There are many Copulas, of which the most two important are Elliptical Copula and Archimedean Copula. Each of them contains many parameter classifications. Different classifications have different characteristics and describe their own correlations, of which the Gumbel Copula's upper tail is correlated but its lower tail is approximately independent. It can describe the correlation between properties in the bull market period properly, but cannot be used for the property relevance in bear market period. In the contrast, Clayton Copula's lower tail has the relevance and the upper tail is independent. Frank Copula has the "symmetrically" related structure.The author chose anther superior method to estimate the parameters of the optimal Copula function. Based on the kernel density function's maximum likelihood estimation this paper estimated the parameters of Copula function, and determined the optimal Copula function according to Kolmogorov-Smirnov principle and minimum variance method. Finally, the author did empirical study on the tail correlation analysis on composite index of Shanghai Stock Exchange and Shenzhen composite index. The thesis has six chapters as follows:The first chapter mainly introduced the background, motivation and present domestic and foreign research situations, and also presented the study direction, mentality, and methods of this article.The second chapter mainly introduced the basic theory of Copula function. The third chapter proposed using Copula method to describe financial market correlations based on the deficiencies of Pearson correlation coefficient. The fourth chapter used the basic kernel density method to estimate the parameter of the Copula function, and chose Kolmogorov-Smirnov principle and minimum variance method to select the optimal Copula function.The 5th chapter empirically studied on China stock market. The author based on Clayton Copula function to analyze the tail correlation, and showed that Shanghai and Shenzheng stock market have strong tail relevance. The lower tail relevance is more obvious. It is very possible that Shenzheng stock market fall when Shanghai stock market falls. However, the possibility of rising simultaneously is quite low.