Time-varying Copula Functions And Its Application In The Study Of Relationship Between The Stock Index

This paper studied the copula functions and its related theory, given a construction methodwith rational function horizontal or vertical sections and proved that there doesn’t existArchimedean copulas with quadratic rational function horizontal or vertical sections. We usednine kinds of copula functions and time-varying copula function on Shanghai composite index,the small and medium-sized plate index, the Hushen300Index to describe the correlationstructure and tail dependence of Chinese stock market, and two methods been used to choosebest fitting copula functions. The empirical result show that: there is a positive correlationbetween the Shanghai Composite index, the small and medium-sized plate index and the Hushen300Index, and they all have stronger lower tail correlation than upper tail correlation. In a bullmarket, the symmetrised-Joe Clayton copula function is the best choice among the given copulafunctions to fitting the dependence structure between indexes; but in the bear market and theconcussion city market, the t-copula function can described the dependence structure betterbetween the given indexes. The symmetrised-Joe Clayton copula function can capture thecorrelation of positive profit which caused by market movements, whether the t-copula functionbe able to capture the negative earnings correlation sensitive no matter in a bear market orconcussion city market. We use time-varying symmetrised-Joe Clayton copula function to fit thestock market indexes in different market conditions. The results show that: the ShanghaiComposite Index and the Hushen300Index has a stable tail correlation coefficient, in a bullmarket, the tail correlation coefficient of the Shanghai Composite Index and the small andmedium-sized plate index has obvious fluctuation, in bear market, the Shanghai Composite indexlower tail dependence coefficient and the small and medium-sized plate index has obviousfluctuation, while in the concussion city market, the upper tail correlation coefficient and lowertail correlation coefficient both have obvious fluctuation.