Dependence Research About Chinese Stock Market Based On Copula

Nowadays, financial crises happen very frequently, and the relationship between financial markets becomes more and more complicated. People find it represent non-normal, non-linear, asymmetric and tail dependence. Fortunately, Copula function can describe all of those characteristics, so it has unique superiority in financial market dependence analysis.In theoretical aspects, this paper introduced the definition and the related properties of Copula function, then discussed several kinds of dependence, including Kendall dependence coefficient r, Spearman dependence coefficient p and tail dependence coefficientλU,λL. Subsequently, the paper carried on the detailed introduction of Gumbel Copula, Clayton Copula and C Copula. After that we emphatically researched their dependence, especially the tail dependence. Finally, the paper introduced several methods for estimating Copula parameters and several test methods for selecting optimal Copula.In empirical aspects, this research chose three Indexes prices from 2006 to 2009 as data samples, they were Shanghai Composite Index, Shenzhen Composite Index and Hengsheng Index. Then test their logarithmic rate whether normal, autocorrelation or not. The results showed that they were non-normality and non-autocorrelation. Subsequently, the paper fitted those returns with Gumbel, Clayton and C Copula, tested Copulas by the measure of Q-Q, K-S, and minimum variance and found the conclusion that C Copula did better in describing the dependence between Shanghai Index and Shenzhen Index, Clayton Copula got better result in describing the dependence between Shanghai Index and Hengsheng Index, Clayton Copula performed well in capturing the dependence between Shenzheng Index and Hengsheng Index. Finally, through the research of tail dependence between Shanghai Index and Shenzhen Index based on C Copula, we demonstrated that the upper and lower tail dependence between Shanghai Index and Shenzhen Index was strong. Through the tail dependence research between Shanghai Index and Hengsheng Index based on Clayton Copula, we showed that the lower tail dependence between Shanghai Index and Hengsheng Index was stronger than the upper tail dependence between them. Through the tail dependence research between Shenzheng Index and Hengsheng Index based on Clayton Copula, we got the result that the lower tail dependence between Shenzheng Index and Hengsheng Index was much stronger than the upper tail dependence between them.The research of dependence of stock market, especially the tail dependence, is very significance in financial risk management. Risk managers can measure financial risks by analyzing the tail dependence of stock markets. This dependence research about the three stock markets provides a good theoretical basis when investing stock portfolio.