Copula Function And Its Application In The Dependence Analysis Between Stock Markets

With the development of economic globalization, information technology and financial advancement, a deepened mutual reliance and influence has occurred in the world-wild financial markets. The circulation of risk capital in a world wild scale makes the resources allocation more efficient and effective. However, the joined movement between stock market returns makes the volatility in one market transfer to the other one more easily and rapid. Modeling the dependency between stock market return is worth to do now.In order to avoid the limits of linear correlation coefficient and classical analysis methods, Copula theory was introduced to financial analysis. Take the great advantage of Copula; I apply it to the measure the dependence among the daily returns of four major stock markets. After summarized the copula theory and researches about its application in modeling the financial dependence, I investigated the measure of non-liner dependency and measure of tail dependency that could be derived from copulas.After discussed the modeling of multivariate financial time series, five main copulas was introduced to model the dependency between Shanghai Company Index and S&P500, Shanghai Company Index and Shenzhen Company Index, Shanghai Company Index and Hang Sang Index. After the setting of two-step MLE, I choose the best Copula. And with the estimated dependency parameter, Kendall's tau and tail dependence parameters, the types and the degrees of dependency were analyzed among four markets. The results showed that the types of dependence are different among different markets which should be described with different copulas. The results also suggested that the dependence between Shanghai Company Index and S&P500, Shanghai Company Index and Hang Sang Index are very low.At last, time-varying normal copula model and time-varying Joe-Clayton copula model are investigated to model the dynamics of the dependency of parameter. The empirical results suggested that time-varying copulas are better than constant copula in the ability of description the dynamic dependence between return series.