Copula Function In The Financial Applications

This paper focus on the modeling methods of the Chinese financial market based on the Copula function, the following problems are mainly solved.1. The Gaussian Copula is used to model dependence by some scholars, but it doesn't have upper tail dependence and lower tail dependence. So t-Copula is used to measure the dependence and the tail coefficients are calculated, covering the shortage of Gaussian Copula. Then, we find the t-Copula is more suitable than the Gaussian Copula by the values of AIC.2. Three Archimedean Copulas, Gumble Copula, Clayton Copula, and BB1 Copula are researched, the parameters are estimated by the relationship between the Kendall's tau and the unknown parameters. At last, the distances are computed between the fitted Copulas and the empirical ones, the results indicate that the Gumble Copula is more adapt to Chinese financial market.3. Though the t-Copula has a good result in measuring the China stock markets, the t-Copula is symmetric and the true financial data is not symmetric. So the skew t-Copula is constructed by the skew multivariate t distribution in the paper, the simulating algorithm of the skew t-Copula is obtained, they are simulated in different free degrees, different correlate coefficient, different dependent structures. By that, the dissymmetric of the skew t-Copula and the influence by the free degrees, correlate coefficients are saw. At last, the MLE algorithm of the skew t-Copula are obtained, then the correlate matrix between the Shenzhen and Shanghai stock market are computed.4. The bivariate extreme value theory is applied to research the heavy-tail characteristic of the joint distribution of the Shanghai and Shenzhen stock market by a new extreme Copula, t-EV-Copula. The results indicate that the t-EV-Copula, compared with the Gumble Copula, not only simulate the extreme data very well, but also can catch the upper dependence and the lower dependence, then the distribution function of the tail joint distribution based on the t-EV-Copula are obtained, and it's figure is also obtained, at last VaR is used to describe the tail character .