The Research In Dependence Of Financial Risk Based On Copula Theory

With the development of the financial markets, the dependent relationship between them become more and more complicated and represent nonlinear, asymmetric and tail dependence. Methods based on the linear correlation coefficients can not describe the dependence pattern accurately. Sklar's theory of copulas believe that the information about the dependence is whole contained in the copula function. In this dissertation, we research the dependence pattern of the financial markets by using copula function, and probe into some theory question of the copula and its application in financial analysis.Definition and some basic property and some related theory of copulas are introduced in second chapter, dependent characters of some common copula are analyzed. Several measures of dependence educed by copula function, especially archimedean copula, are analyzed inside out. The copula theory divides the analysis of dependence between financial markets into dependence index and dependence pattern. Every Copula function stands for its dependence pattern.We probe into some measure index of dependence based on copula function, which could clutch the characters of nonlinear, asymmetric and tail dependence. Some common measure indexes of dependency are summarized. Then we conclude that the Kendall's Tau and Spearman's Rho are the right tools to describe nonlinear, asymmetric and tail dependence.In application part, the bivarite copula-t-garch model is introduced in detail, and is applied in the analysis of financial market dependence. We applied it in two steps of hedge of index futures: Dependence pattern between index and its futures, dependence pattern between index and investing portfolio. The conclusion is that Symmetrised Joe-Clayton copula is able to describe the dependence between index and investing portfolio, which means upper and lower tail dependence increased when market varied acutely. And we also found there was remarkable tail dependence between index and its futures. So we advised that, it's the best time to do hedge of index futures when market varied acutely.