Financial Risk Measure Based On Copula Theory

The financial market is full of risk, and there are two questions which investors have to face: the first question is whether the domestic financial market will fluctuate violently when the markets of other country fluctuate greatly? The second issue is when holds an investing portfolio, how much risk the investors are facing and how to measure the value at risk?According to the advantage at measuring the dependence between assets more efficiently, copula has great strength at the problems of dependence measure and VaR calculation, and it can reduce the risk which investors suffer from. This essay will concentrate on the applications of copula on the issues of dependence measure between different financial assets and risk management of financial investing portfolio based on VaR.The first part of empirical analysis in this essay bases on the tail dependence derived from copula function, using the series of logarithmic return yield of four countries'stock index to analyze the changes of dependence structure of international stock market after the breakout of the subprime mortgage crisis. The results indicate that after the subprime crisis the tail dependences become stronger than before. It shows that the subprime crisis has a significant impact on dependence structure of international stock market. During the crisis the correlations of international stock markets become closer.The second part of empirical analysis applies the Copula function to measure the VaR of a portfolio, which is made up of SSE Fund Index and Shanghai Stock Index. Uses backtesting method to measure the efficiency, and then compare the results with those based on traditional methods, such as historical simulation approach, etc. The Copula includes four categories:static Copula, tail-structure changing Copula, time-varying Copula and time-varying Copula with changing tail structure. The three kinds of Copula function other than static Copula improves from static Copula, and time-varying Copula with changing tail structure is a combination of tail-structure Copula and time-varying Copula, which is an innovation. The research shows that the VaR measurement based on Copula functions are more accurate than those using traditional approaches in risk management, the copula methods are able to describe the dependence structure between different assets more accurately and can avoid the disadvantage of underestimating the financial risk caused by traditional methods. The research also shows that the methods of time-varying Copula and time-varying Copula with changing tail structure are better than static Copula. time-varying Copula with changing tail structure brings the best effect, because it considers the changing information of financial markets, and responses to the changing dependence structure between different variables.