Tail-dependence Risk Of China Stock Market

Evaluating financial assets is the foundation and the core of the risk management, the dependence of financial assets is very important. In addition to concerning the dependence of overall assets, we need to concerning the tail dependence. Tail dependence is that when a random variable is larger or smaller value, it will affect the value another random variable.China's stock data doesn't satisfy the normal distribution, but shows the characteristics of peak fat-tail. Classic linear correlation coefficient can't seize related structure of China's stock market data and doesn't accurately reflect the related information of China's stock market. We use Sklar's Copula theory to describe the non-linear correlation relationship between the random variable.The Copula model expresses for the entire joint distribution, it can capture the non-symmetrical and non-normality tail information, so Copula model can describe the tail dependence between the random variable comprehensively and thoroughly.The paper gives definition of tail dependence based on Copula function. Using tail-dependence correlation, we can forecast probability that rising or falling causes another stock rising or falling and forecast changes in market.First, we introduce Copula's development, definition and nature. Give definition and measurement method of tail dependence based on Copula function, use the non-parameter estimation to estimate tail-dependence coefficient. And than combines Copula function and Markowitz model portfolio optimization theory, educe processes and procedures which determine the optimal portfolio. Finally,we give procedure of estimating tail dependence and optimal portfolio Algorithm through actual data and statistical software.There are two innovations in the paper. One is using the non-parameter estimation to estimate tail-dependence coefficient, another is combines Copula function and Markowitz model portfolio optimization theory in order to educing processes and procedures which determine the optimal portfolio.