关键词: 极值Copula, 阈值, 峰值, 集成风险度量

Abstract: The paper measures the value risk of single asset with the application of threshold and peak model of the extreme value theory. We measured the dependence structure of the return rates of Shanghai and Shenzhen Stock Index with copula function, and compared their integrated risks under different copula functions. The results of empirical suggest: Gumble Copula is a better measure of the dependence structure compared with other Copula functions. Threshold of the extreme copula model can measure the integrated risk of portfolio well. At high confidence level(up 0.99),the integrated risk of upper tail (positive return) with Gumble copula and the integrated risk of lower tail(negative return) with Clayton copula are most close to the true value. Straight weighted average method will overestimate risk, while the method of supposing the Shanghai and Shenzhen Stock Index return rates obey duality normal distribution will underestimate the risk. Finally, we draw the conclusion that the integrated risk of peak has big error.

Key words: Extreme Copula, Threshold, Peak, Measurement of Integrated Risk