The Measurement Of Stock Index’s VaR Based On Copula-EVT Model

The financial market is facing with increasingly complex and diversified risks, therefore, effective risk management has become a required course for the financial industry. The core of risk management is to measure the value at risk, so, how to accurately measure the risks in different forms become the focus of financial sector. In the paper, we collected six major world’s stock index to measure different forms of asset’s value according to different investment decisions.A large number of research show that: the yields of financial series usually performance characteristics of the fat tail, volatility clustering, instead of the assumptions of normal distribution. In response to this, the third chapter discusses the CSI300yields’ characteristics and estimate the value at risk. The CSI300yields performances not only a fat tail, volatility clustering, the fluctuations in the accumulation of such characteristics also showed obvious skewed distribution, as a result, we estimate time-varying VaRs based on FIGARCH model and choose skewed t distribution. The test results show that the estimation under skewed t distribution is superior to the traditional normal distribution, student’s t distribution and the GED distribution. In risk management, once a small probability event such as the financial crisis occurs, the results will be extremely serious. So, how to accuratly describe extreme distribution and calculate the extreme value at risk is highly necessary. The fourth chapter describes the extreme distribution of A300, SH, HSI, the N225, ICIX,FCHI and estimate VaR, CVaR of them. In this process, the paper gives the fat-tail judgment, parameter estimation, the selection of the threshold, and the model estimation and testing methods, etc..The fifth chapter is to analysis value at risk of the portfolio based on Copula-the EVT model. Copula introduced into the extreme value theory to measure the risk is become one of the research frontier, Copula theory not only can separate the marginal distribution and the correlation structure of the random variable, but also can simplify complex issues. The Copula theory not only able to capture nonlinear asymmetric relationship between the variables, but also easy to capture the changes of variable tail. In recent years, there are lots of applications of copula function theory. But mainly in double circumstances, multivariate extreme value theory, especially introduce the Copula theory is seldom. The fifth chapter use Copula-EVT model to analyze the portfolio’s VaR on the basis of the second chapter’s theory and the third, fourth empirical analysis. Kupiec test results shows that:under the95%and99%significance level, the failure rate is close to the significance level, indicating that, the multivariate t-Copula model can describe dependency structure of multi-asset, Copula-EVT model is the appropriate choice.The last is a summary of the paper, which analysis of the inadequacies of the paper, and put forward based on the present study of extreme value theory and Copula theory.