Risk Analysis Of The Portfolio Based On The Copula Theory

Risk, which can’t disappear, is highly concerned by people. And the exploration of risk measurement has been one of the hottest issues in the world. The VaR method that was firstly proposed to response to the financial risk in the early90s of the20th century has become the governing method to measure the financial risk. And its enormous scientificity and transparency have been recognized by more and more financial institutions. The last five years has witnessed the eruption, spread and deepening of the financial crisis. The economic situation in the world is extremely serious and complex, and the prevention and resolve of the risks are not only the eternal theme, but also the lifeline in the financial activities. Thus, accurate measure of the risk value is of great significance, especially in nowadays. However, with the deepening research of the metrics model, the imperfection of the traditional model is coming out. Firstly, the normality assumption of the risk factors can not accurately describe the distribution of the return on the assets that often have spikes, thick tail and asymmetry. Secondly, the traditional correlation coefficient matrix can’t express the nonlinear relationship between the assets in the portfolio. Therefore, based on the Copula theory, the Copula-GARCH model is proposed to optimize the calculation of the VaR.In the theoretical research, the definition of VaR and its advantages in financial risk analysis have been introduced firstly, and about its calculation method, the Monte Carlo simulation is highly elaborated, including its principles and steps, which are the preparations for the empirical analysis. Secondly, after brief introduction of the GARCH model, the concept, nature, parameter estimation, model testing and the advantages of some common Copula functions are described in details. Finally, the Copula theory, the GARCH model and the VaR method are combined, and the concrete steps to calculate VaR based on the Copula-GARCH model are put forward.In the empirical analysis, the closing prices of the Shanghai composite index and the Shenzhen composite index during the January4,2000to December31,2011are taken as the sample. Firstly, the GARCH model and its expansion forms are used to fit the marginal distribution function of the asset yield, and after comparing, the GARCH(1,1)-t model is regarded as the best one. Secondly, five common Copula functions were selected to describe the correlation structure, and by comparing the empirical distribution to the theoretical distribution, the Clayton-Copula is regarded as the best one. Finally the VaR can be calculated by Monte Carlo simulation method, and through the Kupiec testing, the results obtained by the Clayton-Copula function has the minimum error, which further illustrates the above evaluation of the degrees of fitting of the Copula function.The Copula model has no restriction to the marginal distribution, so the traditional multivariate normal distribution can be replaced by flexible multivariate Copula function distributions. What’s more, the Copula function can not only describe the non-linear and non-symmetrical relationship, but also capture the structure changes, especially the tail changes, which provide great convenience to the calculation of the VaR. Also, the model testing method based on the empirical distribution function is effective, which provide a good solution to the selection of the Archimedean Copula function.This article is limited to the analysis of the binary static Copula function, and the Copula function in the portfolio of the financial assets can be extended to many aspects. Firstly, the time-varying or variable structure Copula function needs to be further studied; secondly, the mixed Copula can be constructed to describe the complex structure; thirdly, there can be more research on the degrees of fitting; fourthly, the Copula function can be extended to other financial areas.