The Comparisons Of Copula Functions And Its Application In VaR Measurement

The research of correlation is playing a critical role in financial quantitative analysis. As in nowadays, the estimation of single asset risk could no long meet the needs of investment, researches into the risk of investment portfolio is gaining more and more attention among the academic world. In this circumstance, the measurement of VaR is depending greatly on the structure correlation of different assets. Numbers of methods have been carried out to fulfill the need of correlation assessment. Copula, a new tool for evaluating the structure correlation between financial variables, has been developed in recent years. Compared to traditional research methods, Copula shows itself as more precise and flexible.At the beginning of this dissertation, a thorough literature review was conducted on Copula researches both from domestic and overseas. It was found that the comparison between different Copula functions were very limited in China. Besides, the empirical analysis of Copula received little attention. Therefore, based on the basic theories of Copula, this dissertation analyzed and compared two main classes of Copula functions– Elliptical Copulas and Archimedean Copulas. It also focused on some of the popular Copula functions, specifying their own features. The purpose of this was to provide the support for practical use of Copula, so that when coming across a specific set of data, we can choose the proper Copula function based on our experience. In addition, the estimation methods for parameters of Copula were also described in this part of the dissertation and a comparison was made between them.In the next part of the dissertation, a full summarization on VaR estimation methods was given. It generalized the main measuring methods by categorization, including parameter approaches and simulation methods. Additionally, problems of the previous measuring methods were pointed out. These disadvantages had influenced the reliability of both VaR results and the estimation of correlation. In order to overcome these problems, Copula was introduced into one of the assessing tools - Monte Carlo Simulation. To testify the effect of estimating VaR with Copula, empirical analysis was used for the Rate of Return for indices of Shanghai and Shenzhen Stock market. It was found that by introducing Copula, the result was more reliable than those from previous methods. Furthermore, the back-testing outcome shows that compared to the traditional Monte Carlo Simulation method, the new approach with Copula can easily grasp the tail value. This enabled us to avoid the deviation that might be caused by the improper simulation of extreme VaR. Thus we can better evaluate VaR and control the risk.At last, the dissertation analyzed the limitations of Copula, both in its existing theories and its practical applications. Copula was still at its early stage. It has been such a short time since Copula was developed that it was difficult to be perfect. This required us to complement its theoretical system when applying it into practice.