Mixed Copula Model And Its Application In Risk Measurement

This paper introduces a GARCH-Mixed Copula model for VaR(Value-at-Risk) estimation with the background of high development in Chinese fund market. The advantage of this approach is significant. It abandons the assumption of multivariate normality in former research, simplifies the multivariate function's computation and makes the simulation much closer to the reality. The relationship between the whole and the individual risk is also accurately calibrated. It flexibly applies and expands copula models to catch tail information while fully considering the financial data's fat tail traits.The paper's structure is as follows: the first three chapters introduce the definition and properties of copula model and its classifications as elliptical copulas and Archimedean copulas with expressions and simulation scatter plots. Then it takes advantage of the tail traits of the Archimedean copulas to construct mixed copula models. The EM algorithm which is always used in complicated MLE and Akaike information criterion(AIC) are applied in estimating the parameters and model selection. The next two chapters introduce the application of the copula models in risk measurement. GARCH is used to model the asset return series. The residual distributions are taken as the marginal distributions and the copula models are taken as union distributions. Finally I use Monte Carlo method to simulate VaR. At the end of my paper, I choose two stock funds which were both issued at the beginning of 2005 to apply my method and compute VaR in different times. Based on the results, I get the conclusion that the values of VaR are nearly the same in t and mixed copula models. But the mixed copula model can give the tail structure which is superior to t copula.