The Calculation And Empirical Analysis Of VaR And CVaR Based On Hybrid Copula

Copula functions have been widely used in various financial fields because of its good properties in dealing with the non normal joint distribution function.In particular,it has become an extremely important way to solve the problems of risk management,portfolio selection and asset pricing.However,there are some deficiencies in the de-scription of the financial risk when using a single Copula function.Especially in the actual financial market,the relevant structure of financial risk is often more complex,and there will be some limitations when using a single Copula function.On this basis,the mixed Copula constructed by combining several Copula functions together,can better capture the tail dependence of financial markets.The main work and innovation of this paper are as follows:Firstly,this paper introduces the knowledge of Copula and VaR,and the methods of calculating VaR are summarized,including the traditional normal method and the single Copula method.on this basis,The mixed Copula model is constructed by weighted combination of several single Copula functions,and the parameter estimation of mixed Copula function is studied.In the empirical analysis on the risk measurement of specific securities market,a mixed Copula function is constructed by Guassian Copula and t-Copula and Gumbel Copula and Frank Copula,and the parameters are estimated by EM method and the map of the parameters is drawn.Finally,the VaR of the portfolio is calculated by Monte Carlo method based on the normal Copula,t-Copula,Gumbel Copula and mixed Copula.Then,the VaR values of different Copula models are compared.Research shows that the mixed Copula method can capture the tail dependence of financial risk better,and the calculated VaR values are better than the traditional methods.According to the nonlinear characteristics of financial risk in the financial market and asymmetric tail,introduce extreme value theory to model the marginal distribu-tion,and then the mixed Copula model is applied to the risk assets research and VaR calculation.After the empirical study on Shanghai index and Shenzhen index,The POT model can better fit the marginal distribution of the yield with the thick tail,and the mixed Copula function can better reflect the correlation between the two kinds of risks.