Select And Estimate Mixed Copula Model And Its Application

The Copula function is a powerful tool for dealing with the dependence of variables and it has been widely used in risk management, portfolio aggregation, asset pricing and other financial areas. But there are some deficiencies when using the single Copula function to describe the dependence of variables. In particular, the dependence of variables in the actual financial field is often complex, then there are some limitations if we only use a single Copula function. The mixed Copula function mixed by some different Copula functions can better describe the dependence of variables. However, when mixing some different Copula functions, they may be mistakenly selected; therefore it will result in the distortion of model fit. The marginal distributions of the mixed Copula function are often assumed to submit to some certain ones, however, which will cause distortion when fitting the data in complex financial areas. Based on the work of previous studies, this paper mainly researches these problems mentioned above. The main contents are listed as follows:(1) The marginal distributions of the mixed Copula function are estimated by using kernel density estimation.(2) Using the variable selection method in the penalty function, the weight parameters of the mixed Copula function are selected and estimated.(3) Using the EM algorithm and the BFGS algorithm, the dependent parameters of the mixed Copula function are selected and estimated.(4) The above mentioned methods are applied to analyze the Shanghai and Shenzhen stock market.