Copula-EGARCH-Kernel Density Estimation Model And Its Application

Recently, with the rapid development of financial market and increasing complexity of financial derivatives, financial risk management is being more important than ever before. For that, the VaR method which is representative for dynamic risk measure method becomes more and more important. Considering the tradition calculation of time-varying Value at Risk need to suppose that the Standardized residual submits to some distribution based on GARCH model, but the shortcoming of this method is that the error of time-varying Value at Risk is comparatively big. Accelerated by the development of Probability Theory and Statistics and the trend of Their combined use, application researches based on sample analysis and modeling Using nonparametric density estimation attract more and more attentions of researchers. Nonparametric density estimation method can make accurate estimation only based on sample data without the assumption that the forms of the underling densitiesare known. It provides a novel approach to the analysis and modeling of samples which is unknown.In this dissertation, Kernel density estimation method is used to estimate the distribution of Standardized residual under GARCH model, the distribution of Standardized residual is obtained. Then, we construct the Copula-EGARCH-kernel density estimation model base on EGARCH model and Copula theory and use it to reflect the correlation between assets. The main work is as follow:First, we use kernel density estimation method to estimate the distribution of Standardized residual under GARCH model, the calculation of time-varying VaR base on kernel density estimation and GARCH model is obtained, the result showed that a better Time-varying VaR is obtained in the method of this paper.Second, we use kernel density estimation method to improve the estimation method of Copula parameters (IFM), we use kernel density estimation method to estimate marginal distributions.In this method,there is no need to suppose marginal distributions to submit some distribution,such as the normal,T,GED distribution,thus increases the accuration of the estimation of Copula parameters.Third, kernel density estimation method is used to improve Copula-EGARCH model, this new model is named as Copula-EGARCH-kernel density estimation model.Because of dynamic characteristic of the financial risk, and we need to research the conditional correlation between assets. Then, we analyze conditional correlation between financial time series base on Copula-EGARCH- kernel density estimation model. We make conditional dependence analysis for the Shanghai and Shenzhen Stock market index, the results show that this new model is an effective tool for conditional dependence analysis in Chinese stock markets.