Copula Theory & Applications In Correlation Analysis

In this dissertation, Copula theory and its applications in correlation analysis are studied intensively. Based on the thorough study on Copula theory, two kinds of the most common Copula function are compared at first, and then the correlation model in Shanghai and Shenzhen stock markets, based on Copula theory, is put forward, the corresponding joint genotype distribution is obtained through parameter estimation, the application of the Copula model to Credit Derivatives is studied eventually. The main production and innovation of the dissertation are listed as follows:1.The Gaussian Copula is used to model dependence by some scholars, but it cannot have the tail dependence. So t-Copula is used to measure the dependence and the tail coefficients are calculated, covering the shortage of Gaussian Copula. Then, we find the t-Copula is more suitable than the Gaussian Copula by empirical analysis in Shanghai and Shenzhen stock markets and Monte Carlo simulation.2. Correlation analysis is a central problem of multivariable financial analysis. In this paper, correlation analysis of China's Stock Market based on Copula method was described by 10 species Chinese stock index as a case study, proposes parameter estimation of multiple correlation structure was presented. Correlation structure associated with Copula function break the linearity ambit, reflect the variations of the nonlinear change. Then, the multiple joint probability distribution function was given by the correlation structure.3. Recently, Credit Derivatives (CDO) Market has been rapidly developed, Credit Derivatives turned from orienting single credit risk to orienting credit risk portfolio. Default Correlation was higher the possibility of assets default simultaneity is bigger. It will lead loss with extensiveness of Credit Portfolio Measurement. And so, default correlation between assets has become the core of pricing on credit assets portfolio. This paper has studied default correlation between assets in assets pool of Credit Derivatives (CDO) by using Copula theory. Then, the default joint probability distribution function of credit derivatives in assets pool was given.