Copula Theory And Its Applications In Multivariate Financial Time Series Analysis

In this dissertation, copula theory and its applications in multivariate financial time series analysis are studied intensively. As a result of those researches, several multivariate financial time series models based on copula theory are proposed. Methods of constructing dynamic models and applications of copula models in financial risk management are also investigated systematically. The key points and main achievements of this work are listed as follows:1. Copula theory is introduced into financial analysis to avoid defects of linear correlation coefficient and classical analysis methods. Based on fully understanding of copula theory, we investigated measure of non-linear dependence and measure of tail dependence that can be derived from copulas. Applications of copula theory in finance are also studied.2. Dependence analysis is a central issue in multivariate financial analysis. Characters of several important copulas used in dependence analysis are discussed in this thesis and multivariate financial time series models based on copula theory, such as Copula-GARCH model and Copula-SV model, are established. Estimation and test methods of copula models are studied too. Consequentially, M-Copula-GARCH-t model is constructed and used to study the degree and patterns of dependence between Shanghai and Shenzhen stock markets. The empirical results show that strong degree and asymmetrical pattern of dependence between two markets can be described correctly and thoroughly using M-Copula-GARCH-t model. 3. Time-varying normal copula model and time-varying Joe-Clayton copula model are investigated carefully and evolution equations of their parameters are provided particularly. The empirical results from Shanghai stock market show that time-varying Copula-GARCH model is better than constant normal copula in the ability of description and prediction of dependence between financial series.4. Structural change is a key character of financial models. In order to catch dynamic dependence between financial markets, three types of structural changing models are provided. They are staged copula model, RS-Copula model with structural change in tail distribution and copula model with structural change in marginal distribution. At the same time, change-points detection methods of bivariate normal copula model are given in this thesis. Chinese stock markets are studied using staged copula model and RS-Copula model. The empirical results show that bivariate normal copula model with structural change is superior to time-varying bivariate copula model and RS-Copula model prevail against the static copula model in describing dependence between financial series. 5. Financial risk management is an important application area of copula technique. Not only are Monte Carlo simulation techniques which can be use to estimate portfolio Value-at-Risk investigated, but also some applications in financial contagion using structural changing copula models are discussed in this dissertation. The empirical results getting from Shanghai stock markets indicate that estimation method of portfolio Value-at-Risk, which is constructed by combining Copula-GARCH model having different marginal distributions with Monte Carlo simulation techniques, is feasible and effective.