Research On Dependence Struture Among Financial Markets Based On The Copula Theory

Dependencies among financial markets have significantly increased and relationships among them become more complex. This phenomenon is a direct consequence of economic globalization and the globalization of the financial market. As the foundation of risk management and portfolio investment, description on dependence structure correctly in financial markets is very important. So it is necessary to research on the dependence structure among financial markets in financial decision-making in order to increase the correction of decision and to decrease the risk of decision.Copula functions, which are important tool to describe the dependence structure of financial markets, are functions which connect the joint distribution function with its marginal distributions. It is possible to study the dependence structure of random vectors irrespective of their margins by use of the Copula function to construct the multivariate joint distribution. This paper study dependence structure among financial markets based on the Copula theory and discuss some academic question of Copula function and its application in risk management and portfolio investment.The foundation of modeling the dependence among the financial assets by Copula function is the choice of an appropriate parametric copula in a given set of copulas. The commonly used approach to selecting copula is AIC or BIC criterion which relies on the density function of each Copula in the given set of Copulas. However, the explicit expressions of density function of some Copulas may be very complicated or very difficult to obtain, which cause great inconvenience in the application of AIC or BIC criterion. In this sense, a new Copula selection method based on nonparametric kernel density estimation is proposed. Under different marginal distributions, the Copula selection method based on nonparametric kernel density estimation is compared with AIC by means of Monte Carlo simulation Methods.Dependence measures based on Copula functions, which are used commonly, are systemically studied in this paper. From the analysis, the definitions of upper threshold dependence measures and lower threshold of dependence measures are proposed by threshold Copula functions.The dependence structures of financial markets are incessantly changing with the accommodation of market. And asymmetry lies in the influence of positive and negative innovations on the dependence structures of financial market. So, a time-varying Copula model with threshold structure is proposed based on the idea of the threshold GARCH model. By this model, the influence of international and regional stock markets on the dependence structures of domestic financial market is studied.In the aspect of risk management and portfolio investment, financial risk management methods based on VaR and ES are studied. Furthermore, the APD-GARCH model is established. With this model and multivariate Copula functions, the efficient frontier of portfolio optimization based on mean-ES is studied. The experiential result indicates that it is very necessary to consider the asymmetry tail dependence structure in research on risk management and portfolio investment.The research is sponsored by National Natural Science Foundation of China: Research on Long Run Equilibrium in Multivariate Moments Series and Avoiding Tactics of Dynamic Financial Risk (No.70471050).