Applications Of Mixed Copula Functions To Dependence Analysis

Nowadays,with the globalization of economics and integration of financial markets,financial crisis and volatility occur frequently and relationship inside financial markets becomes complex and diversified.So,research into correlation of financial markets gains much more attention.Though the correlation of financial markets appears non-normal,nonlinear,asymmetrical,and present tail dependence,copula functions have their unique advantage to solve the dependence structure among variables,and they have been widely used in financial area.However,because of complexity of financial market,single copula function can not describe correlations in the financial market in all directions.Mixed copula combine different copulas together,which describe correlations among variables.For the margin distributions of copula,we typically assume that they subject to special distributions or use some special methods of estimations.Such data fitting can lack fidelity in the complex financial circumstance.To solve this problem,we do research based on previous work of others.Our research includes the followings:Firstly,to fit the data well,we choose generalized Pareto distribution for tail of margin distribution,and non-parameter kernel estimation for the middle.Secondly,we construct models of mixed copula with one parameter and with two parameters,and then we compare single copula,2-parameter copula,mixed copula with one parameter and mixed copula with 2 parameters to choose the best model.For the parameter estimation,we adopt MLE by using the EM algorithm.Thirdly,we apply the method above to analyze the stocks of Industrial Bank and Huaxia Bank.Result shows that mixed copula models have a better fitting than single one-parameter copula and two-parameter copula.And Industrial Bank and Huaxia Bank have strong tail dependence.