Lending Portfolio Optimization Based On Jump-GARCH Model And Copula

In accordance with the mean-variance, portfolio is to attain the minimum of theportfolio’s risk with the given return or of the maximum of the portfolio’s return withthe given risk. The traditional mean-variance model assumes the marginal distributionof risky asset and the joint distribution of the portfolio are normal distributions at thesame time. However, a large number of empirical studies suggest that the realisticreturn often expressed as volatility clustering, fat tail and jumping. And therelationship between the assets appears a non-linear dependence structure. So simplyusing the traditional mean-variance to find out the best optimization of the portfolio isno longer realistic.In order to overcome these disadvantages, we use the Jump-GARCH model to fitthe marginal distribution of the risky asset and use Copula function to characterize thestructural relationship between assets, and combining the both to descript the jointdistribution. Using Mean-CVaR to solve the borrowing portfolio optimizationproblems, and by calculating the minimum of the CVaR at the given return to find theoptimal borrowing configuration strategy.We use GARCH, SV and Jump-GARCH model respectively to comparativeanalysis on fitting the Shanghai Composite Index, finding the Jump-GARCH model isthe best model to fit the various characteristics of the return. We use Jump-GARCHmodel to study the returns of China Unicom, China Petrochemical and China CYTSTours, and comparing several Copula functions which descript the structure of thethree companies. We finally find the t-Copula function can better build the structure ofthe three companies. We also find the optimal borrowing configuration strategy. at theconstraint of the Mean-CVaR. All of the above provide some theoretical guidance forthe banks when they are making a decision of the loans.