A Study On Coherent Measures Of Credit Risk Portfolio Based Copula Function

The modelling of defaults dependence has been a key field for risk managementof credit portfolio. Using the facility and flexibility of copula function in the modelingof dependence structure, the paper studys the modeling of credit portfolio basedcopula funtion, and analyses the effect of the change of dependence structure ofdefaults on the portfolio loss distribution and coherent risk measure.Firstly, based on the latent variable model, one of the existing models of creditportfolio, and aimed at its drawbacks in dependence structure, the paper proposes amodel framework of credit portfolio, which is based on copula functions and wherethe indexes of industry return are considered as a systematic risk factors, discusses thecalculation of joint probability for various default states of credit portfolio in theframework, illustrates the approach of determining the parameter in the model and thechoose of copula functions. The analysis shows t-copula function is a preferablesubstitute for Gaussian copula of the existing models when using copula functions tomodel dependence structure of defaults.Secondly, due to the fact that,in Chinese, the market of credit bonds aredeveloping, and that the reliable credit datas are not available, using the datainformation provided by the capital market,which is open and effective, the paperconstructs the time series of index of industry return, and estimates the parameters ofthe marginal distribution and dependence structure. When using skew t-GARCH(1,1)to model the marginal distribution of index of industry return, the paper develops anew construction of skew student t distribution based on the existing skew studentt distribution which is lack of flexibility in describing the skewness of distribution.In terms of simulation, It is found that the new skew student t distribution is betterthan the existing in describing the skewness of distribution. Also, the parameters ofdependence structure of index of industry return for Gaussian copula and t-copulafunctions are estimated, respectively. The test results of the good-of-fitness show thatt-copula function has better good-of-fitness than Gaussian copula function, due tot-copula function considering the tail dependence of index of industry return.Lastly, based on the above estimated model of dependence structure, the degree of effect of the change of dependence structure in credit portfolio on the portfolio lossdistribution and coherent risk measure is discussed by a constructed creidit portfolio.In order to improve the estimation accuracy of ES, the paper calculates the portfolioloss distributions and risk measures for the dependence strcture of Gaussian copulafunction and t-copula function by using Important Sampling approach. The resultsshow that the change of dependence strctures has a significant effect on the portfolioloss distribution, especially on the tail of portfolio loss distribution, and this effectmakes the difference between the risk measure caused by the two dependence strcturemodel increase with the confidence level, on the other hand, the difference betweenVaR and ES decreases with the confidence level.