Integrated Risk Measurement Of Credit Portfolios Based On T-copula And Its Empirical Study

The risk of credit portfolio measurement research has always been the focus ofscholars, and there are two kinds of basic models, structural model and reduced formmodel. The ultimate intent of the model is to develop a scientific system to measure therisk for reasonable pricing or prevention of possible future losses. While the study ofstructure correlation of portfolio and portfolio risk estimation is rare, until the outbreakof the financial crisis of2008because of the neglect of tail risk, the sharp increase indefault events attracted scholars’ related study of structures for portfolio. Therefore, wehave a research on the method that can depict the heterogeneity of credit portfolio tailcorrelation and effectively measure its risk, and do empirical analysis of listed shareswith their related data.Firstly, this paper briefly introduces basic theory of models we use. It mainlyintroduces the definition of structural model and its derivative model. Meanwhile, wedetailed the related Copula definition, category, the corresponding parameter estimationand the definition of correlation coefficients based on Copula.Secondly, this paper studied the correlation structure for portfolio. While thetraditional normal Copula portfolio model is used to construct the model correlation,this article uses t-Copula model to construct it and take the tail correlation intoconsideration, measuring the risk values more accurately. At the same time, this articlewill consider the exogenous portfolio rather than the homogeneous, describing thenonlinear relationship, and the results are more close to reality.Then, this paper studies the model of Copula importance sampling technique. Asthe number of the sample increases, the calculation by ordinary Monte Carlo will betime-consuming. So many domestic and international researches for importancesampling technique in statistics are introduced, however relative research andapplication of importance sampling in portfolio risk is less, especially the researchrelated to Copula function. This paper introduces the risk value calculating method ofnormal Copula for portfolio, and then we have a research on t-Copula risk valuecalculation by importance sampling technique. For the mean drift in importancesampling through traditonal Gauss Newton method, this paper introduces the moreintelligent Levenberg-Marquardt algorithm with the advantages of both gradient method and the Newton method. Through numerical simulation comparison of importantsampling technique and ordinary Monte Carlo for normal Copula portfolio and t-Copulaportfolio, we can make a conclusion that importance sampling technique can measurethe risk value more effectively and quickly.Finally, this paper selects the related data of real estate, finance and insurance,retail industries to do empirical analysis. By solving the Black-Scholes Merton model,each stock’s asset value and standard return rate is obtained, and the marginaldistribution of each stock is obtained by kernel density estimation. We obtain the relatedstructure factors of heterogeneous portfolio and by t-Copula and nonlinear estimation,we estimate the overall default probability. Combined with the importance samplingtechnique, we calculate the portfolio risk values of VaR and ES, showing that under theprecondition of ensuring the accuracy importance sampling technique can reduce thesampling variance, and the introduction of ES value is benificial for risk supervision.In summary, this paper considers the nonlinear relationship between heterogeneouscombinations. Through t-Copula function we can accurately describe the defaultprobability and its portfolio structure. Meanwhile, importance sampling technique canmeasure risk values of VaR and ES more effectively, and this paper provides a basis forthe study of extreme events for the allocation of economic capital and risk supervisionof regulators.