Integrated Risk Measuremnet Of Credit Portfolios Based On The Intensity With Mixed Poisson Distributions

With the development of risk supervision and the need of risk management, thefinancial industry is urgent to develop a better and more scientific system to manage thefinancial risks when the credit risks transferred or traded in the market. For this, theprecise measurement of portfolio credit risk is always the heart of attention. However,the dependent structure of portfolios and the computational complexity of portfoliocredit risks do not gain enough attention in relevant fields. Therefore, this paperdevelops the empirical research on the dependent structure and the computationalcomplexity of portfolio credit risks.When constructing the model of portfolio credit risk, we introduce the mixedPoisson model to take place of the Copula model which is more widely used. The mixedPoisson model has been staying on the level of theory for a long time while this paperproposes some innovations on its empirical application. For the default event, it’s hardto predict the specific time that default events occur or the specific amount of defaultloss, while it’s easier if the measurement is based on the portfolio view which contains alarge number of obligors. However, there is exposure to default losses from a largenumber of obligors and the probability of default by any particular obligor is small. Thissituation is well represented by the Poisson distribution. To apply the mixed Poissontheory into empirical study, we also use the classical structure model to measure thecredit risk of single obligor, which links the structure model and the mixed Poissonmodel on the point of the intensity of Poisson variable. Simple point, we use structuremodel to achieve the important parameters of mixed Poisson model. Then we can applythe mixed Poisson model with parameters reflecting actual market situation to constructa credit risk measurement model which can describe the default dependent structure andthe default distribution of large portfolios. The combination of these two methods is anapplicable innovation.For the computational complexity of portfolio credit risk, Monte Carlo simulationis the most widely used technique in the risk measurement. Although MC is morecomprehensive in simulation, it will cost more time and be ineffective for rare eventsimulation. Therefore, this paper develops Importance Sampling method to the mixed Poisson model to obtain default distribution of credit portfolios. IS can overcome theproblem faced when we’re simulating rare events by exponential twisting and measuretransformation. Because the lack of effective data in our empirical study, we propose anexample of numerical simulation to illustrate the superiority of importance samplingmethod. Compared with Monte Carlo simulation, the curve of default loss distribution ismore smooth in importance sampling. Demonstrated by the simulation, ImportanceSampling technique can improve the accuracy when the efficiency is also improved,which has practical value in the field of credit risk measurement. In addition, the valuesof variance reduction ratio calculated by this paper are all bigger than1. As with thedecrease of default probability, the increase of variance reduction ratio is obvious. All ofthe above indicate that Importance Sampling technique is much stronger than MonteCarlo method when dealing with the rate event simulation.To sum up, based on the large portfolio view, the dependent structure constructedby the mixed Poisson model can excellently describe the occurrence and contaminationof default events. Combined with the Importance Sampling technique, the managementof credit risks can be improved on both the accuracy and the efficiency. The research ofthis paper provides foundations for the study of extreme events and the allocation andsupervision of economical capital.