Research On Portfolio Credit Risk Modeling And Its Applications

The study of portfolio credit risk plays an important role in credit risk management andcredit derivative pricing. Since the2008financial crisis, the financial institutions have beenfacing a series of more strict requirements on risk management implemented by the financialregulatory authorities, which means that they have to improve their abilities of managing port-folio risk. On the other hand, the financial crisis has revealed the shortcomings of one-factorGaussian model for pricing the portfolio credit derivative products of which the synthetic CDOis a typical one. In the circumstance of global economic gloom and deteriorated credit quality, itcurrently is a very popular topic in academy and industry that how to build the more reasonableportfolio credit risk models for managing the credit risk and evaluating the credit derivatives.The core of portfolio credit risk modeling is to correlate all the entities, and then to buildthe dependence between the credit migrations of the entities or between defaults. Taking intoaccountthedisadvantagesoftheexistingmodelsforportfoliocreditriskmanagementandmulti-name credit derivative pricing, this paper aims to propose some new models so that they can fitthe empirical facts or market data better. The specific work and contributions of this thesis areas follows.First, we apply grouped t-copula to study the default risk of the bond portfolio. Due to thefact that the bond issuers are from different industry sectors and each industry sector bears itsown specific risk, though they are subject to systematic risks, the difference between industrysectors should be taken into account when modeling the credit risk of a bond portfolio. Inthe thesis, we apply grouped t-copula to study the credit risk from sector to sector, and thencombine them together. This model means that the default dependence between firms from thesame industry sectors is stronger than that from different ones. Besides, the empirical analysisshows that the grouped t-copula model can characterize the extremal tail risk of loss distributionbetter than the usual t-copula.Second, extreme value theroy is used to build a discrete-form first passage time credit riskmodel for studying the default risk of the bond portfolio. The annual or semi-annual maximumnegative daily return is regarded as the state variable in the model, and the distributions of themare derived by extreme value theory. Because it is observed in reality that defaults cluster in the same industry sector or in the same region, hierarchical Gumbel copula which is an extremevalue copula is used to link the marginal distributions of state varibles. The proposed modelcan be regarded as the counterpart of CreditMertrics under the framework of Black-Cox defaultmodel. The empirical analysis indicates that the high-quantile tail of the loss distribution result-ing from the proposed model is heavier than those from CreditMetrics and the usual Gumbelcopula models, namley, the proposed model is relatively more conservative in terms of stresstesting.Third, under the framework of structural default model, default correlation is studied intwo cases in which asset processes are constrcuted by applying business time (time-changed)Brownian motions and Hawkes jump-diffusion processes, respectively. Due to the unexpect-edness of some defaults, we build a model in which a set of business times are taken as thebasis vector and the business time for each film is assumed to be the linear combination of thosebusiness times. The proposed model is able to characterize extensive default correlation fromindependence to perfect dependence. On the other hand, because of the existence of volatilityclustering in financial markets, that is, large changes tend to be followed by large changes ofeither sign, the asset value is modelled by Hawkes jump-diffusion process rather than Poissonjump-diffusion process, and they are correlated by common Hawkes process as well as correlat-ed Brownian motions. The numerical examples illustrate that the default correlation coefficientwon’t necessarily increase as the expected common jump times increase; however, the moreclustering of the jumps in the common Hawkes process are, the larger the default correlation is.What is more, the more clustering of the jumps in idiosyncratic Hawkes process, the less thedefault correlation is.Forth, MGB2distribution is applied to model the default times and evaluate the syntheticCDO. Similar to the implied volatility smile arising in option market, implied correlation smileis observed in synthetic CDO market. That means that the standard model of pricing syntheticCDO which is one-factor Gaussian model is not good enough. Since implied correlation doesnot always exist, it is more reasonable to take base correlation as the tool to judge a model.From the perspective of base correlation, MGB2model is so flexible that it can generates manypatterns of base correlation with varying parameters. Furthermore, MGB2model can matchthe market implied base correlation as well as double t model does, which Gaussian model and Clayton model cannot make.