摘要
信用风险是银行业面临的最主要风险。信用风险的基本要素包括:违约率、违约损失率、违约暴露和年期。在组合层次上,除了以上四个基本要素外,还包括违约和信用质量相关性、信用集中性。对信用风险基本要素的研究是信用风险研究的基础。论文对违约率、违约损失率进行了研究。在回收率为随机变量的条件下,研究了信用组合损失的分布。另外还用定量分析的方法研究了信用集中性对组合损失的影响。
违约率估计的方法有很多种,其中有的方法已经提出并研究了很长的时间。论文对目前研究还不多的基于评级模型方法进行了研究。违约数据记录很少的低违约组合违约率的估计是一个比较困难的问题,最大谨慎原则对于解决这个问题是一个有用的方法。但这种方法对违约率的估计过于保守。论文将最大谨慎原则与极大似然估计方法相结合,研究了违约率估计问题,得到的违约率估计值明显地降低了保守度,并避免了仅使用最大谨慎原则需选择置信水平等不好把握的问题。
关于回收率或违约损失率的研究工作相对比较少。目前的研究工作主要集中于对回收率影响因素的分析研究、对回收率分布规律的研究、对回收率和违约率之间关系的研究等方面。论文对回收率的分布规律进行了研究。针对Beta分布等模型不能准确表示回收率分布的问题,提出了一个新的回收率分布模型即双Beta分布模型。它以Beta分布模型为特例,具有Beta模型的优良性质,同时还具有双峰分布的特征。根据现实中回收率数据,证实了双Beta模型表示回收率分布的优越性。论文还在双Beta模型基础上建立了双Beta回归模型,利用该模型讨论了系统因素对回收率的影响。有关回收率的研究是论文的核心部分。
估计信用组合的损失分布是相对比较困难的问题,尤其是在回收率具有随机性的情况下,难度又有所增加。常用的方法是MonteCarlo模拟法,该方法虽然有效,但需要消耗大量时间。Vasicek模型可以避免MonteCarlo模拟,其模型思想在新巴塞尔资本协议中有所体现,但该模型的前提假设回收率为0,与现实难以相符。我们在Vasicek模型的基础上,考虑回收率随机性的影响,并引入违约率与回收率的相关性,建立了新的模型,给出了组合损失分布和概率密度的解析表达式,拓展了Vasicek模型。利用组合损失分布函数可以方便地对组合损失进行估计。利用新模型考虑了违约率与回收率相关性的优势,进一步研究了衰退期违约损失率与随机违约损失率之间的关系。这部分研究也是论文的核心部分。
信用集中性对组合损失有比较大的影响。在组合中信用集中性的表现就是违约暴露向一些资产过于集中。对信用集中的组合,不能依据组合不变性度量损失风险和计算资本要求。目前用定量分析方法研究信用集中性对组合损失影响的工作还不多。随着信用集中性的增加,组合的异质性增加,估计组合损失变得很困难,一些有用的工具如鞍点近似法也出现比较大的估计误差。论文引入了Herfindahl指数度量违约暴露集中度,对违约暴露集中的组合,建立了递归模型用于估计组合损失,讨论了违约暴露集中度对组合损失的影响。
Credit risk is the ma in risk facing to banks. The fundamenta l factors of creditrisk include the probability of default(PD), the loss given default(LGD), theexposure at default(EAD) and the maturity(M). At portfolio level, the fundamenta lfactors also include the default and credit quality correla tion, and the creditconcentration besides those four factors. The study of credit risk is based on thestudy of the fundamenta l factors. In this paper, the factors of PD and LGD arestudied. On condition that the recovery rate(RR) is a random variable, thedistribution function of credit portfolio loss is derived. Moreover, the impact onportfolio loss imposed by credit concentration is measured by quantitative method.
There are ma ny kinds of methods used to estimate PD, and some of themwere studied for a long time. In this paper, the rating-based model about which theresearch work is relatively little is studied. The PD estimate of low default creditratings which have rare default data is quite a difficult problem. The most prudentprinciple method is a useful tool to solve this problem, but the estimate values ofPD obtained using this method tend to be conservative. In this paper, we combinethe prudent principle method with the ma ximum likelihood estimate method tostudy the PD estimate problem. Compared with by using the most prudentprinciple method only, the PD estimate values obtained by above mixed methodare much less conservative, and the embarrass problem of choosing confidencelevel can be avoided.
The amount of research work about the recovery rate or the LGD is rela tivelylittle. At present time, the research work ma inly focus on the impact factors of theRR, the distribution of the random RR, and relationship between the RR and thePD and so on. In this paper, the distribution of the random RR is studied. To solvethe problem that Beta model can not denote the distribution of the RR accurately,we propose a new model for the RR distribution, namely double Beta distributionmodel. The double Beta distribution model includes Beta model as its specia l case,and has good properties as Beta model. Moreover, its probability density function has characteristic of two peaks under some parameter value. According to the RRdata from reality world, the double Beta model is proved to denote RR distributionmore properly tha n Beta model. Furthermore, a double Beta regression model isestablished based on the double Beta model. Making use of this new model, westudy the extent that the system factor affects the RR. The study about the RR is acore part of the paper.
The estimate problem about the distribution of credit portfolio loss isrelatively difficult. The difficulty specia lly increases when the RR is a randomvariable. A popular estimate method is Monte Carlo simulation. This method iseffective, but it needs to consume large amount of time. Vasicek model whosethought is reflected in the new Basel capital accord can avoid Monte Carlosimulation, but it assume the RR to be zero, and that assumption usua lly can notmeet the reality requirement. Basing Vasicek model, we presume the RR is arandom variable and it is correla ted with the PD, and we propose a new model. Wederive the analytica l formulas of portfolio loss distribution function andprobability density function which genera lize Vasicek model. The portfolio losscan be estimated conveniently by using these formulas. Taking advantage of theincluding of correla tion between the RR and the PD in the model, we study therelationship between downturn LGD and random LGD. The relative work is a corepart of the paper.
The credit concentration has great impact on the portfolio loss. In a portfolio,the credit concentration mea ns the exposure at default concentrate overly to someassets. In a portfolio with credit concentration, the loss risk can not be measuredand the capital charge can not be calculated by portfolio-invaria nt. At present time,the research work, which use quantitative analysis method to study the impactimposed by credit concentration on portfolio loss, is not too much. With theincreasing of credit concentration, the heterogeneity of portfolio also increases,and the estimate of portfolio loss becomes very difficult. Many useful tools forinsta nce the saddle point approxima tion method become inaccurate. In this paper,the Herfinda hl index is introduced to measure the EAD concentration extent. Theregression model is established to estimate loss for EAD concentration portfolios,and the impact imposed by EAD concentration extent on portfolio loss is studied.
引文
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