The Study On Some Problems About The Estimation Of The Parameters Of Credit Risk

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.