The Research On The Distribution Characteristics And Estimation Methods To Loss Given Default

Loss Given Default (LGD) is an important parameter to calculate regulation capital, and also a parameter that need to be self-estimated by the bank who implements Advanced Approach of The Internal Rating-Based Approach according to the New Basel Capital Agreement. This thesis analyzes and studies the influencing factors, distribution characteristics and measurement methods of LGD and discusses its application in reality.At present, the level of credit risk management in Chinese commercial banks is comparatively lower than international advanced banks, the internal rating system is especially imperfect, which shows in the apparent unidimensionality characteristics of rating system - more emphasis on the identification of credit risk and the evaluation of default, i.e. more emphasis on the study of Probability of Default and less empirical analysis on LGD.This thesis concludes the following influencing factors based on the existing literatures' study on influencing factors of LGD: economic period, industry, mortgage guarantee, debt contract, loan size and specific factors of company. The author takes the loan data of a commercial bank as a sample, use T-test, significance test and other statistic methods to make empirical analysis on the relationship of those influencing factors with LGD. Key influencing factors are determined by main factor analysis: one is secure method of loan; the other is the credit level of enterprise. This result is to be applied in the modeling of conditional recovery rate in Chapter 5. PD and LGD are generally considered as independent variable in current credit risk measurement model, which is same in the New Capital Agreement of Basel Committee on Banking Supervision. Using analysis of variance, the conclusion of this thesis is that PD has positive effect on LGD.Chapter 3 is mainly engaged in the theory deduction of measurement method of single debt's LGD. After defining Default and Loss, the author concludes the confirmation and calculation methods of Recovery Rate(RR) under different definitions. Since the sum of RR and LGD is 1, these two concepts have been used intercrossing in this thesis for the convenience of study. Using the market prices of securities, the author deducts the securities' LGD implied in credit spread; using option model, the author deducts the theoretical valuation of the loan Recovery Rate of the bank.With consideration of the uncertainty of recovery rate, to obtain more accurate loan recovery rate, the measurement of loan recovery rate's actual distribution shall be based on numerous default loan samples. Most present studies are following the theoretical models, many empirical studies overseas are just descriptions of the mean and variance of classified data. In Chapter 4, the author starts from the distribution of recovery rate, usesβdistribution for data fitting according to the characteristics of recovery rate.βdistribution has many advantages, it only needs mean and variance to determine distribution function. The study result shows that the significance level of recovery rate complying withβdistribution is acceptable on the level of 5%. While the level of recovery rate complying withβdistribution also has two defects: one is that when considering the final value of recovery rate, the model can't proceed with the probability density of all the points observed, including that in [0,1] section; the other is that the basic figure ofβdistribution is only the study result of recovery rate experience, this simple approximation can achieve good fitting most of the time, but is limited when coming to the fitting of bimodal distribution.To overcome the limitation ofβdistribution to the fitting of such cases, e.g. bimodal distribution, non-parameter kernel density method is introduced to estimate LGD in Chapter 5. The key points in kernel estimation are the selection of kernel and weight functions and the determination of optimal window-width. Sinceβkernel is non-symmetric, there will be problem in the precision of graduation if using kernel graduation method, because, generally, kernel function is supposed to be symmetric in kernel graduation method, thus will cause boundary deviation in actual application. Thus Gaussian kernel is selected as the weight function in this thesis. After deducting the optimal window-width, Matlab software is used to estimate the density function of random variable.Data fitting is a description to recovery rate distribution. Using the analysis result regarding the influencing factors of LGD in Chapter 2 and giving consideration to the factors of mortgage guarantee and credit level of enterprise, the author introduces the modeling method of conditional recovery rate. Since current data is not enough to effectively analyze the conditional recovery rate, simulation method of random data that is usually used in actuarial calculation is applied to study the conditional recovery rate. The author uses acceptance-rejection method to simulate recovery rate with the random values ofβdistribution, and calculate simulation times needed based on given error range and degree of confidence. Using assumed explained variable condition, applying the maximum entropy principle and with the condition probability distribution complying with that of sample data and prior distribution, the author finally estimates an optimal conditional probability density of the LGD. We can estimate not only the mean and variance of LGD with this model, but also the distribution density of LGD. Furthermore, this model has specific economics meaning. Backtrack test shows that this model has better estimation effect to bimodal distribution.At the end of the thesis, the author concludes the methods and conclusions studied, gives related policy suggestions and states further study direction.The major contribution of this thesis:(1) Making empirical study on the influencing factors to LGD; using the market prices of securities to deduct the securities' LGD implied in credit spread; using option model to deduct the theoretical valuation of the loan recovery rate of the bank.(2) Introducing non-parameter kernel density method in the estimation method of LGD, using the key factors influencing LGD from empirical study, putting forward that using conditional recovery rate modeling to investigate LGD.(3) Giving related policy suggestions based on LGD study and the actual situations in China.