基于最优负债系数的上市银行违约概率测算模型与实证

The Probability of Default Calculation Model of Listed Banks Based on Long Term Liability Coefficient Optimization

当上市银行的长期负债系数γ的取值不同时,应用KMV模型测算出的银行违约概率大相径庭。根据债券的实际信用利差可以推算出上市银行的违约概率PDi,CS,根据长期负债系数γ可以运用KMV模型确定上市银行的理论违约概率PDi,KMV。本文通过理论违约率与实际违约率的总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型的最优长期负债γ系数;通过最优长期负债系数γ建立了未发债上市银行的违约率测算模型、并实证测算了我国14家全部上市银行的违约概率。本文的创新与特色一是采用KMV模型计算的银行违约概率PDi,KMV与实际信用利差确定的银行违约概率PDi,CS总体差异∑ni=1|PDi,KMV-PDi,cs|最小的思路建立规划模型,确定了KMV模型中的最优长期负债γ系数;使γ系数的确定符合资本市场利差的实际状况,解决了现有研究中在0和1之间当采用不同的长期负债系数γ、其违约概率的计算结果截然不同的问题。二是实证研究表明,当长期负债系数γ=0.7654时,应用KMV模型测算出的我国上市银行违约概率与我国债券市场所接受的上市银行违约概率最为接近。三是实证研究表明国有上市银行违约概率最低,区域性的上市银行违约概率较高,其他上市银行的违约概率居中。

When the long term liability coefficient γ equals various values, the default probabilities of listed banks calculated by KMV model are quite different. The real default probabilities of listed banks PDiCS can be measured by the credit spreads of financial bond issued by banks. The theoretical default probabilities of listed banks PDiKMV can be calculated by KMV model with a certain coefficient γ of long term liability. A programming model is established to calculate the optimal value of long term liability coefficient γ following the idea to minimize the total differences ^n∑i=1｜PDi,KMV-PDi,cs｜ between the theoretical default probabilities PDiKMV and real default probabilities PD^cs. We applg the optimal γ to calculate the default probabilities of listed banks which did not issue financial bond. The default probabilities of all 14 listed banks in China are estimated empirically. The innovation and characteristics of the paper is as follows. Firstly, the optimal value of long term liability coefficient γ is calculated by a programming model established following the idea to minimize the total differences ^n∑i=1｜PDi,KMV-PDi,cs｜ between the default probabilities PDikmv and PDics, calculated by KMV model and credit spreads respectively, so as to make the value of γ suit the situation of credit market and solve the problem： the value γ for calculation of default point is uncertain. Secondly, the empirical study shows, when the long term liability coefficient γ = 0.75, the default probabilities of listed banks calculated by KMV model have minimum errors compared with the default probabilities accepted by the credit market in China. Thirdly, the empirical study shows that the default probabilities of state owned listed banks are lower, the default probabilities of regional listed banks are higher, and the default probabilities of other listed banks are moderate.