基于信用差异度最大的信用等级划分优化方法

信用评级对当代社会有极其重要的影响,若信用等级划分不合理,必将误导债权人和社会公众.信用评级结果的变动直接反映经济状态的变化,2011年标准普尔把美国的主权信用评级从AAA级降为AA+,引起全球金融市场的动荡.信用评级的本质是合理区分客户的信用状况,揭示不同等级客户的信用风险水平.国际上比较流行的标普、穆迪的信用评级针对中国客户的评级结果往往存在信用等级很高、违约损失率反而不低的不合理现象.本研究以信用差异度和违约金字塔为标准,构建非线性规划模型划分信用等级,并以中国小企业贷款数据为样本进行实证研究·本研究的创新与特色一是根据第k个信用等级中最后一个样本的信用评分P_(mk)~k与第k+1个信用等级中第一个样本的信用评分P_1~(k+1)确定相邻两个等级的信用评分差值,以所有信用等级的评分差值之和∑(P_(mk)~k-P_1~(k+1))最大为目标函数,确保最大程度的保证信用评分差异大的客户划分为不同信用等级.避免了把信用状况差异较大的客户划分成同一个信用等级的不合理现象.二是以信用等级由高到低的违约损失率严格递增为约束条件建立信用等级划分模型,保证信用等级划分结果满足信用等级越高、违约损失率越低的违约金字塔标准,避免出现信用等级很高、违约损失率反而不低的不合理现象.三是1814笔工业小企业贷款数据的实证研究表明,本研究的信用等级划分方法不仅满足信用等级越高、违约损失率越低的违约金字塔标准,还能保证信用状况差异大的客户划分为不同信用等级.

Optimal method of credit rating division based on maximum credit difference degree

Credit rating has an extremely important impact on modern society. It will mislead the creditors and social public if the credit rating division is unreasonable. In 2011, Standard & Poor's lowered the sovereign credit rating of United States to AA+ from AAA which caused the turmoil in the global financial markets. The essence of credit rating is to classify the customers according to their credit level which means customers with different credit risk level should be included in different credit rating. The internationally popular credit rating agencies like Moody, often has the unreasonable phenomenon that customers with higher loss given default (LGD) while the credit level not low for China's loan customers. Our research constructs nonlinear programming model to divide the credit rating according to the LGD pyramid and maximum credit difference degree as the standard, and then we make an empirical research with the loan data of a bank in China. The special and contributions of this paper lie in three aspects:Firstly, we build up a nonlinear programming model to divide the credit rating with the objective function that the sum of credit score difference ∑(P_mk^k-P₁^k+1) is maximum, which ensure customers with different credit status are more likely to be divided into different credit level, we can avoid the unreasonable phenomenon that customers with big credit status difference are divided into the same level. Secondly, we construct a nonlinear programming model to divide the credit rating with the constraint that the LGD is strictly increasing with credit rating from high to low, which can meet the pyramid standard that customers with lower LGD should be divided in higher level, we can avoid the unreasonable phenomenon that customers with higher LGD while the credit level not low. Thirdly, we make an empirical study with 1814 small business loan data of a Chinese commercial bank in recent 20 years and its research result indicates that the method of credit rating division in this paper not only meet the pyramid standard that customers with lower LGD should be divided in higher level, but also own the advantage that it can ensure the customers with different credit status are divided into the different level.