关键词: 信用评级, 信用等级划分, 违约概率, 指数分布, 小企业

Abstract: Credit rating is not simply a ranking of customers’ credit worthiness, but involves a further analysis of customers’ default probability to determine the distribution of default risk among customers with different credit ratings. Currently, credit rating is dominated by institutions like Standard & Poor’s and Moody’s, while third-party credit rating agencies in China are still in their infancy. Their rating systems are not tailored to the characteristics of small businesses in China. If the existing rating system is used to assess small enterprises, commercial banks may reject many small enterprises with potential for development due to low credit ratings, thus constraining their growth.
Therefore, this paper proposes a credit rating classification model based on default probability following any given exponential distribution. By examining the credit rating outcomes of authoritative rating agencies such as Standard & Poor’s and Moody’s, we observe an exponential distribution pattern between credit rating and default probability. We introduce an optimal classification method for credit rating, where the default probability conforms to an exponential distribution. The credit ratings are ranked from high to low, with the objective function minimizing the sum of differences between the default probability of each rating and the ideal default probability. This ensures that the credit rating classification results adhere to the pattern where default probability follows an exponential distribution. A genetic algorithm is employed to solve the established nonlinear credit rating classification model, overcoming the limitations of manual implementation and the tendency of general optimization algorithms to get trapped in local optima. This approach addresses the inadequacies of existing credit rating classification methods, which often overlook the systematic relationship between credit ratings and default probabilities.
This study uses empirical data from a commercial bank in China, comprising 3,045 settled loan transactions of small enterprises distributed across 28 regions including Beijing, Tianjin, Dalian, and Chengdu. The research investigates the default patterns of different credit ratings within this bank and further compares the distribution patterns of credit ratings given by Standard & Poor’s and Moody’s across various regions, such as Asian enterprises, emerging market enterprises, and Chinese enterprises. The comparison of rating results under different distribution patterns validates the effectiveness and adaptability of the proposed model.
The proposed research on credit rating in this paper presents a specific credit rating methodology tailored for small enterprises in commercial banks. Under the premise of controlling default risk in commercial banks, this method involves classifying customers into different credit ratings. By referencing the rating results of investment grade and speculative grade from Standard & Poor’s and Moody’s, the study evaluates the credit worthiness of small enterprises. This classification helps determine which credit rating categories correspond to credit worthy customers and which require close monitoring.
The default probability and loss given default parameters provided in the loan credit rating classification are core parameters for calculating default loss compensation in loan pricing. In the next step of the research, under the assumption that the default probability follows an exponential distribution, the distribution pattern of loss given default will also be considered. This will enable the investigation of the default probability and loss given default for small enterprises across different credit ratings.

Key words: credit rating, credit rating division, default probability, exponential distribution, small enterprises