Abstract
As an important part of the national economy, small enterprises are now facing the problem of financing difficulties, so a scientific and reasonable credit rating method for small enterprises is very important. This paper proposes a credit rating model of small enterprises based on optimal discriminant ability; the credit score gap of small enterprises within the same credit rating is the smallest, and the credit score gap of small enterprises between different credit ratings is the largest, which is the dividing principle of credit rating of small enterprises based on the optimal discriminant ability. Based on this principle, a nonlinear optimization model for credit rating division of small enterprises is built, and the approximate solution of the model is solved by a recursive algorithm with strong reproducibility and clear structure. The small enterprise credit rating division not only satisfies the principle that the higher the credit grade, the lower the default loss rate, but also satisfies the principle that the credit group of small enterprises matches the credit grade, with credit data of 3111 small enterprises from a commercial bank for empirical analysis. The innovation of this study is the maximum ratio of the sum of the dispersions of credit scores between different credit ratings and the sum of the dispersions of credit scores within the same credit rating as the objective function, as well as the default loss rate of the next credit grade strictly larger than the default loss rate of the previous credit grade as the inequality constraint; a nonlinear credit rating optimal partition model is constructed. It ensures that the small enterprises with small credit score gap are of the same credit grade, while the small enterprises with large credit score gap are of different credit grades, overcoming the disadvantages of the existing research that only considers the small enterprises with large credit score gap and ignores the small enterprises with small credit score gap. The empirical results show that the credit rating of small enterprises in this study not only matches the reasonable default loss rate but also matches the credit status of small enterprises. The test and comparative analysis with the existing research based on customer number distribution, K-means clustering, and default pyramid division show that the credit rating model in this study is reasonable and the distribution of credit score interval is more stable.
Highlights
Credit rating plays an extremely important role in the global economy. e unreasonable classification of credit rating may lead to the bankruptcy of enterprises, banks, and other institutions at the least or to financial crisis at the worst
We propose a credit rating model of small enterprises based on optimal discriminant ability, the maximum ratio of the sum of the dispersions of credit scores between different credit ratings and the sum of the dispersions of credit scores within the same credit rating as the objective function, and the default loss rate of the credit grade strictly larger than the default loss rate of the previous credit grade as the inequality constraint, as well as through recursive algorithm to solve the model. It ensures that the small enterprises with small credit score gap are of the same credit grade, while the small enterprises with large credit score gap are of different credit grades, which overcomes the disadvantages of the existing research that only considers the small enterprises with large credit score gap and ignores the small enterprises with small credit score gap
When the objective function value is 44951, the sample number and default loss rate corresponding to each credit grade are listed in column 2 and column 6 of Table 5 respectively. e credit score interval is determined by the credit score of the last small enterprise in each credit grade and is listed in column 4 of Table 5. e interval length is the value of the right endpoint of the credit score interval minus the left endpoint. e maximum value of the interval length is 31.3853, and the minimum value of the interval length is 1.6911, which has obvious differentiation and is listed in column 5 of Table 5
Summary
Credit rating plays an extremely important role in the global economy. e unreasonable classification of credit rating may lead to the bankruptcy of enterprises, banks, and other institutions at the least or to financial crisis at the worst. Gupton, based on the credit measurement model of Credit Metrics, divided the loan customers into eight credit grades of AAA, AA, A, BBB, BB, B, CCC, and D according to their different default probabilities [5]. Zhang used the characteristic function to describe the characteristics of the number of loans during the investigation period and proposed a default probability measurement method based on default intensity, which provided a new idea for banks and other financial institutions to conduct credit rating [7]. According to the bell-shaped distribution of the number of customers, Chi et al divided peasant households’ credit scores into 9 credit grades, such as AAA, AA, and A, so as to avoid the unreasonable phenomenon of excessive concentration of samples in AAA or C levels and ensure that most samples are concentrated in A and BBB levels [11]. Zhang and Chi established a multiobjective programming model with the minimum absolute value of the difference between the actual customer ratio and the ideal customer ratio based on normal distribution as the first objective function and the minimum difference between the loss rates of adjacent credit grades as the second objective function
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