Credit Rating Model of Small Enterprises Based on Optimal Discriminant Ability and Its Empirical Study

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.