Combination of linear discriminant analysis and expert opinion for the construction of credit rating models: The case of SMEs

The construction of an internal rating model is the main task for the bank in the framework of the IRB-foundation approach the fact that it is necessary to determine the probability of default by rating class. As a result, several statistical approaches can be used, such as logistic regression and linear discriminant analysis to express the relationship between the default and the financial, managerial and organizational characteristics of the enterprise. In this paper, we will propose a new approach to combine the linear discriminant analysis and the expert opinion by using the Bayesian approach. Indeed, we will build a rating model based on linear discriminant analysis and we will use the bayesian logic to determine the posterior probability of default by rating class. The reliability of experts' estimates depends on the information collection process. As a result, we have defined an information collection approach that allows to reduce the imprecision of the estimates by using the Delphi method. The empirical study uses a portfolio of SMEs from a Moroccan bank. This permitted the construction of the statistical rating model and the associated Bayesian models; and to compare the capital requirement determined by these models.