Cost-sensitive classification for rare events: an application to the credit rating model validation for SMEs

Receiver Operating Characteristic (ROC) curve is used to assess the discriminatory power of credit rating models. To identify the optimal threshold on the ROC curve, the iso-performance lines are used. The ROC curve and the iso-performance line assume equal classification error costs and that the two classification groups are relatively balanced. These assumptions are unrealistic in the application to credit risk. In order to remove these hypotheses, the curve of Classification Error Costs is proposed. Coherent with this curve, a methodology to identify the optimal threshold is suggested. Monte Carlo simulations that reproduce similar characteristics to the empirical credit scoring models for SMEs show that our proposal performs better that the iso-performance line. Finally, we apply the suggested methodologies to empirical data on Italian Small and Medium Enterprises (SMEs).