Which Curve Fits Best: Fitting ROC Curve Models to Empirical Credit-Scoring Data

In the practice of credit-risk management, the models for receiver operating characteristic (ROC) curves are helpful in describing the shape of an ROC curve, estimating the discriminatory power of a scorecard, and generating ROC curves without underlying data. The primary purpose of this study is to review the ROC curve models proposed in the literature, primarily in biostatistics, and to fit them to actual credit-scoring ROC data in order to determine which models could be used in credit-risk-management practice. We list several theoretical models for an ROC curve and describe them in the credit-scoring context. The model list includes the binormal, bigamma, bibeta, bilogistic, power, and bifractal curves. The models are then tested against empirical credit-scoring ROC data from publicly available presentations and papers, as well as from European retail lending institutions. Except for the power curve, all the presented models fit the data quite well. However, based on the results and other favourable properties, it is suggested that the binormal curve is the preferred choice for modelling credit-scoring ROC curves.