Calibration and mapping of credit scores by riding the cumulative accuracy profile

Marco van der Burgt

Abstract

A lot of literature on credit risk scoring techniques exists, but less research is available regarding the mapping of credit scores to ratings and the calibration of ratings. This paper introduces an algorithm for mapping credit scores to credit ratings and estimating a probability of default (PD) per rating grade. The algorithm is based on stepwise partitioning of the cumulative accuracy profile, such that requirements like stable ratings and a monotonous PD scale, as stated by the European Banking Association’s regulatory technical standards, are fulfilled. We test the algorithm by simulating different PD models and score distributions. These tests reveal that the algorithm maps credit scores to significantly different rating grades. Each rating cor- responds to a PD, which is a monotonous function of the rating grade. The tests also show that the total number of rating grades, which result from the mapping algorithm, strongly depends on the ability of the scoring model to discriminate between defaulting and nondefaulting counterparties.