Optimization Heuristics for Determining Internal Rating Grading Scales

Basel II imposes regulatory capital on banks related to the default risk of their creditportfolio. Banks using an internal rating approach compute the regulatory capital frompooled probabilities of default. These pooled probabilities can be calculated by clusteringcredit borrowers into different buckets and computing the mean PD for each bucket. Theclustering problem can become very complex when Basel II regulations and real-worldconstraints are taken into account. Search heuristics have already proven remarkableperformance in tackling this problem. A Threshold Accepting algorithm is proposed, whichexploits the inherent discrete nature of the clustering problem. This algorithm is found tooutperform alternative methodologies already proposed in the literature, such as standardk-means and Differential Evolution. Besides considering several clustering objectives for agiven number of buckets, we extend the analysis further by introducing new methods todetermine the optimal number of buckets in which to cluster banks' clients.