The Rating Scale Paradox: An Application to the Solvency 2 Framework

Abstract

This work aims to identify the optimal rating scale for the rating system used by a credit insurance company subjected to the Solvency 2 regulatory framework. To do so, we apply and further develop a previously published result concerning the rating scale properties. The partition underlying a given rating scale must satisfy two needs of the rating model user: efficient information synthesis and stable semantics. Those needs cannot be addressed together in general. Nonetheless, it is possible to specify the partition as a linear combination of the two choices that meet one requirement each. We numerically show that, in general, the optimal combination is nontrivial under realistic assumptions and is mainly driven by the target return fixed by the company’s stakeholders and the debtors’ probability of default distribution.