Enhanced PD-implied ratings by targeting the credit rating migration matrix

Abstract

A high-quality and granular probability of default (PD) model is on many practical dimensions far superior to any categorical credit rating system. Business adoption of a PD model, however, needs to factor in the long-established business/regulatory conventions built around letter-based credit ratings. A mapping methodology that converts granular PDs into letter ratings via referencing the historical default experience of some credit rating agency exists in the literature. This paper improves the PD implied rating (PDiR) methodology by targeting the historical credit migration matrix instead of simply default rates. This enhanced PDiR methodology makes it possible to bypass the reliance on arbitrarily extrapolated target default rates for the AAA and AA⁺ categories, a necessity due to the fact that the historical realized default rates on these two top rating grades are typically zero.