A Markov approach to credit rating migration conditional on economic states

TL;DR

This paper models credit rating migrations using a Markov chain that incorporates economic state fluctuations, analyzing different rating philosophies and their asymptotic behaviors to improve credit risk assessment.

Contribution

It introduces a Markov-based framework for credit rating migration that accounts for economic states and formalizes PIT and TTC rating methodologies.

Findings

Analysis of asymptotic behavior of rating processes

Formalization of PIT and TTC rating philosophies

Application to a Merton-type firm-value process

Abstract

We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain. While the rating process itself possesses the Markov property only under restrictive conditions, methods from Markov theory can be used to derive the rating process' asymptotic behaviour. We use the mathematical framework to formalise and analyse different rating philosophies, such as point-in-time (PIT) and through-the-cycle (TTC) ratings. Furthermore, we introduce stochastic orders on the bivariate process' transition matrix to establish a consistent notion of "better" and "worse" ratings. Finally, the construction of PIT and TTC ratings is illustrated on a Merton-type firm-value process.