2024/03/21 by Michael Kalkbrener, Kalkbrener, Michael, Natalie Packham +1
Economics, Econometrics and Finance · #60E15 #60J05 #60J20 #91G40 #Credit Risk and Financial Regulations #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Risk Management (q-fin.RM)
paper · pdf · doi:10.48550/arxiv.2403.14868
openalex publication_date 2024/03/21 · openalex created_date 2024/03/26 · openalex updated_date 2026/07/28
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.