A Continuous-Time Hidden Markov Model of Credit Quality Underlying Published Agencies' Ratings

This paper presents a Continuous-Time Hidden Markov Model (CT-HMM) of debt issuers' credit quality dynamics. We observe ratings published by several agencies (e.g., Standard & Poor's, Moody's, Fitch) for one or several issuers (e.g., countries) and assume that we can find a maximum-likelihood estimate of the "true" rating underlying data. Using CT-HMM instead of the standard discrete HMM enables to deal with irregular credit events. Our model is specifically adapted to handle several agencies and/or several debt issuers: we can infer the hidden rating of a group without using a mean approximation. The model parameters are estimated using the Expectation-Maximization algorithm, with adapted filters and an ad-hoc numerical method with no discretization error. A set of experiments on both simulated and real sovereign credit ratings illustrates our approach