A Dependent Hidden Markov Model of Credit Quality

We propose a dependent hidden Markov model of credit quality. We suppose that the "true" credit quality is not observed directly but only through noisy observations given by posted credit ratings. The model is formulated in discrete time with a Markov chain observed in martingale noise, where "noise" terms of the state and observation processes are possibly dependent. The model provides estimates for the state of the Markov chain governing the evolution of the credit rating process and the parameters of the model, where the latter are estimated using the EM algorithm. The dependent dynamics allow for the so-called "rating momentum" discussed in the credit literature and also provide a convenient test of independence between the state and observation dynamics. 1. Introduction Credit ratings summarise a range of qualitative and quantitative information about the credit worthiness of debt issuers and are therefore a convenient signal for the credit quality of the debtor. The estimation of credit quality transition matrices is at the core of credit risk measures with applications to pricing and portfolio risk management. In view of pending regulations regarding the calculation of capital requirements for banks, there is renewed interest in efficiency of credit ratings as indicators of credit quality and models of their dynamics (Basel Committee on Banking Supervision [1]). In the study of credit quality dynamics, it is convenient to assume that the credit rating process is a time-homogeneous Markov chain, with past changes in credit quality characterised by a transition matrix. The assumptions of time homogeneity and Markovian behaviour of the rating process have been challenged by some empirical studies; see, for example, Bangia et al. [2] or Lando and Sk？deberg [3]. In particular, it has been proposed that ratings exhibit “rating momentum” or “drift,” where a rating change in response to a change in credit quality does not fully reflect that change in credit quality. As pointed out by L？ffler in [4, 5], these violations of information efficiency could be the result of some of the agencies’ rating policies, namely, rating through the cycle and avoiding rating reversals. In recent years, a number of modelling alternatives were suggested to address departures from the Markov assumption. In Frydman and Schuermann [6], a mixture of two independent continuous time homogeneous Markov chains is proposed for the ratings migration process, so that the future distribution of a firm’s ratings depends not only its current rating but also on the past history of