Christensen, Jens, Ernst Hansen, and David Lando, "Confidence Sets for Continuous-time Rating Transition Probabilities", Journal of Banking & Finance, Vol. 28, No. 11, (November 2004), pp. 2575-2602.
Abstract: This paper addresses the estimation of default probabilities and associated confidence sets with special focus on rare events. Research on rating transition data has documented a tendency for recently downgraded issuers to be at an increased risk of experiencing further downgrades compared to issuers that have held the same rating for a longer period of time. To capture this non-Markov effect we introduce a continuous-time hidden Markov chain model in which downgrades firms enter into a hidden, 'excited' state. Using data from Moody's we estimate the parameters of the model, and conclude that both default probabilities and confidence sets are strongly influenced by the introduction of hidden excited states.