Confidence Sets for Continuous-Time Rating Transition Probabilities

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 downgraded firms enter into a hidden, 'excited' state. Using data from Moody's we show how to estimate the model, and conclude that both default probabilities and confidence sets are strongly influenced by the introduction of hidden, excited states.