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Confidence sets for continuous-time rating

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This paper addresses the estimation of default probabilities and associatedconfidence sets with special focus on rare events. Research on rating transitiondata has documented a tendency for recently downgraded issuers tobe at an increased risk of experiencing further downgrades compared to issuersthat have held the same rating for a longer period of time. To capturethis non-Markov effect we introduce a continuous-time hidden Markov chainmodel in which downgrades firms enter into a hidden, ’excited’ state. Usingdata from Moody’s we estimate the parameters of the model, and concludethat both default probabilities and confidence sets are strongly influenced bythe introduction of hidden excited states.

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Jens Christensen, Ernst Hansen, David Lando

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