Efficient estimation of transition rates between credit ratings from observations at discrete time points

The paper demonstrates how discrete time credit rating data (e.g. annual observations) can be analysed by means of a continuous-time Markov model. Two methods for estimating the transition intensities are given: the EM algorithm and an MCMC approach. The estimated transition intensities can be used to estimate the matrix of probabilities of transitions between all credit ratings, including default probabilities, over any time horizon. Thus the advantages of a continuous-time model can be obtained without continuous-time data. Estimates of the variance of estimators as well as confidence and credibility intervals are presented, and a test for equality of two intensity matrices is proposed. The methods are demonstrated by analysis of a large data set drawn from Moody's Corporate Bond Default Database, where reasonable estimates are obtained from annual observations.