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We present two methodologies on the estimation of rating transitionprobabilities within Markov and non-Markov frameworks. We first estimate acontinuous-time Markov chain using discrete (missing) data and derive a simplerexpression for the Fisher information matrix, reducing the computational timeneeded for the Wald confidence interval by a factor of a half. We provide anefficient procedure for transferring such uncertainties from the generatormatrix of the Markov chain to the corresponding rating migration probabilitiesand, crucially, default probabilities.  For our second contribution, we assume access to the full (continuous) dataset and propose a tractable and parsimonious self-exciting marked pointprocesses model able to capture the non-Markovian effect of rating momentum.Compared to the Markov model, the non-Markov model yields higher probabilitiesof default in the investment grades, but also lower default probabilities insome speculative grades. Both findings agree with empirical observations andhave clear practical implications.  We illustrate all methods using data from Moody's proprietary corporatecredit ratings data set. Implementations are available in the R package ctmcd.

Capturing Model Risk and Rating Momentum in the Estimation of Probabilities of Default and Credit Rating Migrations