Before revision:  We provide an efficient procedure to transfer such uncertainties to the rating migrations and probabilities of default, which is of usefulness for practitioners. When a full data set is available, we propose a tractable and parsimonious model based on self-exciting marked point processes that captures the non-Markovian effect of rating momentum.
After revision:  We provide an efficient procedure for transferring such uncertainties from the generator matrix of the Markov chain to the corresponding rating migration probabilities and, crucially, default probabilities. For our second contribution, we assume access to the full (continuous) data set and propose a tractable and parsimonious model based on self-exciting marked point processes that captures the non-Markovian effect of rating momentum.