This paper focuses on estimating, in Markov and non-Markov setups, rating transition probabilities crucial in financial regulation. We first deal with the estimation of a continuous time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computation time of Wald confidence intervals to less than half of the current standard. We provide an efficient procedure to transfer such uncertainties to the rating migrations and probabilities of default, which is of usefulness for practitioners.
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