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. 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. Compared to the Markov model, the non-Markov model yields higher probabilities of default in the investment grades, but also lower default probabilities in some speculative grades. This agrees with empirical observations and has clear practical implications. We illustrate all methods using data from Moody's proprietary corporate credit ratings data set. Implementations are available in the R package ctmcd.
We present two methodologies on the estimation of rating transition probabilities within Markov and non-Markov frameworks . We first estimate a continuous-time Markov chain using discrete (missing) data and derive a simpler expression for the Fisher information matrix, reducing the computational time needed for the Wald confidence interval by a factor of a half . 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 self-exciting marked point processes model able to capture the non-Markovian effect of rating momentum. Compared to the Markov model, the non-Markov model yields higher probabilities of default in the investment grades, but also lower default probabilities in some speculative grades. Both findings agree with empirical observations and have clear practical implications. We illustrate all methods using data from Moody's proprietary corporate credit ratings data set. Implementations are available in the R package ctmcd.
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