Capturing model risk and rating momentum in the estimation of probabilities of default and credit rating migrations

Gonçalo dos Reis, M. Pfeuffer, Greig Smith

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
21 Downloads (Pure)


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 use Moody's proprietary corporate credit rating data set. Parts of our implementation are available in the R package ctmcd.

Original languageEnglish
Pages (from-to)1069-1083
Number of pages15
JournalQuantitative Finance
Issue number7
Publication statusPublished - 2 Jul 2020


  • Confidence intervals
  • Generator matrix
  • Markov chain
  • Point-process
  • Primary: 60G55
  • Rating momentum
  • Secondary: 62F15, 91G40


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