Model Risk and Rating Momentum in Default and Migration Probabilities

Summary

The document presents two approaches to estimating credit rating transitions and default probabilities. The first estimates a continuous-time Markov chain from discrete, potentially incomplete observations. It derives a simpler Fisher information expression to reduce computation for Wald confidence intervals, then describes how to propagate uncertainty from the transition generator to migration and default probabilities.

The second approach uses continuous observations in a self-exciting marked point process to capture rating momentum, a non-Markov effect. Compared with the Markov model, it produces higher default probabilities for investment-grade ratings and lower probabilities for some speculative grades, which the authors say align with empirical observations. The methods are illustrated using Moody’s proprietary corporate ratings data. The excerpt does not provide sample details or performance measures, and the proprietary data may limit independent replication.

Key ideas

• A continuous-time Markov chain can estimate rating transitions from discrete and incomplete data.
• A simplified Fisher information calculation reduces the computation required for Wald confidence intervals.
• Uncertainty in the transition generator can be transferred to migration and default probability estimates.
• A self-exciting marked point process captures rating momentum when continuous data are available.
• The non-Markov model changes estimated default probabilities differently across investment and speculative grades.

Tags

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


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









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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