Modeling rating transitions with instantaneous default

The time-continuous discrete-state Markov process is a common model for rating transitions. We present a low-dimensional model that jointly models defaults as a consequence of a cascade of downgrades, as well as an instantaneous default from a good rating grade, and study the resulting maximum-likelihood estimator. By using a martingale limit theorem, we show asymptotic normality. Using a regional cooperative bank portfolio as a sample, reveals that an increase in credit quality is more likely for corporate debtors with poor ratings, while for good ratings, a downgrade is more likely. The effect can be described as a contraction toward medium rating grades.