Infinitesimal Generator Estimation with an Application to Credit Risk

Credit risk migration is often modeled as a first-order, time-homogeneous Markov chain. Due to the high cost of continuously monitoring an obligor, most financial institutions risk-rate loans and other fixed-income securities on an infrequent basis, resulting in discrete point-in-time transition-probability matrices for credit risk management and/or reporting. Several methods have been proposed for approximating the infinitesimal generator matrix, the matrix exponential of which approximates the observed point-in-time matrix. We motivate and propose a novel non-parametric method for approximating a generator matrix for bond ratings in practice, and compare the results to existing empirical methods. The results suggest that our method has merit and may be more flexible than existing ones. Further, in some cases, the best method to use appears to depend on the bond rating itself.