Specification Analysis of Reduced-Form Credit Risk Models

This paper employs non-parametric specification tests developed in Hong and Li (2005) to evaluate several one-factor reduced-form credit risk models for actual default intensities. Using estimates for actual default probabilities provided by Moody’s KMV from 1994 to 2005 for 106 U.S. firms in seven industry groups, we strongly reject popular univariate affine model specifications. As a good compromise between goodness-of-fit and model simplicity we propose to assume that the logarithm of the actual default intensity follows an Ornstein-Uhlenbeck process, also known as the Black-Karasinski (BK) model. For the BK model specification, we find that there is substantial mean-reversion in actual log-default intensities, with an average half-time of roughly 18 months. Our results also show that the level of pairwise correlation in log-default intensities differs across industries. It is higher among oil and gas companies, and lower for healthcare firms.