Predictions of Default Probabilities by Models with Dynamic Leverage Ratios

Abstract

This paper examines the term structures of default probabilities that are generated by the Collin-Dufresne and Goldstein model and a dynamic-leverage-ratio model. The dynamic-leverage-ratio model is capable of producing term structures of default probabilities which are consistent with some empirical observed default rates. It demonstrates that the leverage ratio is a determinant factor of default risk of firms. The Collin-Dufresne and Goldstein model which considers a leverage ratio mean- reverting towards a constant target leverage ratio however gives default probabilities lower than the empirical observed default rates. The predicted default probabilities of the models are sensitive to the dynamics of the leverage ratio, in particular the mean-reverting property of the leverage ratio towards a constant target leverage ratio.