Predictions of Default Probabilities in Structural Models of Debt
Hayne E. Leland
Volume 2, Number 2, Second Quarter 2004
This paper examines default probabilities predicted by alternative “structural” models of risky corporate debt. We focus on default probabilities rather than credit spreads because (i) they are not affected by additional market factors such as liquidity and tax differences; and (ii) prediction of the relative likelihood of default is often stated as the objective of bond ratings. We have three objectives:
(1) To distinguish “exogenous default” from “endogenous default” models
(2) To compare these models’ predictions of default probabilities, given common inputs
(3) To examine how well these models capture actual average default frequencies, as reflected in Moody’s (2001) corporate bond default data 1970-2000.
We find that endogenous and exogenous default boundary models fit observed default frequencies very well for horizons 5 years and longer, for both investment grade and non-investment grade ratings. Shorter-term default frequencies tend to be underestimated. This suggests that a jump component should be included in asset value dynamics.
Both types of structural models fit available default data equally well. But the models make different predictions about how default probabilities and recovery rates change with changes in debt maturity or asset volatility. Further data and testing will be needed to test these differences. Finally, we compare and contrast these structural models’ default predictions with a simplified version of the widely-used Moody’s-KMV “distance to default” model described in Crosbie and Bohn (2002).