The Credit Market Handbook: Advanced Modeling Issues

CHAPTER 2

Predictions of Default Probabilities in Structural Models of Debt

Hayne E. Leland^a

This chapter examines default probabilities predicted by alternative “structural” models of risky coporate debt. We focus on default probabilities rather then credit spreads because (1) they are not affected by additional market factors such as liquidity and tax differences, and (2) 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 the endogenous and exogenous default boundary models fit observed default frequencies very well for horizons 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 ...