Debt Dynamics and Default Probabilities

Abstract

We derive a simple integral equation for the default probability over a finite time horizon of a company that makes coupon payments on its debt and infrequently returns to its leverage target by increasing its debt unless it defaults on its debt. Compared to the conventional (constant default barrier) formula, our formula permits the default barrier to change dynamically (i.e., is ratcheted up) over time. Hence it addresses the misspecification problem stemming from existing default probability predictions that do not take into the account that firms alter (optimally) their capital structure. We quantify the importance of our solution by (i) comparing it to the correct formula for a static model and (ii) analyzing default probabilities for different dynamic models.

Keywords: Bankruptcy, Barrier Options, Capital Structure, Default Probability, Integral Equation, Refinancing, Trade-off Model

JEL Classification: G13, G32, G33