Debt Dynamics and Default Probabilities

Posted: 12 Jan 2020

See all articles by Dirk Hackbarth

Dirk Hackbarth

Boston University - Questrom School of Business; Centre for Economic Policy Research (CEPR); European Corporate Governance Institute (ECGI)

Yerkin Kitapbayev

Khalifa University

Date Written: December 15, 2019


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

Suggested Citation

Hackbarth, Dirk and Kitapbayev, Yerkin, Debt Dynamics and Default Probabilities (December 15, 2019). Available at SSRN: or

Dirk Hackbarth (Contact Author)

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

Centre for Economic Policy Research (CEPR) ( email )

United Kingdom

European Corporate Governance Institute (ECGI) ( email )

c/o the Royal Academies of Belgium
Rue Ducale 1 Hertogsstraat
1000 Brussels

Yerkin Kitapbayev

Khalifa University ( email )

Abu Dhabi
United Arab Emirates

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