Contingent Capital, Tail Risk, and Debt-Induced Collapse

Chen, Nan; Glasserman, Paul; Nouri, Behzad; Pelger, Markus

doi:10.2139/ssrn.2361304

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Contingent Capital, Tail Risk, and Debt-Induced Collapse

Columbia Business School Research Paper No. 13-90

49 Pages Posted: 29 Nov 2013 Last revised: 18 Jun 2015

See all articles by Nan Chen

Nan Chen

The Chinese University of Hong Kong (CUHK)

Markus Pelger

Stanford University - Department of Management Science & Engineering

Date Written: March 2015

Abstract

Contingent capital in the form of debt that converts to equity as a bank approaches financial distress offers a potential solution to the problem of banks that are too big to fail. This paper studies the design of contingent convertible bonds and their incentive effects in a structural model with endogenous default, debt rollover, and tail risk in the form of downward jumps in asset value. We show that once a firm issues contingent convertibles, the shareholders’ optimal bankruptcy boundary can be at one of two levels: a lower level with a lower default risk or a higher level at which default precedes conversion. An increase in the firm’s total debt load can move the firm from the first regime to the second, a phenomenon we call debt-induced collapse because it is accompanied by a sharp drop in equity value. We show that setting the contractual trigger for conversion sufficiently high avoids this hazard. With this condition in place, we investigate the effect of contingent capital and debt maturity on capital structure, debt overhang, and asset substitution. We also calibrate the model to past data on the largest U.S. bank holding companies to see what impact contingent convertible debt might have had under the conditions of the financial crisis.

Keywords: Contingent convertible debt, bail-in debt, capital structure, too big to fail

JEL Classification: G12, G13, G32

Suggested Citation: Suggested Citation

Chen, Nan and Glasserman, Paul and Nouri, Behzad and Pelger, Markus, Contingent Capital, Tail Risk, and Debt-Induced Collapse (March 2015). Columbia Business School Research Paper No. 13-90, Available at SSRN: https://ssrn.com/abstract=2361304 or http://dx.doi.org/10.2139/ssrn.2361304