A Structural Model of Contingent Bank Capital

46 Pages Posted: 24 Apr 2010 Last revised: 31 Aug 2010

Date Written: April 23, 2010

Abstract

This paper develops a structural credit risk model of a bank that issues deposits, shareholders’ equity, and fixed or floating coupon bonds in the form of contingent capital or subordinated debt. The return on the bank’s assets follows a jump-diffusion process, and default-free interest rates are stochastic. The equilibrium pricing of the bank’s deposits, contingent capital, and shareholders’ equity is studied for various parameter values characterizing the bank’s risk and the contractual terms of its contingent capital. Allowing for the possibility of jumps in the bank’s asset value, as might occur during a financial crisis, has distinctive implications for valuing contingent capital. Credit spreads on contingent capital are higher the lower is the value of shareholders’ equity at which conversion occurs and the larger is the conversion discount from the bond’s par value. The effect of requiring a decline in a financial stock price index for conversion (dual price trigger) is to make contingent capital more similar to non-convertible subordinated debt. The paper also examines the bank’s incentive to increase risk when it issues different forms of contingent capital as well as subordinated debt. In general, a bank that issues contingent capital has a moral hazard incentive to raise its assets’ risk of jumps, particularly when the value of equity at the conversion threshold is low. However, moral hazard when issuing contingent capital tends to be less than when issuing subordinated debt. Because it reduces effective leverage and the pressure for government bailouts, contingent capital deserves serious consideration as part of a package of reforms that stabilize the financial system and eliminate “Too-Big-to-Fail.”

Suggested Citation

Pennacchi, George G., A Structural Model of Contingent Bank Capital (April 23, 2010). FRB of Cleveland Working Paper No. 10-04. Available at SSRN: https://ssrn.com/abstract=1595080

George G. Pennacchi (Contact Author)

University of Illinois ( email )

4041 BIF, Box 25
515 East Gregory Drive
Champaign, IL 61820
United States
217-244-0952 (Phone)

HOME PAGE: http://www.business.illinois.edu/gpennacc/

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