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A structural model of contingent bank capital

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  • George Pennacchi

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 haracterizing 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

  • George Pennacchi, 2010. "A structural model of contingent bank capital," Working Paper 1004, Federal Reserve Bank of Cleveland.
  • Handle: RePEc:fip:fedcwp:1004
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    Cited by:

    1. Daniël Vullings, 2016. "Contingent convertible bonds with floating coupon payments: fixing the equilibrium problem," DNB Working Papers 517, Netherlands Central Bank, Research Department.
    2. Feldman, Ron J. & Stern, Gary H., 2010. "The Squam Lake Report: Observations from two policy professionals," Journal of Monetary Economics, Elsevier, vol. 57(7), pages 903-912, October.
    3. Yehning Chen & Iftekhar Hasan, 2011. "Subordinated Debt, Market Discipline, and Bank Risk," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(6), pages 1043-1072, September.
    4. Hilscher, Jens & Raviv, Alon, 2014. "Bank stability and market discipline: The effect of contingent capital on risk taking and default probability," Journal of Corporate Finance, Elsevier, vol. 29(C), pages 542-560.
    5. Mendicino, Caterina & Nikolov, Kalin & Suarez, Javier, 2017. "Equity versus bail-in debt in banking: an agency perspective," ESRB Working Paper Series 50, European Systemic Risk Board.
    6. Murphy, Gareth & Walsh, Mark & Willison, Matthew, 2012. "Financial Stability Paper No 16: Precautionary contingent capital," Bank of England Financial Stability Papers 16, Bank of England.
    7. Paul Glasserman & Behzad Nouri, 2012. "Contingent Capital with a Capital-Ratio Trigger," Management Science, INFORMS, vol. 58(10), pages 1816-1833, October.
    8. Masror Khah, Sara Abed & Vermaelen, Theo & Wolff, Christian C, 2015. "The Determinants of CoCo Bond Prices," CEPR Discussion Papers 10996, C.E.P.R. Discussion Papers.
    9. Acharya, Viral V. & Mehran, Hamid & Thakor, Anjan V., 2010. "Caught between Scylla and Charybdis? Regulating bank leverage when there is rent seeking and risk shifting," Staff Reports 469, Federal Reserve Bank of New York, revised 01 Dec 2014.
    10. Degryse, Hans & Smedts, Kristien & Van Hulle, Cynthia, 2017. "Risk-sharing benefits and the capital structure of insurance companies," CEPR Discussion Papers 11838, C.E.P.R. Discussion Papers.
    11. Das, Sanjiv R. & Kim, Seoyoung, 2015. "Credit spreads with dynamic debt," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 121-140.
    12. Markus Buergi, 2013. "Pricing contingent convertibles: a general framework for application in practice," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(1), pages 31-63, March.
    13. repec:ces:ifodic:v:7:y:2009:i:3:p:14567082 is not listed on IDEAS
    14. Gupta, Anshul & Akuzawa, Toshinao & Nishiyama, Yoshihiko, 2013. "Quantitative evaluation of contingent capital and its applications," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 457-486.
    15. Barucci, Emilio & Del Viva, Luca, 2012. "Countercyclical contingent capital," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1688-1709.
    16. Atreya, Nikhil & Mjøs, Aksel & Persson, Svein-Arne, 2015. "Making Bank: Why High Bank Leverage is Optimal - for the Bank's Shareholders," Discussion Papers 2015/33, Norwegian School of Economics, Department of Business and Management Science.
    17. Dandan Song & Zhaojun Yang, 2016. "Contingent Capital, Real Options, and Agency Costs," International Review of Finance, International Review of Finance Ltd., vol. 16(1), pages 3-40, March.
    18. Lo, Chien-Ling & Lee, Jin-Ping & Yu, Min-Teh, 2013. "Valuation of insurers’ contingent capital with counterparty risk and price endogeneity," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5025-5035.
    19. George M. von Furstenberg, 2011. "Concocting Marketable Cocos," Working Papers 222011, Hong Kong Institute for Monetary Research.
    20. McDonald, Robert L., 2013. "Contingent capital with a dual price trigger," Journal of Financial Stability, Elsevier, vol. 9(2), pages 230-241.
    21. Allen, Linda & Tang, Yi, 2016. "What’s the contingency? A proposal for bank contingent capital triggered by systemic risk," Journal of Financial Stability, Elsevier, vol. 26(C), pages 1-14.
    22. B. Espen Eckbo, 2010. "Banking System Bailout-Scandinavian Style," Journal of Applied Corporate Finance, Morgan Stanley, vol. 22(3), pages 85-93.

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    Keywords

    Bank capital ; Risk ; Bank failures;

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