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Contingent Capital with a Capital-Ratio Trigger

Author

Listed:
  • Paul Glasserman

    () (Graduate School of Business, Columbia University, New York, New York 10027)

  • Behzad Nouri

    () (Industrial Engineering and Operations Research Department, Columbia University, New York, New York 10027)

Abstract

Contingent capital in the form of debt that converts to equity when a bank faces financial distress has been proposed as a mechanism to enhance financial stability and avoid costly government rescues. Specific proposals vary in their choice of conversion trigger and conversion mechanism. We analyze the case of contingent capital with a capital-ratio trigger and partial and ongoing conversion. The capital ratio we use is based on accounting or book values to approximate the regulatory ratios that determine capital requirements for banks. The conversion process is partial and ongoing in the sense that each time a bank's capital ratio reaches the minimum threshold, just enough debt is converted to equity to meet the capital requirement, so long as the contingent capital has not been depleted. We derive closed-form expressions for the market value of such securities when the firm's asset value is modeled as geometric Brownian motion, and from these we get formulas for the fair yield spread on the convertible debt. A key step in the analysis is an explicit expression for the fraction of equity held by the original shareholders and the fraction held by converted investors in the contingent capital. This paper was accepted by Gérard P. Cachon, stochastic models and simulation.

Suggested Citation

  • Paul Glasserman & Behzad Nouri, 2012. "Contingent Capital with a Capital-Ratio Trigger," Management Science, INFORMS, vol. 58(10), pages 1816-1833, October.
  • Handle: RePEc:inm:ormnsc:v:58:y:2012:i:10:p:1816-1833
    DOI: 10.1287/mnsc.1120.1520
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    File URL: http://dx.doi.org/10.1287/mnsc.1120.1520
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    References listed on IDEAS

    as
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    3. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Suresh Sundaresan & Zhenyu Wang, 2010. "Design of contingent capital with a stock price trigger for mandatory conversion," Staff Reports 448, Federal Reserve Bank of New York, revised 01 Nov 2011.
    6. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    7. Samu Peura & Jussi Keppo, 2006. "Optimal Bank Capital with Costly Recapitalization," The Journal of Business, University of Chicago Press, vol. 79(4), pages 2163-2202, July.
    8. Pennacchi, George & Vermaelen, Theo & Wolff, Christian C. P., 2014. "Contingent Capital: The Case of COERCs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(3), pages 541-574, June.
    9. Alon Raviv, 2004. "Bank Stability and Market Discipline: Debt-for-Equity Swap versus Subordinated Notes," Finance 0408003, University Library of Munich, Germany.
    10. George Pennacchi, 2010. "A structural model of contingent bank capital," Working Papers (Old Series) 1004, Federal Reserve Bank of Cleveland, revised 2010.
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