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An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds

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  • Ali Bora Yigibasioglu

    ()
    (ICMA Centre, University of Reading)

  • Carol Alexandra

    ()
    (ICMA Centre, University of Reading)

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    Abstract

    Arbitrage-free price bounds for convertible bonds are obtained assuming a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. Equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior are accommodated within this approach. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects, showing that uncertain volatility can capture the call premia so often observed in issuer’s call policies. Increasingly pessimistic values for the issuer’s substitution asset obtain as we introduce more uncertainty during the notice period. Volatility uncertainty is thus a useful mechanism to explain issuers delayed call policies.

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    Bibliographic Info

    Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2004-07.

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    Length: 42 pages
    Date of creation: Jun 2004
    Date of revision:
    Handle: RePEc:rdg:icmadp:icma-dp2004-07

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    Related research

    Keywords: call notice period; call premium; convertible bond; delayed calls; equity-linked default; stochastic interest rates; volatility uncertainty;

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    References

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    1. Asquith, Paul & Mullins, David W, Jr, 1991. " Convertible Debt: Corporate Call Policy and Voluntary Conversion," Journal of Finance, American Finance Association, vol. 46(4), pages 1273-89, September.
    2. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(04), pages 907-929, November.
    3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    4. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
    6. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    7. Ingersoll, Jonathan E, Jr, 1977. "An Examination of Corporate Call Policies on Convertible Securities," Journal of Finance, American Finance Association, vol. 32(2), pages 463-78, May.
    8. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 21-52.
    9. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    10. McConnell, John J & Schwartz, Eduardo S, 1986. " LYON Taming," Journal of Finance, American Finance Association, vol. 41(3), pages 561-76, July.
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    Cited by:
    1. Zhou, Qi-Yuan & Wu, Chong-Feng & Feng, Yun, 2007. "Decomposing and valuing callable convertible bonds: a new method based on exotic options," MPRA Paper 7421, University Library of Munich, Germany.

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