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Convertible Bonds: Risks and Optimal Strategies

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  • Huang, Haishi

Abstract

Within the structural approach for credit risk models we discuss the optimal exercise of the callable and convertible bonds. The Vasiček-model is applied to incorporate interest rate risk into the firm’s value process which follows a geometric Brownian motion. Finally, we derive pricing bounds for convertible bonds in an uncertain volatility model, i.e. when the volatility of the firm value process lies between two extreme values.

Suggested Citation

  • Huang, Haishi, 2010. "Convertible Bonds: Risks and Optimal Strategies," Bonn Econ Discussion Papers 07/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    • Handle: RePEc:zbw:bonedp:072010
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    References listed on IDEAS

    as
    1. Albert Menkveld & Ton Vorst, 2000. "A Pricing Model for American Options with Gaussian Interest Rates," Annals of Operations Research, Springer, vol. 100(1), pages 211-226, December.
    2. RØdiger Frey, 2000. "Superreplication in stochastic volatility models and optimal stopping," Finance and Stochastics, Springer, vol. 4(2), pages 161-187.
    3. Adam Smith, 2002. "American options under uncertain volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 123-141.
    4. Pascal Francois, 2004. "Capital Structure and Asset Prices: Some Effects of Bankruptcy Procedures," The Journal of Business, University of Chicago Press, vol. 77(2), pages 387-412, April.
    5. Brennan, M J & Schwartz, Eduardo S, 1977. "Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion," Journal of Finance, American Finance Association, vol. 32(5), pages 1699-1715, December.
    6. Viral V. Acharya & Jennifer N. Carpenter, 2002. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy," Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1355-1383.
    7. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(2), pages 239-248, June.
    8. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    9. 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.
    10. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    11. Bert Menkveld & Ton Vorst, 1998. "A Pricing Model for American Options with Stochastic Interest Rates," Tinbergen Institute Discussion Papers 98-028/2, Tinbergen Institute.
    12. Ingersoll, Jonathan E, Jr, 1977. "An Examination of Corporate Call Policies on Convertible Securities," Journal of Finance, American Finance Association, vol. 32(2), pages 463-478, May.
    13. Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
    14. Christoph Kühn & Andreas E. Kyprianou, 2007. "Callable Puts As Composite Exotic Options," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 487-502, October.
    15. 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.
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    More about this item

    Keywords

    Convertible bond; game option; uncertain volatility; interest rate risk;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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