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Convertible Bonds: Risks and Optimal Strategies

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  • Haishi Huang

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    Abstract

    Within the structural approach for credit risk models we discuss the optimal exercise of the callable and convertible bonds. The Vasi˘cek–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.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse07_2010.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse07_2010.

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    Length: 29
    Date of creation: 12 Dec 2009
    Date of revision:
    Handle: RePEc:bon:bonedp:bgse07_2010

    Contact details of provider:
    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: Convertible bond; game option; uncertain volatility; interest rate risk;

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    1. 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.
    2. Christoph Kühn & Andreas E. Kyprianou, 2007. "Callable Puts As Composite Exotic Options," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 487-502.
    3. 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.
    4. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    5. RØdiger Frey, 2000. "Superreplication in stochastic volatility models and optimal stopping," Finance and Stochastics, Springer, vol. 4(2), pages 161-187.
    6. 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, 05.
    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. 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.
    9. Adam Smith, 2002. "American options under uncertain volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 123-141.
    10. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(02), pages 239-248, June.
    11. 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.
    12. 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.
    13. Bert Menkveld & Ton Vorst, 1998. "A Pricing Model for American Options with Stochastic Interest Rates," Tinbergen Institute Discussion Papers 98-028/2, Tinbergen Institute.
    14. 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.
    15. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
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