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Theoretical And Numerical Valuation Of Callable Bonds

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  • Dejun Xie

Abstract

This paper studies the value of a callable bond and the bond issuer’s optimal financial decision regarding whether to continue the investment on the market or call the bond. Assume the market investment return follows a stochastic model, the value of contract is formulated as a partial differential equation system embedded with a free boundary, defining the level of market return rate at which it is optimal for the issuer to call the bond. A fundamental solution of the partial differential equation is derived, and used to formulate the value of the bond. A bisection scheme is implemented to solve the problem numerically.

Suggested Citation

  • Dejun Xie, 2009. "Theoretical And Numerical Valuation Of Callable Bonds," The International Journal of Business and Finance Research, The Institute for Business and Finance Research, vol. 3(2), pages 71-82.
  • Handle: RePEc:ibf:ijbfre:v:3:y:2009:i:2:p:71-82
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    References listed on IDEAS

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    1. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2008. "Simulation-based pricing of convertible bonds," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 310-331, March.
    2. 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.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    6. Brennan, Michael J. & Schwartz, Eduardo S., 1977. "Savings bonds, retractable bonds and callable bonds," Journal of Financial Economics, Elsevier, vol. 5(1), pages 67-88, August.
    7. Lishang Jiang, 2005. "Mathematical Modeling and Methods of Option Pricing," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5855, February.
    8. Buttler, Hans-Jurg, 1995. "Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy," Economic Journal, Royal Economic Society, vol. 105(429), pages 374-384, March.
    9. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(2), pages 235-254, June.
    10. 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.
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    Cited by:

    1. Saied Simozar, 2020. "Near Exact Calculation of American Options," Applied Economics and Finance, Redfame publishing, vol. 7(3), pages 55-69, May.

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    More about this item

    Keywords

    Callable Bonds; optimal financial decision; stochastic model;
    All these keywords.

    JEL classification:

    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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