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Pricing Callable Bonds By Means Of Green'S Function1

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  • Hans‐Jürg Büttler
  • Jorg Waldvogel

Abstract

This paper derives a closed‐form solutin for the price of the European and semi‐Amirican callable bond for two popular one‐factor models of the term structure of interest rates which have been proposed by Vasicek as well as Cox, Ingersoll, and Ross. the price is derived by means of repeated use of Green's function, which, in turn, is derived from a series solution of the partial differential equation to value a discount bond. the boundary conditions which lead to the well‐known formulae for the price of a discount bond are also identified. the algorithm to implement the explicit solution relies on numerical quadrature involving Green's function. It offers both higher accuracy and higher speed of computation than finite difference methods, which suffer from numerical instabilites due to discontinuous boundary values. For suitably small time steps, the proposed algorithm can also be applied to American callable bonds or to any American‐type option with Green's function being explicitly known.

Suggested Citation

  • Hans‐Jürg Büttler & Jorg Waldvogel, 1996. "Pricing Callable Bonds By Means Of Green'S Function1," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 53-88, January.
    • Handle: RePEc:bla:mathfi:v:6:y:1996:i:1:p:53-88
    DOI: 10.1111/j.1467-9965.1996.tb00112.x
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    Cited by:

    1. Barone-Adesi, Giovanni & Bermudez, Ana & Hatgioannides, John, 2003. "Two-factor convertible bonds valuation using the method of characteristics/finite elements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1801-1831, August.
    2. Ben-Ameur, Hatem & Breton, Michele & Karoui, Lotfi & L'Ecuyer, Pierre, 2007. "A dynamic programming approach for pricing options embedded in bonds," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2212-2233, July.
    3. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
    4. Marie-Claude Vachon & Anne Mackay, 2024. "A Unifying Approach for the Pricing of Debt Securities," Papers 2403.06303, arXiv.org, revised Oct 2024.
    5. Dmitry Muravey, 2014. "Interest rate models and Whittaker functions," Papers 1405.2459, arXiv.org.
    6. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 171-202, November.
    7. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    8. Lim, Dongjae & Li, Lingfei & Linetsky, Vadim, 2012. "Evaluating callable and putable bonds: An eigenfunction expansion approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1888-1908.

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