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A numerical PDE approach for pricing callable bonds

Author

Listed:
  • Y. D'Halluin
  • P. A. Forsyth
  • K. R. Vetzal
  • G. Labahn

Abstract

Many debt issues contain an embedded call option that allows the issuer to redeem the bond at specified dates for a specified price. The issuer is typically required to provide advance notice of a decision to exercise this call option. The valuation of these contracts is an interesting numerical exercise because discontinuities may arise in the bond value or its derivative at call and/or notice dates. Recently, it has been suggested that finite difference methods cannot be used to price callable bonds requiring notice. Poor accuracy was attributed to discontinuities and difficulties in handling boundary conditions. As an alternative, a semi-analytical method using Green's functions for valuing callable bonds with notice was proposed. Unfortunately, the Green's function method is limited to special cases. Consequently, it is desirable to develop a more general approach. This is provided by using more advanced techniques such as flux limiters to obtain an accurate numerical partial differential equation method. Finally, in a typical pricing model an inappropriate financial condition is required in order to properly specify boundary conditions for the associated PDE. It is shown that a small perturbation of such a model is free from such artificial conditions.

Suggested Citation

  • Y. D'Halluin & P. A. Forsyth & K. R. Vetzal & G. Labahn, 2001. "A numerical PDE approach for pricing callable bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(1), pages 49-77.
    • Handle: RePEc:taf:apmtfi:v:8:y:2001:i:1:p:49-77
    DOI: 10.1080/13504860110046885
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    References listed on IDEAS

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    Cited by:

    1. Dongjae Lim & Lingfei Li & Vadim Linetsky, 2012. "Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach," Papers 1206.5046, arXiv.org.
    2. Marie-Claude Vachon & Anne Mackay, 2024. "A Unifying Approach for the Pricing of Debt Securities," Papers 2403.06303, arXiv.org, revised Oct 2024.
    3. Erik Ekstrom & Per Lotstedt & Johan Tysk, 2009. "Boundary Values and Finite Difference Methods for the Single Factor Term Structure Equation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 253-259.
    4. d'Halluin, Y. & Forsyth, P.A. & Vetzal, K.R., 2007. "Wireless network capacity management: A real options approach," European Journal of Operational Research, Elsevier, vol. 176(1), pages 584-609, January.
    5. C.K. Anderson & M. Davison & H. Rasmussen, 2004. "Revenue management: A real options approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 686-703, August.
    6. 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.
    7. Hatem Ben-Ameur & Michèle Breton, 2004. "A Dynamic Programming Approach for Pricing Options Embedded in Bonds," Computing in Economics and Finance 2004 237, Society for Computational Economics.
    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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