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Evaluating callable and putable bonds: An eigenfunction expansion approach

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  • Lim, Dongjae
  • Li, Lingfei
  • Linetsky, Vadim
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    Abstract

    We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and put dates, the callable and putable bond pricing function is the value function of a stochastic game with stopping times. Under some technical conditions, it is shown to have an eigenfunction expansion in eigenfunctions of the pricing operator with the expansion coefficients determined through a backward recursion. For popular short rate diffusion models, such as CIR, Vasicek, 3/2, the method is orders of magnitude faster than the alternative approaches in the literature. In contrast to the alternative approaches in the literature that have so far been limited to diffusions, the method is equally applicable to short rate jump–diffusion and pure jump models constructed from diffusion models by Bochner's subordination with a Lévy subordinator.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 36 (2012)
    Issue (Month): 12 ()
    Pages: 1888-1908

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    Handle: RePEc:eee:dyncon:v:36:y:2012:i:12:p:1888-1908

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Interest rate models; Callable bonds; Options embedded in bonds; Optimal stopping; Stochastic games; Eigenfunction expansions; Option pricing; Stochastic time changes;

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    1. 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.
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    13. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78.
    14. Egami, Masahiko, 2010. "A game options approach to the investment problem with convertible debt financing," Journal of Economic Dynamics and Control, Elsevier, vol. 34(8), pages 1456-1470, August.
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    16. 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.
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    Cited by:
    1. Li, Lingfei & Linetsky, Vadim, 2014. "Optimal stopping in infinite horizon: An eigenfunction expansion approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 122-128.

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