Evaluating callable and putable bonds: An eigenfunction expansion approach
AbstractWe 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 InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 36 (2012)
Issue (Month): 12 ()
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Web page: http://www.elsevier.com/locate/jedc
Interest rate models; Callable bonds; Options embedded in bonds; Optimal stopping; Stochastic games; Eigenfunction expansions; Option pricing; Stochastic time changes;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Vyacheslav Gorovoy & Vadim Linetsky, 2007. "Intensity-Based Valuation Of Residential Mortgages: An Analytically Tractable Model," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 541-573.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Hans-Jürg Büttler & Jorg Waldvogel, 1996. "Pricing Callable Bonds By Means Of Green'S Function," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 53-88.
- Alan L. Lewis, 1998. "Applications of Eigenfunction Expansions in Continuous-Time Finance," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 349-383.
- Markus Leippold & Liuren Wu, 2002.
"Asset Pricing Under The Quadratic Class,"
- 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.
- Consiglio, Andrea & Zenios, Stavros A., 1997. "A model for designing callable bonds and its solution using tabu search," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1445-1470, June.
- 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.
- 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.
- Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-62.
- 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.
- 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.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- O. E. Barndorff-Nielsen & S. Z. Levendorskii, 2001. "Feller processes of normal inverse Gaussian type," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 318-331.
- 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.
- 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.
- 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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