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On the Suboptimality of Single-Factor Exercise Strategies for Bermudan Swaptions

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  • Svenstrup, Mikkel

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    (Department of Finance, Aarhus School of Business)

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    Abstract

    In this paper we examine the cost of using recalibrated single-factor models to determine the exercise strategy for Bermudan swaptions in a multi-factor world. We demonstrate that single-factor exercise strategies applied in a multi-factor world only give rise to economically insignificant losses. Furthermore, we find that the conditional model risk as defined in Longstaff, Santa-Clara & Schwartz (2001), is statistically insignificant given the number of observations. Additional tests using the Primal-Dual algorithm of Andersen & Broadie (2001) indicate that losses found in Longstaff et al. (2001) cannot as claimed be ascribed to the number of factors. Finally we find that for valuation of Bermudan swaptions with long exercise periods, the simple approach proposed in Andersen (2000) is outperformed by the Least Square Monte Carlo method of Longstaff & Schwartz (2001) and, surprisingly, also by the exercise strategies from the single-factor models.

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    Bibliographic Info

    Paper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series Finance Working Papers with number 02-24.

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    Length: 38 pages
    Date of creation: 09 May 2003
    Date of revision:
    Handle: RePEc:hhb:aarfin:2002_024

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    Postal: The Aarhus School of Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
    Fax: + 45 86 15 19 43
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    Related research

    Keywords: Bermudan swaption; American option; Least Square Monte Carlo; Libor Market Model; Model Risk; Model Calibration;

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    1. Miltersen, K. & K. Sandmann & D. Sondermann, 1994. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Discussion Paper Serie B 308, University of Bonn, Germany.
    2. Litzenberger, Robert H, 1992. " Swaps: Plain and Fanciful," Journal of Finance, American Finance Association, vol. 47(3), pages 831-50, July.
    3. Driessen, J.J.A.G. & Klaassen, P. & Melenberg, B., 2000. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Discussion Paper 2000-93, Tilburg University, Center for Economic Research.
    4. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    5. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
    6. Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, vol. 62(1), pages 39-66, October.
    7. Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
    8. Gupta, Anurag & Subrahmanyam, Marti G., 2005. "Pricing and hedging interest rate options: Evidence from cap-floor markets," Journal of Banking & Finance, Elsevier, vol. 29(3), pages 701-733, March.
    9. T. Clifton Green & Stephen Figlewski, 1999. "Market Risk and Model Risk for a Financial Institution Writing Options," Journal of Finance, American Finance Association, vol. 54(4), pages 1465-1499, 08.
    10. Wolfgang Bühler & Marliese Uhrig-Homburg & Ulrich Walter & Thomas Weber, 1999. "An Empirical Comparison of Forward-Rate and Spot-Rate Models for Valuing Interest-Rate Options," Journal of Finance, American Finance Association, vol. 54(1), pages 269-305, 02.
    11. Pierre Collin-Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, 08.
    12. Rasmussen, Nicki Søndergaard, 2002. "Efficient Control Variates for Monte-Carlo Valuation of American Options," Finance Working Papers 02-17, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    13. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    14. Jensen, Malene Shin & Svenstrup, Mikkel, 2002. "Efficient Control Variates and Strategies for Bermudan Swaptions in a Libor Market Model," Finance Working Papers 02-23, University of Aarhus, Aarhus School of Business, Department of Business Studies.
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