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Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options

  • Reik Borger
  • Jan van Heys
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    This work discusses the calibration of instantaneous Libor correlations in the Libor market model. We extend the existing calibration strategies by the incorporation of spread option implied correlation information. The correlation structure implied by constant maturity swap (CMS) spread options observed in the present-day market motivates us to extend the existing parameterizations of ratio correlations by a new three-parameter approach. For the first time, this paper presents an extensive empirical study of different parameterizations and their capability to match market correlations. We can show that our approach leads to stable calibrations and gives a satisfactory fit to the market. We conclude our investigation with the pricing of a callable swap on CMS spread using the parameterizations compared before.

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    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 17 (2010)
    Issue (Month): 5 ()
    Pages: 453-469

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    Handle: RePEc:taf:apmtfi:v:17:y:2010:i:5:p:453-469
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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Alan Brace & Dariusz G¬łatarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
    3. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
    4. Damiano Brigo & Jan Liinev, 2005. "On the distributional distance between the lognormal LIBOR and swap market models," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 433-442.
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