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On the distributional distance between the lognormal LIBOR and swap market models

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  • Damiano Brigo
  • Jan Liinev

Abstract

We consider the distributional difference in forward swap rates from the LIBOR market model (LFM) and the swap market model (LSM), the two fundamental market models for interest-rate derivatives. We explain how the Kullback-Leibler information (KLI) can be used to measure the distance of a given distribution from the lognormal (exponential) family of densities and then apply this to our models' comparison. The volatility of the projection of the LFM swap-rate distribution onto the lognormal family is compared to an industry synthetic swap volatility approximation in the LFM. Finally, we analyse how the above distance changes, in some cases, according to the parameter values and to the parameterizations themselves. We find a small distance in all cases.

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  • 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.
    • Handle: RePEc:taf:quantf:v:5:y:2005:i:5:p:433-442
    DOI: 10.1080/14697680500305162
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    References listed on IDEAS

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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. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 53-64, May.
    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 409-430, March.
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    Cited by:

    1. Jacques Van Appel & Thomas A. Mcwalter, 2018. "Efficient Long-Dated Swaption Volatility Approximation In The Forward-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-26, June.
    2. Lixin Wu, 2013. "Inflation-rate Derivatives: From Market Model to Foreign Currency Analogy," Papers 1302.0574, arXiv.org.
    3. Rudiger Kiesel & Gero Schindlmayr & Reik Borger, 2009. "A two-factor model for the electricity forward market," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 279-287.
    4. Reik Borger & Jan van Heys, 2010. "Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 453-469.
    5. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811.
    6. Brigo, Damiano & Mercurio, Fabio & Morini, Massimo, 2005. "The LIBOR model dynamics: Approximations, calibration and diagnostics," European Journal of Operational Research, Elsevier, vol. 163(1), pages 30-51, May.

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