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A jump-diffusion Libor model and its robust calibration

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  • Denis Belomestny
  • John Schoenmakers

Abstract

In this paper we propose a jump-diffusion Libor model with jumps in a high-dimensional space (ℝm) and test a stable non-parametric calibration algorithm that takes into account a given local covariance structure. The algorithm returns smooth and simply structured Levy densities, and penalizes the deviation from the Libor market model. In practice, the procedure is FFT based, thus fast, easy to implement, and yields good results, particularly in view of the severe ill-posedness of the underlying inverse problem.

Suggested Citation

  • Denis Belomestny & John Schoenmakers, 2010. "A jump-diffusion Libor model and its robust calibration," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 529-546.
    • Handle: RePEc:taf:quantf:v:11:y:2010:i:4:p:529-546
    DOI: 10.1080/14697680903295176
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    1. Denis Belomestny & John Schoenmakers, 2010. "A jump-diffusion Libor model and its robust calibration," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 529-546.
    2. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    3. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    4. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    5. 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.
    6. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
    7. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    8. Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410, July.
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    Cited by:

    1. Denis Belomestny & John Schoenmakers, 2010. "A jump-diffusion Libor model and its robust calibration," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 529-546.
    2. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.
    3. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-Lévi approximations to Lévi driven LIBOR models," CREATES Research Papers 2011-22, Department of Economics and Business Economics, Aarhus University.
    4. L. Steinruecke & R. Zagst & A. Swishchuk, 2015. "The Markov-switching jump diffusion LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 455-476, March.
    5. Mathias Trabs, 2011. "Calibration of selfdecomposable Lévy models," SFB 649 Discussion Papers SFB649DP2011-073, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Belomestny Denis & Mathew Stanley & Schoenmakers John, 2009. "Multiple stochastic volatility extension of the Libor market model and its implementation," Monte Carlo Methods and Applications, De Gruyter, vol. 15(4), pages 285-310, January.
    7. Marcel Ladkau & John G. M. Schoenmakers & Jianing Zhang, 2012. "Libor model with expiry-wise stochastic volatility and displacement," Papers 1204.5698, arXiv.org.
    8. Denis Belomestny & Stanley Matthew & John Schoenmakers, 2007. "A stochastic volatility Libor model and its robust calibration," SFB 649 Discussion Papers SFB649DP2007-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866, arXiv.org, revised Jan 2012.
    10. Jakob Söhl, 2014. "Confidence sets in nonparametric calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 18(3), pages 617-649, July.
    11. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 257-275.

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    More about this item

    Keywords

    LIBOR market models; American options; Monte Carlo methods; Statistical methods;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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