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A stochastic volatility Libor model and its robust calibration

Author

Listed:
  • Denis Belomestny
  • Stanley Matthew
  • John Schoenmakers

Abstract

In this paper we propose a Libor model with a high-dimensional specially structured system of driving CIR volatility processes. A stable calibration procedure which takes into account a given local correlation structure is presented. The calibration algorithm is FFT based, so fast and easy to implement.

Suggested Citation

  • 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.
  • Handle: RePEc:hum:wpaper:sfb649dp2007-067
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2007-067.pdf
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    References listed on IDEAS

    as
    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. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    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. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. 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.
    8. Christian Kahl & Peter Jackel, 2006. "Fast strong approximation Monte Carlo schemes for stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 513-536.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Libor modelling; stochastic volatility; CIR processes; calibration;

    JEL classification:

    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • I19 - Health, Education, and Welfare - - Health - - - Other
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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