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A stochastic volatility libor model and its robust calibration

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  • Belomestny, Denis
  • Matthew, Stanley
  • Schoenmakers, John G. M.

Abstract

In this paper we propose a Libor model with a high-dimensional specially structured system of driving CIR volatility processes. A stable calibration prodecure 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

  • Belomestny, Denis & Matthew, Stanley & Schoenmakers, John G. M., 2007. "A stochastic volatility libor model and its robust calibration," SFB 649 Discussion Papers 2007-067, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2007-067
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    References listed on IDEAS

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    1. 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.
    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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. 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.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    7. 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.
    8. Belomestny, Denis & Schoenmakers, John G. M., 2006. "A jump-diffusion Libor model and its robust calibration," SFB 649 Discussion Papers 2006-037, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. 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.
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    More about this item

    Keywords

    Libor modelling; stochastic volatility; CIR processes; calibration;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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    This paper has been announced in the following NEP Reports:

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