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Multiple stochastic volatility extension of the Libor market model and its implementation

Author

Listed:
  • Belomestny Denis

    (Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany. Email: belomest@wias-berlin.de)

  • Mathew Stanley

    (Johann Wolfgang Goethe-Universität, Senckenberganlage 31, 60325 Frankfurt am Main, Germany. Email: mathew@math.uni-frankfurt.de)

  • Schoenmakers John

    (Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany. Email: schoenma@wias-berlin.de)

Abstract

In this paper we propose an extension of the Libor market model with a high-dimensional specially structured system of square root volatility processes, and give a road map for its calibration. As such the model is well suited for Monte Carlo simulation of derivative interest rate instruments. As a key issue, we require that the local covariance structure of the market model is preserved in the stochastic volatility extension. In a case study we demonstrate that the extended Libor model allows for stable calibration to the cap-strike matrix. The calibration algorithm is FFT based, so fast and easy to implement.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:mcmeap:v:15:y:2009:i:4:p:285-310:n:1
    DOI: 10.1515/MCMA.2009.016
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    References listed on IDEAS

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    Cited by:

    1. Antonis Papapantoleon, 2009. "Old and new approaches to LIBOR modeling," Papers 0910.4941, arXiv.org, revised Apr 2010.
    2. 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.

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