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

Belomestny Denis, Mathew Stanley and Schoenmakers John
Additional contact information
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

Monte Carlo Methods and Applications, 2009, vol. 15, issue 4, 285-310

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.

Keywords: Libor modeling; stochastic volatility; CIR processes; calibration (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1515/MCMA.2009.016

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