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Systematic Generation of Parametric Correlation Structures for the LIBOR Market Model

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  • John Schoenmakers

    (Weierstrass Institute, Mohrenstrasse 39, D-10117 Berlin, Germany;
    Delft University of Technology–SWON, IS, Department of Applied Analysis, Large Scale Systems, Mekelweg 4, 2628CD Delft, The Netherlands)

  • Brian Coffey

    (Merrill Lynch, Ropemaker Place, 25 Ropemaker Street, London EC2Y 9LY, UK)

Abstract

We present a conceptual approach of deriving parsimonious correlation structures suitable for implementation in the LIBOR market model. By imposing additional constraints on a known ratio correlation structure, motivated by economically sensible assumptions concerning forward LIBOR correlations, we yield a semi-parametric framework of non-degenerate correlation structures with realistic properties. Within this framework we derive systematically low parametric structures with, in principal, any desired number of parameters. As illustrated, such structures may be used for smoothing a matrix of historically estimated LIBOR return correlations. In combination with a suitably parametrized deterministic LIBOR volatility norm we so obtain a parsimonious multi-factor market model which allows for joint calibration to caps and swaptions. See Schoenmakers [14] for a stable full implied calibration procedure based on the correlation structures developed in this paper.

Suggested Citation

  • John Schoenmakers & Brian Coffey, 2003. "Systematic Generation of Parametric Correlation Structures for the LIBOR Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 507-519.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:05:n:s0219024903002055
    DOI: 10.1142/S0219024903002055
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    Citations

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    Cited by:

    1. Jacques Van Appel & Thomas A. Mcwalter, 2018. "Efficient Long-Dated Swaption Volatility Approximation In The Forward-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-26, June.
    2. Matheus R Grasselli & Tsunehiro Tsujimoto, 2011. "Calibration of Chaotic Models for Interest Rates," Papers 1106.2478, arXiv.org.
    3. Rebonato, Riccardo & Ronzani, Riccardo, 2021. "Is convexity efficiently priced? Evidence from international swap markets," Journal of Empirical Finance, Elsevier, vol. 63(C), pages 392-413.
    4. Packham, Natalie & Woebbeking, Fabian, 2021. "Correlation scenarios and correlation stress testing," IRTG 1792 Discussion Papers 2021-012, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    5. Packham, N. & Woebbeking, C.F., 2019. "A factor-model approach for correlation scenarios and correlation stress testing," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 92-103.
    6. Packham, N. & Woebbeking, F., 2023. "Correlation scenarios and correlation stress testing," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 55-67.
    7. N. Packham & F. Woebbeking, 2021. "Correlation scenarios and correlation stress testing," Papers 2107.06839, arXiv.org, revised Sep 2022.
    8. A. Goia & E. Salinelli, 2016. "Exploring the total positivity of yields correlations," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 605-624, April.
    9. Reik Borger & Jan van Heys, 2010. "Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(5), pages 453-469.
    10. Thomas A. McWalter & Erik Schlögl & Jacques van Appel, 2023. "Analysing Quantiles in Models of Forward Term Rates," Risks, MDPI, vol. 11(2), pages 1-18, January.

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