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A Joint Empirical And Theoretical Investigation Of The Modes Of Deformation Of Swaption Matrices: Implications For Model Choice

Author

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  • RICCARDO REBONATO

    (Quantitative Research Centre, Group Risk, Royal Bank of Scotland, 2nd Floor, Waterhouse Square, 138–142, Holborn, London, EC1N 2TH, UK;
    Oxford Financial Research Centre, Oxford University, Oxford, OX1 2JD, UK)

  • MARK JOSHI

    (Quantitative Research Centre, Group Risk, Royal Bank of Scotland, 2nd Floor, Waterhouse Square, 138–142, Holborn, London, EC1N 2TH, UK)

Abstract

We present a joint empirical/theoretical analysis of the changes in the implied volatility swaption matrix for two currencies (USD and DEM/EUR). We recognize the existence of a small number of recognizable shape patterns, and comment about the speed of transition between them. By Principal/Component/Analyzing the associated correlation and covariance matrices we highlight a non/trivial interpretation for the leading eigenvectors. We also compare the empirically obtained eigenvectors and eigenvalues with the corresponding quantities produced by the stochastic/volatility LIBOR market model of Joshi and Rebonato[10]. This allows us to perform a measure-independent comparison that is of intrinsic interest, and that can also provide a general blueprint for analyzing the realism of and choosing among similarly-fitting stochastic models. We find that mean reversion of the instantaneous volatility is a necessary condition in order to obatin the market-observed shape of the first eigenvector associated with the covariance matrix.

Suggested Citation

  • Riccardo Rebonato & Mark Joshi, 2002. "A Joint Empirical And Theoretical Investigation Of The Modes Of Deformation Of Swaption Matrices: Implications For Model Choice," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(07), pages 667-694.
    • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:07:n:s0219024902001651
    DOI: 10.1142/S0219024902001651
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    Citations

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    Cited by:

    1. Carol Alexander & Dimitri Lvov, 2003. "Statistical Properties of Forward Libor Rates," ICMA Centre Discussion Papers in Finance icma-dp2003-03, Henley Business School, University of Reading.
    2. L. Steinruecke & R. Zagst & A. Swishchuk, 2015. "The Markov-switching jump diffusion LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 455-476, March.
    3. Mark Joshi & Riccardo Rebonato, 2003. "A displaced-diffusion stochastic volatility LIBOR market model: motivation, definition and implementation," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 458-469.
    4. Riccardo Rebonato & Valerio Gaspari, 2006. "Analysis of drawdowns and drawups in the US$ interest-rate market," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 297-326.
    5. Baaquie, Belal E. & Tang, Pan, 2012. "Simulation of nonlinear interest rates in quantum finance: Libor Market Model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1287-1308.

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