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Forward-Rate Volatilities And The Swaption Matrix: Why Neither Time-Homogeneity Nor Time-Dependence Are Enough

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  • RICCARDO REBONATO

    (Quantitative Research Team, Royal Bank of Scotland, 135 Bishopsgate, London, EC2M 3UR, UK;
    Oxford Center for Industrial and Applied Mathematics, Oxford University, UK;
    Tanaka Business School, Imperial College, London, UK)

Abstract

This work presents the first systematic analysis of the whole swaption matrix by fitting a parsimonious, nonlinear, financially-inspired volatility model to market data. The study uses several years of data spanning period of major market volatility. We find that the quality of the fits is good (on average of the same magnitude as the bid-offer spread), and better when a displaced-diffusion approach is chosen, but some systematic shortcomings are observed and discussed. The analysis suggests that a two-regime Markov chain approach may be more successful and better financially motivated.More generally, the present study highlights the shortcomings of purely time-dependent or time-homogenous approaches. These findings should be applicable to other option markets as well.Finally, we find that the present (nonlinear) model vastly outperforms PCA-based approaches when in comes to predicting moves in implied volatilities.

Suggested Citation

  • Riccardo Rebonato, 2006. "Forward-Rate Volatilities And The Swaption Matrix: Why Neither Time-Homogeneity Nor Time-Dependence Are Enough," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(05), pages 705-746.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:05:n:s0219024906003767
    DOI: 10.1142/S0219024906003767
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    References listed on IDEAS

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    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. 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.
    3. Riccardo Rebonato, 2003. "Which Process Gives Rise To The Observed Dependence Of Swaption Implied Volatility On The Underlying?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 419-442.
    4. Mark Joshi & Jochen Theis, 2002. "Bounding Bermudan swaptions in a swap-rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 370-377.
    5. Miroslav Misina, 2003. "What does the risk-appetite index measure?," Economics Bulletin, AccessEcon, vol. 28(6), pages 1-6.
    6. Bruce Choy & Tim Dun & Erik Schlögl, 2003. "Correlating Market Models," Research Paper Series 105, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Riccardo Rebonato & Dherminder Kainth, 2004. "A Two-Regime, Stochastic-Volatility Extension Of The Libor Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 555-575.
    8. repec:ebl:ecbull:v:28:y:2003:i:6:p:a6 is not listed on IDEAS
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    Cited by:

    1. Massimo Costabile & Ivar Massabó & Emilio Russo, 2013. "A Path-Independent Humped Volatility Model for Option Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(3), pages 191-210, July.

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