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Consistent calibration of HJM models to cap implied volatilities

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  • Flavio Angelini
  • Stefano Herzel

Abstract

This article proposes a calibration algorithm that fits multifactor Gaussian models to the implied volatilities of caps with the use of the respective minimal consistent family to infer the forward‐rate curve. The algorithm is applied to three forward‐rate volatility structures and their combination to form two‐factor models. The efficiency of the consistent calibration is evaluated through comparisons with nonconsistent methods. The selection of the number of factors and of the volatility functions is supported by a principal‐component analysis. Models are evaluated in terms of in‐sample and out‐of‐sample data fitting as well as stability of parameter estimates. The results are analyzed mainly by focusing on the capability of fitting the market‐implied volatility curve and, in particular, reproducing its characteristic humped shape. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1093–1120, 2005

Suggested Citation

  • Flavio Angelini & Stefano Herzel, 2005. "Consistent calibration of HJM models to cap implied volatilities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(11), pages 1093-1120, November.
    • Handle: RePEc:wly:jfutmk:v:25:y:2005:i:11:p:1093-1120
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    Cited by:

    1. A. Falco & LL. Navarro & J. Nave, 2010. "On the calibration of a Gaussian Heath-Jarrow-Morton model using consistent forward rate curves," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 495-504.
    2. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2016. "The stochastic string model as a unifying theory of the term structure of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 217-237.
    3. Hans-Peter Bermin, 2014. "On Dynamic Forward Rate Modeling And Principal Component Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-20.
    4. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    5. Antonio Falcó & Juan Nave & Lluís Navarro, 2008. "A multiobjective approach using consistent rate curves to the calibration of a Gaussian Heath-Jarrow-Morton model," Working Papers. Serie AD 2008-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    6. Claudio Fontana & Giacomo Lanaro & Agatha Murgoci, 2024. "The geometry of multi-curve interest rate models," Papers 2401.11619, arXiv.org.

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