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Heston Model: The Variance Swap Calibration

Author

Listed:
  • Florence Guillaume

    (K.U. Leuven)

  • Wim Schoutens

    (K.U. Leuven)

Abstract

This paper features a market implied methodology to infer adequate starting values for the spot and long-run variances and for the mean reversion rate of a calibration exercise under the Heston model. More particularly, these initial parameters are obtained by matching the term structure of the future expected total variance, inferred from the volatility surface, with the model term structure. In the numerical study, we compare the goodness of fit and the parameter stability of the Heston model calibrated by using either plausible random or market implied starting values for a one-year sample period including the recent credit crunch. In particular, we show that the proposed methodology avoids getting stuck in one “bad” local minimum and stabilizes the calibrated parameters through time.

Suggested Citation

  • Florence Guillaume & Wim Schoutens, 2014. "Heston Model: The Variance Swap Calibration," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 76-89, April.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-013-0331-7
    DOI: 10.1007/s10957-013-0331-7
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    References listed on IDEAS

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    1. David Murphy, 2009. "The causes of the credit crunch: a backwards look?," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 775-790.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
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    9. Florence Guillaume & Wim Schoutens, 2012. "Calibration risk: Illustrating the impact of calibration risk under the Heston model," Review of Derivatives Research, Springer, vol. 15(1), pages 57-79, April.
    10. Florence Guillaume & Wim Schoutens, 2013. "A moment matching market implied calibration," Quantitative Finance, Taylor & Francis Journals, vol. 13(9), pages 1359-1373, September.
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    Cited by:

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    2. Alan Bain & Matthieu Mariapragassam & Christoph Reisinger, 2019. "Calibration of Local-Stochastic and Path-Dependent Volatility Models to Vanilla and No-Touch Options," Papers 1911.00877, arXiv.org.

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