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Calibration Design of Implied Volatility Surfaces

Author

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  • Kai Detlefsen
  • Wolfgang Härdle

Abstract

The calibration of option pricing models leads to the minimization of an error functional. We show that its usual specification as a root mean squared error implies fluctuating exotics prices and possibly wrong prices. We propose a simple and natural method to overcome these problems, illustrate drawbacks of the usual approach and show advantages of our method. To this end, we calibrate the Heston model to a time series of DAX implied volatility surfaces and then price cliquet options.

Suggested Citation

  • Kai Detlefsen & Wolfgang Härdle, 2006. "Calibration Design of Implied Volatility Surfaces," SFB 649 Discussion Papers SFB649DP2006-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-002
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-002.pdf
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    References listed on IDEAS

    as
    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    More about this item

    Keywords

    calibration; data design; implied volatility surface; Heston model; cliquet option;
    All these keywords.

    JEL classification:

    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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