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Calibration Risk for Exotic Options

Author

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  • Kai Detlefsen
  • Wolfgang Härdle

Abstract

Option pricing models are calibrated to market data of plain vanillas by minimization of an error functional. From the economic viewpoint, there are several possibilities to measure the error between the market and the model. These different specifications of the error give rise to different sets of calibrated model parameters and the resulting prices of exotic options vary significantly. These price differences often exceed the usual profit margin of exotic options. We provide evidence for this calibration risk in a time series of DAX implied volatility surfaces from April 2003 to March 2004. We analyze in the Heston and in the Bates model factors influencing these price differences of exotic options and finally recommend an error functional. Moreover, we determine the model risk of these two stochastic volatility models for the time series and consider its relation to calibration risk.

Suggested Citation

  • Kai Detlefsen & Wolfgang Härdle, 2006. "Calibration Risk for Exotic Options," SFB 649 Discussion Papers SFB649DP2006-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2006-001
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-001.pdf
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    References listed on IDEAS

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
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    Cited by:

    1. Stahl, Gerhard & Sibbertsen, Philipp & Bertram, Philip, 2011. "Modellrisiko = Spezifikation + Validierung," Hannover Economic Papers (HEP) dp-468, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.

    More about this item

    Keywords

    calibration risk; calibration; model risk; Heston model; Bates model; barrier option; cliquet option;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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