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Calibration Risk for Exotic Options

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Author Info

  • 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.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-001.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-001.

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Length: 30 pages
Date of creation: Jan 2006
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2006-001

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

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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 327-43.
  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.

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