Calibration Risk for Exotic Options
AbstractOption 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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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-001.
Length: 30 pages
Date of creation: Jan 2006
Date of revision:
calibration risk; calibration; model risk; Heston model; Bates model; barrier option; cliquet option;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-01-24 (All new papers)
- NEP-FIN-2006-01-24 (Finance)
- NEP-FMK-2006-01-24 (Financial Markets)
- NEP-RMG-2006-01-24 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Stahl, Gerhard & Sibbertsen, Philipp & Bertram, Philip, 2011. "Modellrisiko = Spezifikation + Validierung," Diskussionspapiere der Wirtschaftswissenschaftlichen FakultÃ¤t der Leibniz UniversitÃ¤t Hannover dp-468, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
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