Calibration Risk for Exotic Options

SFB 649 Discussion Paper 2006-001

30 Pages Posted: 9 Jan 2017

See all articles by Kai Detlefsen

Kai Detlefsen

Humboldt University of Berlin - Institute for Statistics and Econometrics

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Date Written: January 6, 2006

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.

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

JEL Classification: C13, G12

Suggested Citation

Detlefsen, Kai and Härdle, Wolfgang K., Calibration Risk for Exotic Options (January 6, 2006). SFB 649 Discussion Paper 2006-001, Available at SSRN: https://ssrn.com/abstract=2894410 or http://dx.doi.org/10.2139/ssrn.2894410

Kai Detlefsen

Humboldt University of Berlin - Institute for Statistics and Econometrics ( email )

Spandauer Str. 1
Berlin, D-10178
Germany

Wolfgang K. Härdle (Contact Author)

Blockchain Research Center ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Chiao Tung University ( email )

No. 1001 Ta Hsueh Road
Hsinchu 300
Taiwan

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

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