Calibration risk for exotic options

Abstract

Equity derivative pricing models are calibrated to market data of plain vanilla options 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. We provide evidence for this calibration risk in a time series of DAX implied volatility surfaces from April 2003 to March 2004. We analyze factors influencing these price differences for exotic options in the Heston and in the Bates models and recommend an error functional. Moreover, we determine the model risk of these two stochastic volatility models for the time series and compare it to calibration risk.