It is already well documented that model risk is an important issue regarding the pricing of exotics (see Schoutens et al., in A perfect calibration! Now what?, Wilmott Magazine, March 2004: pp 66-78, 2004. Arguments have been made to put this into the perspective of bid-ask pricing using the theory of conic finance and pricing to acceptability (Cherny and Madan Review of Financial Studies, 22: 2571Studies, 22: -2606Studies, 22: , 2009. In this paper we show also the presence and importance of calibration risk. More particularly, we point out that a variety of plausible calibration methods lead again to serious price differences for exotics and different distributions of the P&L of the delta-hedging strategy. This is illustrated under the popular Heston stochastic volatility model, which is used among practitioners to price all kinds of exotic and structured products. This paper shows that it is prudent to take some additional safety margin into account for the pricing of these structured notes.

This paper features the calibration performance of the Heston model for two different calibration procedures. The first consists of the standard calibration on the whole parameter set and the second one, called reduced calibration consists of a calibration on the reduced parameter set {κ, λ, ρ} where the spot variance v0 and the long run variance η are inferred beforehand from the time series of the VIX volatility index. It is shown that both calibration procedures lead to an accurate fit of the vanilla option surface. Furthermore both the computation time and the calibration risk of the reduced calibration procedure turns out to be significantly lower, which might turn out to be a considerable advantage for practitioners. This paper also features a comparison of the price of different exotic options for the two calibration procedures.