Calibration risk: Illustrating the impact of calibration risk under the Heston model

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: 2571–2606, 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.