Hedging Under Model Mis-Specification: All Risk Factors are Equal, But Some are More Equal than Others ...

Branger Nicole, Krautheim Eva, Schlag Christian, Seeger Norman

Abstract
It is often difficult to distinguish among different option pricing models that consider stochastic volatility and/or jumps based on a cross-section of European option prices. This can result in model misspecification. We analyze the hedging error induced by model misspecification and show that it can be economically significant in the cases of a delta hedge, a minimum-variance hedge, and a delta-vega hedge. Furthermore, we explain the surprisingly good performance of a simple ad-hoc Black-Scholes hedge. We compare realized hedging errors (an incorrect hedge model is applied) and anticipated hedging errors (the hedge model is the true one) and find that there are substantial differences between the two distributions, particularly depending on whether stochastic volatility is included in the hedge model. Therefore, hedging errors can be useful for identifying model misspecification. Furthermore, model risk has severe implications for risk measurement and can lead to a significant misestimation, specifically underestimation, of the risk to which a hedged position is exposed.

Keywords
Hedging; Model Risk; Risk Measurement; Model Identi cation; Delta Hedge; Delta-Vega Hedge; Minimum-Variance Hedge