Robustness of Delta Hedging in a Jump-Diffusion Model

Suppose an investor aims at Delta hedging a European contingent claim h(S(T)) in a jump-diffusion model, but incorrectly specifies the stock price's volatility and jump sensitivity, so that any hedging strategy is calculated under a misspecified model. When does the erroneously computed strategy approximate the true claim in an appropriate sense? If the misspecified volatility and jump sensitivity dominate the true ones, we show that following the misspecified Delta strategy does superreplicate h(S(T)) in expectation among a wide collection of models. We also show that if a robust pricing operator with a whole class of models is used, the corresponding hedge is dominating the contingent claim under each model in expectation. Such a hedging error is also called a good-deal or a \rho -arbitrage. Moreover, in general the misspecified price of the option dominates the true one if the volatility and the jump sensitivity are overestimated. Our results rely on proving stochastic flow properties of the jump-diffusion and the convexity of the contingent claim's value function.