On the performance of delta hedging strategies in exponential Lévy models

Abstract

We consider the performance of non-optimal hedging strategies in exponential Lévy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform approach of Hubalek et al. [Ann. Appl. Probab., 2006, 16(2), 853–885] to derive semi-explicit formulas for the resulting mean-squared hedging error in terms of the cumulant generating function of the underlying Lévy process. In two numerical examples, we apply these results to compare the efficiency of the Black–Scholes hedge and the model delta with the mean–variance optimal hedge in a normal inverse Gaussian and a diffusion-extended CGMY Lévy model.

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