On the performance of delta hedging strategies in exponential L�vy models

Stephan Denkl, Martina Goy, Jan Kallsen, Johannes Muhle-Karbe and Arnd Pauwels

Quantitative Finance, 2013, vol. 13, issue 8, 1173-1184

Abstract: We consider the performance of non-optimal hedging strategies in exponential L�vy 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 L�vy 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 L�vy model.

Date: 2013
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DOI: 10.1080/14697688.2013.779742

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