On the Performance of Delta Hedging Strategies in Exponential Lévy Models

Details On the Performance of Delta Hedging Strategies in Exponential Lévy Models On the Performance of Delta Hedging Strategies in Exponential Lévy Models

2009-11-25

arxiv.org/abs/0911.4859v3

Economy

Quantitative Finance

Computational Finance

25 pages, 5 figures. Second numerical example added

Scientific paper

We consider the performance of non-optimal hedging strategies in exponential L\'evy 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. (2006) to derive semi-explicit formulas for the resulting mean squared hedging error in terms of the cumulant generating function of the underlying L\'evy process. In two numerical examples, we apply these results to compare the efficiency of the Black-Scholes hedge and the model delta to the mean-variance optimal hedge in a normal inverse Gaussian and a diffusion-extended CGMY L\'evy model.

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