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On the Performance of Delta Hedging Strategies in Exponential L\'evy Models

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

Abstract

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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  • Stephan Denkl & Martina Goy & Jan Kallsen & Johannes Muhle-Karbe & Arnd Pauwels, 2009. "On the Performance of Delta Hedging Strategies in Exponential L\'evy Models," Papers 0911.4859, arXiv.org, revised May 2011.
    • Handle: RePEc:arx:papers:0911.4859
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    Cited by:

    1. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    2. Flavio Angelini & Stefano Herzel, 2015. "Evaluating discrete dynamic strategies in affine models," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 313-326, February.
    3. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.

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