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

Suggested Citation

  • Stephan Denkl & Martina Goy & Jan Kallsen & Johannes Muhle-Karbe & Arnd Pauwels, 2013. "On the performance of delta hedging strategies in exponential L�vy models," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1173-1184, July.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:8:p:1173-1184
    DOI: 10.1080/14697688.2013.779742
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    Cited by:

    1. Takuji Arai & Yuto Imai, 2016. "On the difference between locally risk-minimizing and delta hedging strategies for exponential L\'evy models," Papers 1610.09085, arXiv.org.
    2. Johannes Ruf & Weiguan Wang, 2020. "Hedging with Linear Regressions and Neural Networks," Papers 2004.08891, arXiv.org, revised Jun 2021.

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