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Hedging in L\'evy Models and the Time Step Equivalent of Jumps

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  • Alev{s} v{C}ern'y
  • Stephan Denkl
  • Jan Kallsen

Abstract

We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The results are obtained by considering the L\'evy model as a perturbation of the Black-Scholes model. The approximations depend on the first four moments of logarithmic stock returns in the L\'evy model and option price sensitivities (greeks) in the limiting Black-Scholes model. We illustrate numerically that our formulas work well for a variety of L\'evy models suggested in the literature. From a theoretical point of view, it turns out that jumps have a similar effect on hedging errors as discrete-time hedging in the Black-Scholes model.

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  • Alev{s} v{C}ern'y & Stephan Denkl & Jan Kallsen, 2013. "Hedging in L\'evy Models and the Time Step Equivalent of Jumps," Papers 1309.7833, arXiv.org, revised Jul 2017.
    • Handle: RePEc:arx:papers:1309.7833
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    References listed on IDEAS

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    Cited by:

    1. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2016. "Hedging with Small Uncertainty Aversion," Papers 1605.06429, arXiv.org.
    2. Sebastian Herrmann & Johannes Muhle-Karbe & Frank Thomas Seifried, 2017. "Hedging with small uncertainty aversion," Finance and Stochastics, Springer, vol. 21(1), pages 1-64, January.
    3. Zorana Grbac & David Krief & Peter Tankov, 2015. "Approximate Option Pricing in the L\'evy Libor Model," Papers 1511.08466, arXiv.org, revised Jul 2016.
    4. Alev{s} v{C}ern'y, 2016. "Discrete-Time Quadratic Hedging of Barrier Options in Exponential L\'{e}vy Model," Papers 1603.03747, arXiv.org.

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