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Hedging in L\'evy models and the time step equivalent of jumps

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  • Ale\v{s} \v{C}ern\'y
  • Stephan Denkl
  • Jan Kallsen
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    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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    File URL: http://arxiv.org/pdf/1309.7833
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    Paper provided by arXiv.org in its series Papers with number 1309.7833.

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    Date of creation: Sep 2013
    Date of revision: Nov 2013
    Handle: RePEc:arx:papers:1309.7833

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