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

Ale\v{s} \v{C}ern\'y, Stephan Denkl and Jan Kallsen
Authors registered in the RePEc Author Service: Aleš Černý

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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.

Date: 2013-09, Revised 2017-07
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Citations: View citations in EconPapers (4)

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