Hedging in Lévy Models and the Time Step Equivalent of Jumps

2013/09/30 by Černý, Aleš, Denkl, Stephan, Kallsen, Jan
#60G51 #90C59 #91G20 #Computational Finance (q-fin.CP) #FOS: Economics and business #Risk Management (q-fin.RM)

paper · doi:10.48550/arxiv.1309.7833

Abstract

We consider option hedging in a model where the underlying follows an exponential Lévy 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 Lévy model as a perturbation of the Black-Scholes model. The approximations depend on the first four moments of logarithmic stock returns in the Lévy model and option price sensitivities (greeks) in the limiting Black-Scholes model. We illustrate numerically that our formulas work well for a variety of Lévy 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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