  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.
