  This paper presents hedging strategies for European and exotic options in a
Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con-
structed under different market assumptions, such as the existence of power
jump assets or moment swaps. In the case of European options or baskets of
European options, static hedging is implemented. It is shown that perfect
hedging can be achieved. Delta and gamma hedging strategies are extended to
higher moment hedging by investing in other traded derivatives depending on the
same underlying asset. This development is of practical importance as such
other derivatives might be readily available. Moment swaps or power jump assets
are not typically liquidly traded. It is shown how minimal variance portfolios
can be used to hedge the higher order terms in a Taylor expansion of the
pricing function, investing only in a risk-free bank account, the underlying
asset and potentially variance swaps. The numerical algorithms and performance
of the hedging strategies are presented, showing the practical utility of the
derived results.
