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

Hedging strategies and minimal variance portfolios for European and exotic options in a Levy market