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

Yip, Wing and Stephens, David and Olhede, Sofia (2008): Hedging strategies and minimal variance portfolios for European and exotic options in a Levy market. Forthcoming in: Mathematical Finance

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Hedging Strategies; Levy processes; Variance Gamma; Choatic Representation Property; Power Jump Processs; Variance Swaps; Moment Swaps
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C0 - General

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