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Hedging strategies and minimal variance portfolios for European and exotic options in a Lévy market (2008)
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@MISC{Yip08hedgingstrategies,
author = {Wing Yan Yip and David Stephens and Sofia Olhede},
title = {Hedging strategies and minimal variance portfolios for European and exotic options in a Lévy market},
year = {2008}
}
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Abstract
This paper presents hedging strategies for European and exotic options in a Lévy market. By applying Taylor’s Theorem, dynamic hedging portfolios are constructed 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.
Keyphrases
minimal variance portfolio vy market exotic option power jump asset underlying asset european option numerical algorithm dynamic hedging portfolio moment swap order term risk-free bank account perfect hedging static hedging practical utility practical importance taylor expansion derived result gamma hedging strategy pricing function variance swap taylor theorem moment hedging hedging strategy different market assumption
