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

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

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Yip, Wing
Stephens, David
Olhede, Sofia

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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11176.

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Date of creation: 03 Oct 2008
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Handle: RePEc:pra:mprapa:11176

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Find related papers by JEL classification:
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C0 - Mathematical and Quantitative Methods - - General

This paper has been announced in the following NEP Reports:

NEP-ALL-2008-10-21 (All new papers)

References listed on IDEAS
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Wim Schoutens, 2005. "Moment swaps," Quantitative Finance, Taylor and Francis Journals, vol. 5(6), pages 525-530, December. [Downloadable!] (restricted)
Philip Protter & Michael Dritschel, 1999. "Complete markets with discontinuous security price," Finance and Stochastics, Springer, vol. 3(2), pages 203-214. [Downloadable!] (restricted)
Windcliff, H. & Forsyth, P.A. & Vetzal, K.R., 2006. "Pricing methods and hedging strategies for volatility derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 409-431, February. [Downloadable!] (restricted)

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