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

Wing Yip, David Stephens and Sofia Olhede

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Hedging Strategies; Levy processes; Variance Gamma; Choatic Representation Property; Power Jump Processs; Variance Swaps; Moment Swaps (search for similar items in EconPapers)
JEL-codes: C0 C51 C6 (search for similar items in EconPapers)
Date: 2008-10-03
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/11176/4/MPRA_paper_11176.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:11176

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().