Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models
This paper considers the valuation of exotic path-dependent options in L\'evy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener--Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a L\'evy process. Combined with general results on Fourier methods for option pricing, we provide formulas for the valuation of one-touch options, lookback options and equity default swaps in L\'evy models.
|Date of creation:||Nov 2009|
|Date of revision:||Oct 2010|
|Publication status:||Published in Advanced Mathematical Methods for Finance, pp. 223-245, Springer, 2011|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Oleg Kudryavtsev & Sergei Levendorskiǐ, 2006. "Pricing Of First Touch Digitals Under Normal Inverse Gaussian Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(06), pages 915-949.
- Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
- Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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