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Analyticity of the Wiener–Hopf Factors and Valuation of Exotic Options in Lévy Models

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Advanced Mathematical Methods for Finance

Abstract

This paper considers the valuation of exotic path-dependent options in Lévy 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 Lévy 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 Lévy models.

K. Glau would like to thank the DFG for financial support through project EB66/11-1, and the Austrian Science Fund (FWF) for an invitation under grant P18022. A. Papapantoleon gratefully acknowledges the financial support from the Austrian Science Fund (FWF grant Y328, START Prize).

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Notes

  1. 1.

    The historical reasons leading to the adoption of the terminology “Wiener–Hopf” are outlined in Sect. 6.6 in [33].

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Author information

Authors and Affiliations

  1. Department of Mathematical Stochastics, University of Freiburg, Eckerstr. 1, 79104, Freiburg, Germany

    Ernst Eberlein & Kathrin Glau

  2. Institute of Mathematics, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Antonis Papapantoleon

  3. Quantitative Products Laboratory, Deutsche Bank AG, Alexanderstr. 5, 10178, Berlin, Germany

    Antonis Papapantoleon

Authors
  1. Ernst Eberlein
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  2. Kathrin Glau
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  3. Antonis Papapantoleon
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Correspondence to Ernst Eberlein .

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Editors and Affiliations

  1. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Giulia Di Nunno

  2. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Bernt Øksendal

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Eberlein, E., Glau, K., Papapantoleon, A. (2011). Analyticity of the Wiener–Hopf Factors and Valuation of Exotic Options in Lévy Models. In: Di Nunno, G., Øksendal, B. (eds) Advanced Mathematical Methods for Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18412-3_8

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