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

In: Advanced Mathematical Methods for Finance

Author

Listed:
  • Ernst Eberlein

    (University of Freiburg, Department of Mathematical Stochastics)

  • Kathrin Glau

    (University of Freiburg, Department of Mathematical Stochastics)

  • Antonis Papapantoleon

    (TU Berlin, Institute of Mathematics
    Deutsche Bank AG, Quantitative Products Laboratory)

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.

Suggested Citation

  • Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2011. "Analyticity of the Wiener–Hopf Factors and Valuation of Exotic Options in Lévy Models," Springer Books, in: Giulia Di Nunno & Bernt Øksendal (ed.), Advanced Mathematical Methods for Finance, chapter 0, pages 223-245, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18412-3_8
    DOI: 10.1007/978-3-642-18412-3_8
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