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Analysis of Fourier transform valuation formulas and applications

Author

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  • Ernst Eberlein
  • Kathrin Glau
  • Antonis Papapantoleon

Abstract

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.

Suggested Citation

  • Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    • Handle: RePEc:arx:papers:0809.3405
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    References listed on IDEAS

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    1. 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.
    2. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
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    4. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Papers 0809.0301, arXiv.org, revised Nov 2009.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Svetlana I Boyarchenko & Sergei Z Levendorskii, 2002. "Non-Gaussian Merton-Black-Scholes Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4955, January.
    7. Biagini, Francesca & Bregman, Yuliya & Meyer-Brandis, Thilo, 2008. "Pricing of catastrophe insurance options written on a loss index with reestimation," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 214-222, October.
    8. Martin Keller-Ressel & Antonis Papapantoleon & Josef Teichmann, 2009. "The affine LIBOR models," Papers 0904.0555, arXiv.org, revised Jul 2011.
    9. T. R. Hurd & Zhuowei Zhou, 2009. "A Fourier transform method for spread option pricing," Papers 0902.3643, arXiv.org.
    10. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    11. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
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    Cited by:

    1. Federico De Olivera & Ernesto Mordecki, 2014. "Computing Greeks for L\'evy Models: The Fourier Transform Approach," Papers 1407.1343, arXiv.org.
    2. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2009. "Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models," Papers 0911.0373, arXiv.org, revised Oct 2010.
    3. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2009. "Variance Optimal Hedging for continuous time processes with independent increments and applications," Papers 0912.0372, arXiv.org.

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