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Analysis of Fourier Transform Valuation Formulas and Applications

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  • Ernst Eberlein
  • Kathrin Glau
  • Antonis Papapantoleon
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    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 Levy and stochastic volatility models.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903326669
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 17 (2010)
    Issue (Month): 3 ()
    Pages: 211-240

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    Handle: RePEc:taf:apmtfi:v:17:y:2010:i:3:p:211-240

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    Related research

    Keywords: Option valuation; Fourier transform; semimartingales; Levy processes; stochastic volatility models; options on several assets;

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    Cited by:
    1. Manabu Asai & Michael McAleer, 2013. "Leverage and Feedback E ects on Multifactor Wishart Stochastic Volatility for Option Pricing," Documentos de Trabajo del ICAE 2013-02, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    2. Samuel Drapeau & Michael Kupper & Antonis Papapantoleon, 2012. "A Fourier Approach to the Computation of CV@R and Optimized Certainty Equivalents," Papers 1212.6732, arXiv.org, revised Dec 2013.
    3. Manabu Asai & Michael McAleer, 2013. "Leverage and Feedback Effects on Multifactor Wishart Stochastic Volatility for Option Pricing," Tinbergen Institute Discussion Papers 13-003/III, Tinbergen Institute.
    4. St\'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    5. Zorana Grbac & Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2014. "Affine LIBOR models with multiple curves: theory, examples and calibration," Papers 1405.2450, arXiv.org, revised Jun 2014.
    6. Robert Stelzer & Jovana Zavi\v{s}in, 2014. "Derivative pricing under the possibility of long memory in the supOU stochastic volatility model," Papers 1404.1773, arXiv.org.
    7. Zorana Grbac & Antonis Papapantoleon, 2012. "A tractable LIBOR model with default risk," Papers 1202.0587, arXiv.org, revised Oct 2012.
    8. Yannis G. Yatracos, 2013. "Option pricing, Bayes risks and Applications," Papers 1304.5156, arXiv.org.
    9. Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216, arXiv.org, revised Jun 2014.

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