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Analysis of Fourier Transform Valuation Formulas and Applications

Author

Listed:
  • 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 Levy and stochastic volatility models.

Suggested Citation

  • Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
  • Handle: RePEc:taf:apmtfi:v:17:y:2010:i:3:p:211-240
    DOI: 10.1080/13504860903326669
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    Citations

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    Cited by:

    1. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    2. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    3. repec:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500078 is not listed on IDEAS
    4. Yannis G. Yatracos, 2013. "Option pricing, Bayes risks and Applications," Papers 1304.5156, arXiv.org.
    5. Zorana Grbac & Antonis Papapantoleon, 2012. "A tractable LIBOR model with default risk," Papers 1202.0587, arXiv.org, revised Oct 2012.
    6. Stephane Crepey & Andrea Macrina & Tuyet Mai Nguyen & David Skovmand, 2015. "Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments," Papers 1502.07397, arXiv.org.
    7. Fred Espen Benth & Hanna Zdanowicz, 2016. "Pricing And Hedging Of Energy Spread Options And Volatility Modulated Volterra Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-22, February.
    8. 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.
    9. repec:bla:jrinsu:v:84:y:2017:i:1:p:209-238 is not listed on IDEAS
    10. Robert Stelzer & Jovana Zaviv{s}in, 2014. "Derivative pricing under the possibility of long memory in the supOU stochastic volatility model," Papers 1404.1773, arXiv.org.
    11. Stefan Waldenberger, 2015. "The affine inflation market models," Papers 1503.04979, arXiv.org.
    12. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2015. "Random Time Forward Starting Options," Papers 1504.03552, arXiv.org.
    13. Maximilian Ga{ss} & Kathrin Glau & Maximilian Mair, 2015. "Magic points in finance: Empirical integration for parametric option pricing," Papers 1511.00884, arXiv.org, revised Nov 2016.
    14. Fajardo, José, 2016. "Power Style Contracts Under Asymmetric Lévy Processes," MPRA Paper 71813, University Library of Munich, Germany.
    15. Mesias Alfeus & Erik Schlögl, 2018. "On Numerical Methods for Spread Options," Research Paper Series 388, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Yannick Armenti & Stephane Crepey & Samuel Drapeau & Antonis Papapantoleon, 2015. "Multivariate Shortfall Risk Allocation and Systemic Risk," Papers 1507.05351, arXiv.org, revised Mar 2017.
    17. Hieber, Peter, 2017. "Cliquet-style return guarantees in a regime switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 138-147.
    18. 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 Aug 2015.
    19. Michael Schmutz & Thomas Zürcher, 2014. "Static Hedging with Traffic Light Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(7), pages 690-702, July.
    20. Christian Bayer & John Schoenmakers, 2015. "Option pricing in affine generalized Merton models," Papers 1512.03677, arXiv.org.
    21. Fajardo, José, 2015. "Barrier style contracts under Lévy processes: An alternative approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 179-187.
    22. Chunfa Wang, 2017. "Pricing European Options by Stable Fourier-Cosine Series Expansions," Papers 1701.00886, arXiv.org, revised Jan 2017.
    23. Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216, arXiv.org, revised Jun 2014.
    24. Fred Espen Benth & Hanna Zdanowicz, 2014. "Pricing and hedging of energy spread options and volatility modulated Volterra processes," Papers 1409.5801, arXiv.org.

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