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A Fourier transform method for spread option pricing

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  • T. R. Hurd
  • Zhuowei Zhou

Abstract

Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient and flexible enough to apply in general models. The present paper introduces a new formula for general spread option pricing based on Fourier analysis of the spread option payoff function. Our detailed investigation proves the effectiveness of a fast Fourier transform implementation of this formula for the computation of prices. It is found to be easy to implement, stable, efficient and applicable in a wide variety of asset pricing models.

Suggested Citation

  • T. R. Hurd & Zhuowei Zhou, 2009. "A Fourier transform method for spread option pricing," Papers 0902.3643, arXiv.org.
    • Handle: RePEc:arx:papers:0902.3643
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    References listed on IDEAS

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    1. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
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    Cited by:

    1. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "A bivariate Normal Inverse Gaussian process with stochastic delay: efficient simulations and applications to energy markets," Papers 2011.04256, arXiv.org.
    2. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12, July-Dece.
    3. Alexander Kushpel, 2015. "Pricing of high-dimensional options," Papers 1510.07221, arXiv.org.
    4. Ignatieva, Katja & Song, Andrew & Ziveyi, Jonathan, 2016. "Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 286-300.
    5. Fajardo, José & Farias, Aquiles, 2010. "Derivative pricing using multivariate affine generalized hyperbolic distributions," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1607-1617, July.
    6. Mark Joshi & Chao Yang, 2010. "Fast And Accurate Pricing And Hedging Of Long-Dated Cms Spread Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 839-865.
    7. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "Correlating L\'evy processes with Self-Decomposability: Applications to Energy Markets," Papers 2004.04048, arXiv.org, revised Jul 2020.
    8. Matteo Gardini & Piergiacomo Sabino, 2022. "Exchange option pricing under variance gamma-like models," Papers 2207.00453, arXiv.org.
    9. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    10. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2011.
    11. Dilip Madan, 2009. "Capital requirements, acceptable risks and profits," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 767-773.
    12. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2021. "Correlating Lévy processes with self-decomposability: applications to energy markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1253-1280, December.

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