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Fourier inversion formulas for multiple-asset option pricing

Author

Listed:
  • Feunou Bruno

    (Bank of Canada, 234, Wellington Street, Ottawa, ON, K1A 0G9, Canada)

  • Tafolong Ernest

    (National Bank of Canada, 1155 Metcalfe Street, Montreal, QC H3B 4S9, Canada)

Abstract
Plain vanilla options have a single underlying asset and a single condition on the payoff at the expiration date. For this class of options, a well known result of Duffie, Pan, and Singleton (Duffie, D., J. Pan, and K. Singleton. 2000. “Transform Analysis and Asset Pricing for Affine Jump-Diffusions.” Econometrica 68: 1343–1376. http://dx.doi.org/10.1111/1468-0262.00164.) shows how to invert the characteristic function to obtain a closed-form formula for their prices. However, multiple-asset and multiple-condition derivatives such as rainbow options cannot be priced within this framework. This paper provides an analytical solution for options whose payoffs depends on two or more conditions. We take the advantage of the inversion of the Fourier transform, resorting to neither Black and Scholes’s framework, nor the affine models’s settings. Numerical experiments based on the aforementioned class of derivatives are provided to illustrate the usefulness of the proposed approach.

Suggested Citation

  • Feunou Bruno & Tafolong Ernest, 2015. "Fourier inversion formulas for multiple-asset option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 531-559, December.
    • Handle: RePEc:bpj:sndecm:v:19:y:2015:i:5:p:531-559:n:3
    DOI: 10.1515/snde-2014-0034
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    Cited by:

    1. Feunou Bruno & Tafolong Ernest, 2015. "Fourier inversion formulas for multiple-asset option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 531-559, December.
    2. Orzechowski Arkadiusz, 2018. "Pricing Correlation Options: from the P. Carr And D. Madan Approach to the New Method Based on the Fourier Transform," Economics and Business Review, Sciendo, vol. 4(1), pages 16-28, April.
    3. Escobar-Anel, Marcos & Rastegari, Javad & Stentoft, Lars, 2020. "Affine multivariate GARCH models," Journal of Banking & Finance, Elsevier, vol. 118(C).

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    More about this item

    Keywords

    derivatives pricing; Fourier-Stieltjes transform; multiple triggers payoff;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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