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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
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    References listed on IDEAS

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    1. Adrian Buss & Grigory Vilkov, 2012. "Measuring Equity Risk with Option-implied Correlations," Review of Financial Studies, Society for Financial Studies, vol. 25(10), pages 3113-3140.
    2. Patrick Navatte & Christophe Villa, 2000. "The information content of implied volatility, skewness and kurtosis: empirical evidence from long-term CAC 40 options," European Financial Management, European Financial Management Association, vol. 6(1), pages 41-56.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. 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.
    5. Christoffersen, Peter & Feunou, Bruno & Jacobs, Kris & Meddahi, Nour, 2014. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(03), pages 663-697, June.
    6. Chang, Chuang-Chang & Chung, San-Lin & Yu, Min-Teh, 2006. "Loan guarantee portfolios and joint loan guarantees with stochastic interest rates," The Quarterly Review of Economics and Finance, Elsevier, vol. 46(1), pages 16-35, February.
    7. Gourieroux, Christian & Sufana, Razvan, 2010. "Derivative Pricing With Wishart Multivariate Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 438-451.
    8. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    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.

    More about this item

    JEL classification:

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

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