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A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions

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  • Fang, Fang
  • Oosterlee, Kees

Abstract

Here we develop an option pricing method for European options based on the Fourier-cosine series, and call it the COS method. The key insight is in the close relation of the characteristic function with the series coefficients of the Fourier-cosine expansion of the density function. In most cases, the convergence rate of the COS method is exponential and the computational complexity is linear. Its range of application covers different underlying dynamics, including L\'evy processes and Heston stochastic volatility model, and various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal with European options in particular. In a follow-up paper we will present its application to options with early-exercise features.

Suggested Citation

  • Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 7700, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:7700
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    References listed on IDEAS

    as
    1. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.
    2. Alan L. Lewis, 2001. "A Simple Option Formula for General Jump-Diffusion and other Exponential Levy Processes," Related articles explevy, Finance Press.
    3. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    4. Mark Broadie & Yusaku Yamamoto, 2003. "Application of the Fast Gauss Transform to Option Pricing," Management Science, INFORMS, vol. 49(8), pages 1071-1088, August.
    5. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Andricopoulos, Ari D. & Widdicks, Martin & Duck, Peter W. & Newton, David P., 2003. "Universal option valuation using quadrature methods," Journal of Financial Economics, Elsevier, vol. 67(3), pages 447-471, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    option pricing; European options; Fourier-cosine expansion;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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