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Two-dimensional Fourier cosine series expansion method for pricing financial options

  • Marjon Ruijter


  • Kees Oosterlee (CWI)
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    In financial markets, traders deal in assets and options. There exist many types of options and the best-known are the European call and put option. These options give holders the right to buy or sell assets at a specific future time for a predetermined price. This paper examines options of which the payoff depends on two or more different assets. It may involve, for example, an average or the maximum of several asset prices. For pricing options, different types of numerical methods are available, such as Monte Carlo simulation techniques and partial differential equation methods. We apply a method based on Fourier cosine series expansions, called the COS method. We extend this method to higher dimensions with a multidimensional asset-price process and perform extensive numerical experiments. �

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    Paper provided by CPB Netherlands Bureau for Economic Policy Analysis in its series CPB Discussion Paper with number 225.

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    Date of creation: Nov 2012
    Date of revision:
    Handle: RePEc:cpb:discus:225
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    1. Stulz, ReneM., 1982. "Options on the minimum or the maximum of two risky assets : Analysis and applications," Journal of Financial Economics, Elsevier, vol. 10(2), pages 161-185, July.
    2. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    3. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Discussion Paper 2004-19, Tilburg University, Center for Economic Research.
    4. Fang, Fang & Oosterlee, Kees, 2008. "Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions," MPRA Paper 9248, University Library of Munich, Germany.
    5. 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 327-43.
    6. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    7. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(01), pages 1-12, March.
    8. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    9. Stefano, Pagliarani & Pascucci, Andrea & Candia, Riga, 2011. "Expansion formulae for local Lévy models," MPRA Paper 34571, University Library of Munich, Germany.
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