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Fast Fourier Transform for discrete Asian Options

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  • E. Benhamou

Abstract

This paper presents an efficient methodology for the discrete Asian options consistent with different types of underlying densities, especially non-normal returns as suggested by the empirical literature (Mandelbrot (1963) and Fama (1964)). The interest of this method is its flexibility compared to the more standard ones. Based on Fast Fourier Transform, the method is an enhanced version of the algorithm of Caverhill and Clewlow (1992). The contribution of this paper is to improve their algorithm and to adapt it to non-lognormal densities. This enables us to examine the impact of fat-tailed distributions on price as well as on delta. We find evidence that fat tails lead to wider jumps in the delta.

Suggested Citation

  • E. Benhamou, 2001. "Fast Fourier Transform for discrete Asian Options," Computing in Economics and Finance 2001 6, Society for Computational Economics.
  • Handle: RePEc:sce:scecf1:6
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    File URL: http://fmg2.lse.ac.uk/~benhamou/documents/PHD_AsianConvol.pdf
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    References listed on IDEAS

    as
    1. J. A. Nielsen & K. Sandmann, 1996. "The pricing of Asian options under stochastic interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(3), pages 209-236.
    2. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    3. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    4. Jacques, Michel, 1996. "On the Hedging Portfolio of Asian Options," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(02), pages 165-183, November.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    7. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    FFT; Asian Option; Fat Tailed distributions; Convolutions;

    JEL classification:

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

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