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Fast Fourier Transform for discrete Asian Options

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Author Info
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.

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 6.

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Date of creation: 01 Apr 2001
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Handle: RePEc:sce:scecf1:6

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Related research
Keywords: FFT; Asian Option; Fat Tailed distributions; Convolutions;

Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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  1. Nielsen, J. A. & K. Sandmann, 1995. "The Pricing of Asian Options under Stochastic Interest Rates," Discussion Paper Serie B 323, University of Bonn, Germany, revised Dec 1995. [Downloadable!]
  2. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  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 637-54, May-June. [Downloadable!] (restricted)
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