On the Efficacy of Fourier Series Approximations for Pricing European and Digital Options

Stan Hurn (), Kenenth A Lindsay and Andrew McClelland
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Kenenth A Lindsay: Glasgow

No 90, NCER Working Paper Series from National Centre for Econometric Research

Abstract: This paper investigates several competing procedures for computing the price of European and digital options in which the underlying model has a characteristic function that is known in at least semi-closed form. The algorithms for pricing the options investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. The performance of the algorithms is assessed in simulation experiments which price options in a Black-Scholes world where an analytical solution is available and for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the half-range cosine series and the full-range Fourier series. There are however two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together, these two conclusions make a strong case for the merit of pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series.

Pages: 24 pages
Date: 2013-01-24
New Economics Papers: this item is included in nep-cmp
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