On the efficacy of Fourier series approximations for pricing European options

Hurn, A.S., Lindsay, K.A., & McClelland, A.J. (2014) On the efficacy of Fourier series approximations for pricing European options. Applied Mathematics, 5, pp. 2786-2807.

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This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also 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 halfrange cosine series and the full-range Fourier series. However there are 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 case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

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ID Code: 89567
Item Type: Journal Article
Refereed: Yes
Keywords: Fourier Transform, Fourier Series, Characteristic Function, Option Price
DOI: 10.4236/am.2014.517267
ISSN: 2152-7393
Divisions: Current > QUT Faculties and Divisions > QUT Business School
Current > Schools > School of Economics & Finance
Copyright Owner: Copyright 2014 by authors and Scientific Research Publishing Inc.
Copyright Statement: This work is licensed under the Creative Commons Attribution International License (CC BY).
Deposited On: 28 Oct 2015 00:07
Last Modified: 28 Oct 2015 21:27

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