Singular Fourier-Padé Series Expansion of European Option Prices
Article
Chan, R. 2018. Singular Fourier-Padé Series Expansion of European Option Prices. Quantitative Finance. 18 (7), pp. 1149-1171. https://doi.org/10.1080/14697688.2017.1414952
Authors | Chan, R. |
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Abstract | We apply a new numerical method, the singular Fourier-Pade (SFP) method invented by Driscoll and Fornberg (2001, 2011), to price European-type options in Levy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecewise continuous (non-smooth) probability density functions. When techniques such as fast Fourier transforms and Fourier series are applied to price and hedge options with non-smooth probability density functions, they cause the Gibbs phenomenon; accordingly, the techniques converge slowly for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. More-over, we show that our method requires a small number of terms to yield fast error convergence, and it is able to accurately price any European-type option deep in/out of the money and with very long/short maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This new method performs favourably in numerical experiments compared with existing techniques. |
Journal | Quantitative Finance |
Journal citation | 18 (7), pp. 1149-1171 |
ISSN | 1469-7688 |
Year | 2018 |
Publisher | Taylor & Francis |
Accepted author manuscript | License File Access Level Anyone |
Digital Object Identifier (DOI) | https://doi.org/10.1080/14697688.2017.1414952 |
Publication dates | |
Online | 23 Jan 2018 |
Publication process dates | |
Accepted | 06 Dec 2017 |
Deposited | 07 Dec 2017 |
Copyright holder | © 2017 The Author. This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 23/01/2018, available online: http://www.tandfonline.com/10.1080/14697688.2017.1414952 |
https://repository.uel.ac.uk/item/84918
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Accepted author manuscript
SingCFSEuroV13reformatted.pdf | ||
License: All rights reserved | ||
File access level: Anyone |
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