On the Application of Spectral Filters in a Fourier Option Pricing Technique

24 Pages Posted: 18 May 2013

See all articles by Marjon Ruijter

Marjon Ruijter

Center for Mathematics and Computer Science (CWI)

Mark Versteegh

Delft University of Technology

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

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Abstract

When Fourier techniques are employed to specific option pricing cases from computational finance with non-smooth functions, the so-called Gibbs phenomenon may become apparent. This seriously impacts the efficiency and accuracy of the pricing. For example, the Variance Gamma asset price process gives rise to algebraically decaying Fourier coefficients, resulting in a slowly converging Fourier series. We apply spectral filters to achieve faster convergence. Filtering is carried out in Fourier space; the series coefficients are pre-multiplied by a decreasing filter, which does not add significant computational cost. Tests with different filters show how the algebraic index of convergence is improved.

Keywords: Fourier cosine expansion method, spectral filters, European options, Variance Gamma, portfolio loss distribution, Gibbs phenomenon

JEL Classification: C63

Suggested Citation

Ruijter, Marjon and Versteegh, Mark and Oosterlee, Cornelis W., On the Application of Spectral Filters in a Fourier Option Pricing Technique. Journal of Computational Finance, 2015, Available at SSRN: https://ssrn.com/abstract=2266323 or http://dx.doi.org/10.2139/ssrn.2266323

Marjon Ruijter (Contact Author)

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

Mark Versteegh

Delft University of Technology ( email )

Stevinweg 1
Stevinweg 1
Delft, 2628 CN

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands

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