On the Application of Spectral Filters in a Fourier Option Pricing Technique
24 Pages Posted: 18 May 2013
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On the Application of Spectral Filters in a Fourier Option Pricing Technique
On the Application of Spectral Filters in a Fourier Option Pricing Technique
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
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