Refined and Enhanced Fast Fourier Transform Techniques, with an Application to the Pricing of Barrier Options

33 Pages Posted: 24 May 2008 Last revised: 11 Jun 2008

See all articles by Mitya Boyarchenko

Mitya Boyarchenko

University of Michigan - Department of Mathematics

Sergei Levendorskii

Calico Science Consulting

Date Written: June 9, 2008

Abstract

The fast Fourier transform (FFT) technique is now a standard tool for the numerical calculation of prices of derivative securities. Unfortunately, in many important situations, such as the pricing of contingent claims of European type near expiry, and the pricing of barrier options close to the barrier, the standard implementation of this technique leads to serious systematic errors. We propose a new, fast and efficient, variant of the FFT technique, which is free of these problems, and is as easy to implement as the most common version of FFT. As an example, we show how our method leads to a pricing algorithm for down-and-out barrier put options that is the most efficient one to date, both in terms of the speed and in terms of the accuracy of the computations.

Keywords: Option pricing, Fourier transform, FFT, Levy processes, Carr's randomization, barrier options, Wiener-Hopf factorization

JEL Classification: C63, G13

Suggested Citation

Boyarchenko, Mitya and Levendorskii, Sergei Z., Refined and Enhanced Fast Fourier Transform Techniques, with an Application to the Pricing of Barrier Options (June 9, 2008). Available at SSRN: https://ssrn.com/abstract=1142833 or http://dx.doi.org/10.2139/ssrn.1142833

Mitya Boyarchenko (Contact Author)

University of Michigan - Department of Mathematics ( email )

530 Church Street
2074 East Hall
Ann Arbor, MI 48109
United States

Sergei Z. Levendorskii

Calico Science Consulting ( email )

Austin, TX
United States

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