Introduction to Fast Fourier Transform in Finance
29 Pages Posted: 29 Jun 2004
Date Written: February 20, 2006
The Fourier transform is an important tool in Financial Economics. It delivers real time pricing while allowing for a realistic structure of asset returns, taking into account excess kurtosis and stochastic volatility. Fourier transform is also rather abstract and therefore off-putting to many practitioners.
The purpose of this paper is to explain the working of the fast Fourier transform in the familiar binomial option pricing model. We argue that a good understanding of FFT requires no more than some high school mathematics and familiarity with roulette, bicycle wheel, or a similar circular object divided into equally sized segments. The returns to such a small intellectual investment are overwhelming.
Keywords: Fast Fourier transform, option pricing, binomial lattice, chirp-z transform
JEL Classification: C63, G12
Suggested Citation: Suggested Citation