A fast Fourier transform method for Mellin-type option pricing

TL;DR

This paper introduces a rapid Fourier transform-based numerical method for pricing European and American basket put options using Mellin transforms, accounting for asset correlation and dividends, with verified accuracy.

Contribution

It presents a novel fast Fourier transform approach for efficient numerical Mellin inversion in option pricing, improving computational speed and accuracy.

Findings

Accurate pricing of European and American basket options achieved.

The method outperforms existing techniques in numerical accuracy.

Efficient computation at equidistant log asset prices demonstrated.

Abstract

Analytical pricing formulas and Greeks are obtained for European and American basket put options using Mellin transforms. We assume assets are driven by geometric Brownian motion which exhibit correlation and pay a continuous dividend rate. A novel approach to numerical Mellin inversion is achieved via the fast Fourier transform, enabling the computation of option values at equidistant log asset prices. Numerical accuracy is verified among existing methods for American call options.