A Fast Fourier Transform Method for Mellin-type Option Pricing

Following from the previous post on Mellin-type option pricing, analytical pricing formulas and Greeks are obtained for European and American basket put options using Mellin transforms. In the manuscript below, 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.

http://arxiv.org/abs/1403.3756

The close relationship between the Fourier and Mellin transform is well-known. This allows Mellin-type options to be priced using Fourier-based pricing schemes. In a related paper (that should be finished by the end of 2015) we will explore some additional numerical solutions for Mellin-type options and address some alternative approaches to numerical Mellin inversion.
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