Fast Fourier Transform for discrete Asian Options

This paper presents an efficient methodology for the discrete Asian options consistent with different types of underlying densities, especially non-normal returns as suggested by the empirical literature (Mandelbrot (1963) and Fama (1964)). The interest of this method is its flexibility compared to the more standard ones. Based on Fast Fourier Transform, the method is an enhanced version of the algorithm of Caverhill and Clewlow (1992). The contribution of this paper is to improve their algorithm and to adapt it to non-lognormal densities. This enables us to examine the impact of fat-tailed distributions on price as well as on delta. We find evidence that fat tails lead to wider jumps in the delta.