Kyriakos Chourdakis (2005) "Option Pricing Using the Fractional FFT", Journal of Computational Finance, 8(2), 1-18

Abstract: This paper shows how the recently developed fractional FFT algorithm (FRFT) can be used to retrieve option prices from the corresponding characteristic functions. The FRFT algorithm has the advantage of using the characteristic function information in a more efficient way than the straight FFT. Therefore less function evaluations are typically needed and substantial savings in computational time can be made. Two experiments, based on the stochastic volatility and the variance-gamma models, illustrate the benefits of using the fractional version of the FFT and show that option prices can be delivered up to forty-five times faster without substantial losses of result accuracy.

The paper and computer code can be downloaded here