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The goal of this paper is to investigate the method outlined by one of us(PR) in Cherubini et al. (2009) to compute option prices. We name it the SINCapproach. While the COS method by Fang and Osterlee (2009) leverages theFourier-cosine expansion of truncated densities, the SINC approach builds onthe Shannon Sampling Theorem revisited for functions with bounded support. Weprovide several results which were missing in the early derivation: i) arigorous proof of the convergence of the SINC formula to the correct optionprice when the support grows and the number of Fourier frequencies increases;ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothingoptions; iii) a systematic comparison with the COS formula for severallog-price models; iv) a numerical challenge against alternative Fast Fourierspecifications, such as Carr and Madan (1999) and Lewis (2000); v) an extensivepricing exercise under the rough Heston model of Jaisson and Rosenbaum (2015);vi) formulas to evaluate numerically the moments of a truncated density. Theadvantages of the SINC approach are numerous. When compared to benchmarkmethodologies, SINC provides the most accurate and fast pricing computation.The method naturally lends itself to price all options in a smile concurrentlyby means of Fast Fourier techniques, boosting fast calibration. Pricingrequires to resort only to odd moments in the Fourier space. A previous versionof this manuscript circulated with the title `Rough Heston: The SINC way'.

The SINC way: A fast and accurate approach to Fourier pricing