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

49 Pages Posted: 20 Oct 2020 Last revised: 19 May 2021

See all articles by Fabio Baschetti

Fabio Baschetti

affiliation not provided to SSRN

Giacomo Bormetti

University of Bologna - Department of Mathematics

Silvia Romagnoli

University of Bologna - Department of Statistics

Pietro Rossi

Prometeia

Date Written: September 1, 2020

Abstract

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 SINC approach. While the COS method by Fang and Osterlee (2009) leverages the Fourier-cosine expansion of truncated densities, the SINC approach builds on the Shannon Sampling Theorem revisited for functions with bounded support. We provide several results which were missing in the early derivation: i) a rigorous proof of the convergence of the SINC formula to the correct option price when the support grows and the number of Fourier frequencies increases; ii) ready to implement formulas for put, Cash-or-Nothing, and Asset-or-Nothing options; iii) a systematic comparison with the COS formula for several log-price models; iv) a numerical challenge against alternative Fast Fourier specifications, such as Carr and Madan (1999) and Lewis (2000); v) an extensive pricing exercise under the rough Heston model of Jaisson and Rosenbaum (2015); vi) formulas to evaluate numerically the moments of a truncated density. The advantages of the SINC approach are numerous. When compared to benchmark methodologies, SINC provides the most accurate and fast pricing computation. The method naturally lends itself to price all options in a smile concurrently by means of Fast Fourier techniques, boosting fast calibration. Pricing requires to resort only to odd moments in the Fourier space. A previous version of this manuscript circulated with the title `Rough Heston: The SINC way'.

Keywords: option pricing, rough Heston model, Fourier expansion, COS method, Fast Fourier methods

JEL Classification: C6, G12, G13

Suggested Citation

Baschetti, Fabio and Bormetti, Giacomo and Romagnoli, Silvia and Rossi, Pietro, The SINC way: A fast and accurate approach to Fourier pricing (September 1, 2020). Available at SSRN: https://ssrn.com/abstract=3684706 or http://dx.doi.org/10.2139/ssrn.3684706

Fabio Baschetti

affiliation not provided to SSRN

Giacomo Bormetti (Contact Author)

University of Bologna - Department of Mathematics ( email )

Piazza di Porta S. Donato , 5
Bologna, Bologna 40126
Italy

Silvia Romagnoli

University of Bologna - Department of Statistics ( email )

Pietro Rossi

Prometeia ( email )

Italy

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