Notes on the SWIFT method based on Shannon Wavelets for Option Pricing

基于Shannon小波的SWIFT期权定价方法再探讨——回顾

Notes on the SWIFT method based on Shannon Wavelets for Option Pricing -- Revisited

本文回顾了2023年基于Shannon小波的SWIFT期权定价方法，探讨了其潜在改进并揭示了该方法存在的具体缺陷。

SWIFT calibration of the Heston model

In the present work, the European option pricing SWIFT method is extended for Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The proposed calibration machinery appears to be extremely fast, in particular for a single expiry and multiples strikes, outperforming the state-of-the-art method we compare with. Further, the a priori knowledge of SWIFT parameters makes possible a reliable and practical implementation of the presented calibration method. A wide set of stress, speed and convergen…

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

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 incr…