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

Fabien Le Floc'h

TL;DR

This note revisits the SWIFT method, which prices European options using Shannon wavelets and a known characteristic function, with a focus on the Heston model. It analyzes quadrature choices for payoff and density, comparing Vieta-based sinc expansions to Euler–Maclaurin-corrected forms and advocating the trapezoidal rule for practical efficiency. The findings indicate that EM corrections offer limited price benefits beyond improved coefficient accuracy, while trapezoidal rules better support FFT-based implementations; nonetheless, SWIFT faces substantial computational cost in many corner cases similar to the COS method. The study provides guidance on parameter initialization and error control, highlighting that SWIFT remains robust relative to COS but requires careful handling to remain computationally viable in calibration tasks.

Abstract

This note revisits the SWIFT method based on Shannon wavelets to price European options under models with a known characteristic function in 2023. In particular, it discusses some possible improvements and exposes some concrete drawbacks of the method.

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

TL;DR

This note revisits the SWIFT method, which prices European options using Shannon wavelets and a known characteristic function, with a focus on the Heston model. It analyzes quadrature choices for payoff and density, comparing Vieta-based sinc expansions to Euler–Maclaurin-corrected forms and advocating the trapezoidal rule for practical efficiency. The findings indicate that EM corrections offer limited price benefits beyond improved coefficient accuracy, while trapezoidal rules better support FFT-based implementations; nonetheless, SWIFT faces substantial computational cost in many corner cases similar to the COS method. The study provides guidance on parameter initialization and error control, highlighting that SWIFT remains robust relative to COS but requires careful handling to remain computationally viable in calibration tasks.

Abstract

This note revisits the SWIFT method based on Shannon wavelets to price European options under models with a known characteristic function in 2023. In particular, it discusses some possible improvements and exposes some concrete drawbacks of the method.
Paper Structure (8 sections, 14 equations, 3 figures, 3 tables)

This paper contains 8 sections, 14 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Quick summary of the SWIFT method
  3. Choice of SWIFT parameters
  4. Vieta, Mid-points or Trapezoidal?
  5. For the payoff
  6. For the density
  7. Corner cases
  8. Conclusion

Figures (3)

  • Figure S1: Value and error in the coefficients $V_{6,k}$ for the option of strike $K=1.064$, using $m=6, L=8, J=2^4$.
  • Figure S2: Density coefficients and in vanilla option prices for a range of strikes, using $m=6, L=8, J=2^4$.
  • Figure S3: Error in density coefficients and vanilla option prices for a range of strikes, using $m=6, L=8, J=2^4$ for the Heston parameters of Set 2.