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

ArXiv ID: 2401.01758 “View on arXiv”

Authors: Unknown

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.

Keywords: Shannon Wavelets, Option Pricing, Characteristic Function, Spectral Methods, Numerical Methods, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with advanced mathematical derivations, including wavelet expansions, Euler-Maclaurin formulas, and FFT implementations, but focuses on theoretical improvements and parameter selection with minimal concrete backtesting or implementation details.

  flowchart TD
    A["Research Goal: Revisit & Improve<br>SWIFT Method for Option Pricing"] --> B["Methodology: Shannon Wavelets<br>+ Spectral Approximations"]
    B --> C["Inputs: Characteristic Functions<br>from Asset Pricing Models"]
    C --> D["Computational Process:<br>Wavelet Coefficient Calculation"]
    D --> E["Computational Process:<br>Numerical Integration & Option Valuation"]
    E --> F{"Key Findings/Outcomes"}
    F --> G["Identified Method Improvements"]
    F --> H["Exposed Concrete Drawbacks<br>Limitations in Practice"]