Paper: arXiv 2401.01758

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]

Cited References (15)

  1. Coefficients of Euler-Maclaurin formulas for numerical integration (2014)
  2. Pricing early-exercise and discrete barrier options by Shannon wavelet expansions (2017)
  3. SWIFT valuation of discretely monitored arithmetic Asian options (2018)
  4. SWIFT calibration of the Heston model (2021)
  5. Notes on the SWIFT method based on Shannon Wavelets for Option Pricing (2020) — link
  6. Heston…. Again?! Robust High-Precision Option Pricing by Fourier Transforms: Contour Deformations and Double-Exponential Quadrature (2019)
  7. Numerical integration and the redemption of the trapezoidal rule (2011)
  8. The exponentially convergent trapezoidal rule (2014)
and 7 more
  1. The COS Method: An Efficient Fourier Method for Pricing Financial Derivatives (2010)
  2. A highly efficient Shannon wavelet inverse Fourier technique for pricing European options (2016)
  3. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  4. A simple option formula for general jump-diffusion and other exponential L 'e vy processes (2001)
  5. Interest Rate Modeling, Volume I: Foundations and Vanilla Models (2010)
  6. Option pricing with COS method on graphics processing units (2009)
  7. A novel pricing method for European options based on Fourier-cosine series expansions (2008)

0 of 15 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.