Fast Barrier Option Pricing by the COS BEM Method in Heston Model

Paper: arXiv 2301.00648

Authors: A. Aimi, C. Guardasoni, L. Ortiz-Gracia, S. Sanfelici

Abstract

In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among Finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically sophisticated combination of the Fourier-cosine series (COS) method and the Boundary Element Method (BEM) for pricing barrier options under the Heston model, complete with formal error bounds. However, it is primarily a numerical/theoretical valuation paper with little empirical validation or real market data backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal: Fast Barrier Option Pricing in Heston Model"] --> B["Inputs: Model Params, Option Specs & Log-Asset Char Function"]
    B --> C["Combine Fourier-Cosine Series (COS) + Boundary Element Method (BEM)"]
    C --> D["Apply COS-BEM to Benchmark Models (Black-Scholes & Heston)"]
    D --> E["Perform Error Bound Analysis on COS Expansion Terms"]
    E --> F["Key Findings: High Efficiency, Superior to MC & Alternative to Traditional Pricing"]