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

TL;DR

This paper introduces a combined Fourier-cosine series and Boundary Element Method (BEM) approach for rapid barrier option pricing within the Heston model, enhancing computational efficiency over traditional methods.

Contribution

It develops a novel COS BEM methodology tailored for barrier options in the Heston model, improving speed and accuracy compared to Monte Carlo and traditional techniques.

Findings

The method achieves faster computation times.

Error bounds are effectively estimated using characteristic functions.

The approach is practical for finance practitioners.

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.