Fast Barrier Option Pricing by the COS BEM Method in Heston Model (with Matlab code)

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. A Matlab code implementing this technique is attached at the end of the paper.