  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.
