I've rarely used FT methods in the real world (one reason being the wrap-around boundary conditions), and not really followed them. And, not sure whether that paper reflects the current state of the art.
FT methods are different from Fourier-spectral methods which typically have periodic BC requirements. That was not what my question was about.
The method in the paper exactly represents the solution as a Fourier-type integral which must be computed numerically. The error in the quadrature rule is the sole source of pricing error.
I guess whether the extra computational cost in computing those integrals exactly with the method the author used would carry a corresponding financial cost.
