  We clarify the relations among different Fourier-based approaches to option
pricing, and improve the B-spline probability density projection method using
the sinh-acceleration technique. This allows us to efficiently separate the
control of different sources of errors better than the FFT-based realization
allows; in many cases, the CPU time decreases as well. We demonstrate the
improvement of the B-spline projection method through several numerical
experiments in option pricing, including European and barrier options, where
the SINH acceleration technique proves to be robust and accurate.
