  We propose a new method for the numerical solution of backward stochastic
differential equations (BSDEs) which finds its roots in Fourier analysis. The
method consists of an Euler time discretization of the BSDE with certain
conditional expectations expressed in terms of Fourier transforms and computed
using the fast Fourier transform (FFT). The problem of error control is
addressed and a local error analysis is provided. We consider the extension of
the method to forward-backward stochastic differential equations (FBSDEs) and
reflected FBSDEs. Numerical examples are considered from finance demonstrating
the performance of the method.
