  The convolution method for the numerical solution of forward-backward
stochastic differential equations (FBSDEs), introduced in [21], uses a uniform
space grid. In this paper we utilize a tree-like spatial discretization that
approximates the BSDE on the tree, so that no spatial interpolation procedure
is necessary. In addition to suppressing extrapolation error, leading to a
globally convergent numerical solution for the FBSDE, we provide explicit
convergence rates. On this alternative grid the conditional expectations
involved in the time discretization of the BSDE are computed using Fourier
analysis and the fast Fourier transform (FFT) algorithm. The method is then
extended to higher-order time discretizations of FBSDEs. Numerical results
demonstrating convergence are presented using a commodity price model,
incorporating seasonality, and forward prices.
