  We propose a new numerical scheme for Backward Stochastic Differential
Equations based on branching processes. We approximate an arbitrary (Lipschitz)
driver by local polynomials and then use a Picard iteration scheme. Each step
of the Picard iteration can be solved by using a representation in terms of
branching diffusion systems, thus avoiding the need for a fine time
discretization. In contrast to the previous literature on the numerical
resolution of BSDEs based on branching processes, we prove the convergence of
our numerical scheme without limitation on the time horizon. Numerical
simulations are provided to illustrate the performance of the algorithm.
