and CREST

We study a discrete-time approximation for solutions of systems of decou-pled forward-backward stochastic differential equations with jumps. Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the number of time steps n goes to infinity. The rate of conver-gence is at least n−1/2+ε, for any ε> 0. When the jump coefficient of the first variation process of the forward component satisfies a non-degeneracy condi-tion which ensures its inversibility, we achieve the optimal convergence rate n−1/2. The proof is based on a generalization of a remarkable result on the path-regularity of the solution of the backward equation derived by Zhang [25] in the no-jump case. Key words: Discrete-time approximation, forward-backward SDE’s with jumps, Malliavin calculus. MSC Classification (2000): 65C99, 60H07, 60J75