  We generalize the primal-dual methodology, which is popular in the pricing of
early-exercise options, to a backward dynamic programming equation associated
with time discretization schemes of (reflected) backward stochastic
differential equations (BSDEs). Taking as an input some approximate solution of
the backward dynamic program, which was pre-computed, e.g., by least-squares
Monte Carlo, our methodology allows to construct a confidence interval for the
unknown true solution of the time discretized (reflected) BSDE at time 0. We
numerically demonstrate the practical applicability of our method in two
five-dimensional nonlinear pricing problems where tight price bounds were
previously unavailable.
