  We propose a novel algorithm which allows to sample paths from an underlying
price process in a local volatility model and to achieve a substantial variance
reduction when pricing exotic options. The new algorithm relies on the
construction of a discrete multinomial tree. The crucial feature of our
approach is that -- in a similar spirit to the Brownian Bridge -- each random
path runs backward from a terminal fixed point to the initial spot price. We
characterize the tree in two alternative ways: in terms of the optimal grids
originating from the Recursive Marginal Quantization algorithm and following an
approach inspired by the finite difference approximation of the diffusion's
infinitesimal generator. We assess the reliability of the new methodology
comparing the performance of both approaches and benchmarking them with
competitor Monte Carlo methods.
