We propose a novel algorithm which allows to sample paths from an underlyingprice process in a local volatility model and to achieve a substantial variancereduction when pricing exotic options. The new algorithm relies on theconstruction of a discrete multinomial tree. The crucial feature of ourapproach is that -- in a similar spirit to the Brownian Bridge -- each randompath runs backward from a terminal fixed point to the initial spot price. Wecharacterize the tree in two alternative ways: in terms of the optimal gridsoriginating from the Recursive Marginal Quantization algorithm and following anapproach inspired by the finite difference approximation of the diffusion'sinfinitesimal generator. We assess the reliability of the new methodologycomparing the performance of both approaches and benchmarking them withcompetitor Monte Carlo methods.
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