Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach

In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff–Schwartz algorithm: we basically replace the standard least squares regression with a Wiener chaos expansion. This not only allows us to deal with a non-Markovian setting but also breaks the bottleneck induced by the least squares regression, as the coefficients of the chaos expansion are given by scalar products on the L2(Ω) space and can therefore be approximated by independent Monte Carlo computations. This key feature enables us to propose an embarrassingly parallel algorithm to efficiently handle non-Markovian payoff.