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

J\'er\^ome Lelong
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J\'er\^ome Lelong: DAO

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Abstract: 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, in which we basically replace the standard least square regression by a Wiener chaos expansion. Not only does it allow us to deal with a non Markovian setting, but it also breaks the bottleneck induced by the least square regression as the coefficients of the chaos expansion are given by scalar products on the L^2 space and can therefore be approximated by independent Monte Carlo computations. This key feature enables us to provide an embarrassingly parallel algorithm.

Date: 2019-01, Revised 2020-07
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