2019/01/17 by Jérôme Lelong, Lelong, Jérôme
Economics, Econometrics and Finance · Physics and Astronomy · Mathematics · #Stochastic processes and financial applications #stochastic dynamics and bifurcation #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.1901.05672
In this work, we propose a new policy iteration algorithm for pricing\nBermudan options when the payoff process cannot be written as a function of a\nlifted Markov process. Our approach is based on a modification of the\nwell-known Longstaff Schwartz algorithm, in which we basically replace the\nstandard least square regression by a Wiener chaos expansion. Not only does it\nallow us to deal with a non Markovian setting, but it also breaks the\nbottleneck induced by the least square regression as the coefficients of the\nchaos expansion are given by scalar products on the L2 space and can therefore\nbe approximated by independent Monte Carlo computations. This key feature\nenables us to provide an embarrassingly parallel algorithm.\n