Pricing American options using martingale bases


J. Lelong

In this work, we propose an algorithm to price American options by directly solving
the dual minimization problem introduced by Rogers [2002]. Our approach relies on
approximating the set of uniformly square integrable martingales by a finite dimensional
Wiener chaos expansion. Then, we use a sample average approximation technique to
efficiently solve the optimization problem. Unlike all the regression based methods, our
method can transparently deal with path dependent options without extra computations
and a parallel implementation writes easily with very little communication and no
centralized work. We test our approach on several multi–dimensional options with up to
40 assets and show the impressive scalability of the parallel implementation.

Key words: American option, duality, Snell envelope, stochastic optimization, sample
average approximation, high performance computing, Wiener chaos expansion.

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