Dual pricing of American options by Wiener chaos expansion

Jérôme Lelong ()
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Jérôme Lelong: DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA [2016-2019] - Université Grenoble Alpes [2016-2019]

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Abstract: In this work, we propose an algorithm to price American options by directly solving thedual minimization problem introduced by Rogers. 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.

Keywords: high performance computing; stochastic optimization; duality; American option; Snell envelope; Wiener chaos expansion; sample average approximation (search for similar items in EconPapers)
Date: 2018-04-24
Note: View the original document on HAL open archive server: https://hal.science/hal-01299819v3
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Citations: View citations in EconPapers (13)

Published in SIAM Journal on Financial Mathematics, 2018, 9 (2), pp.493-519. ⟨10.1137/16M1102161⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01299819

DOI: 10.1137/16M1102161

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