The Parareal Algorithm for American Options

La méthode pararéelle pour les options américaines

Gilles Pagès (), Olivier Pironneau and Guillaume Sall
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Gilles Pagès: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Olivier Pironneau: LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Guillaume Sall: LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique

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Abstract: This note provides a description of the parareal method, a numerical section to assess the performance of the method for American contracts in the scalar case computed by LSMC and parallelized by parareal time decomposition with two or more levels. It contains also a convergence proof for the two levels pa- rareal Monte-Carlo method when the coarse grid solution is computed by an Euler explicit scheme with time step ∆t > δt, the time step used for the Euler scheme at the fine grid level. Hence the theorem provides a tool to analyze also the multilevel parareal method.

Keywords: Financial securities; risk assessment; American options; LSMC; Parareal (search for similar items in EconPapers)
Date: 2016
Note: View the original document on HAL open archive server: https://hal.sorbonne-universite.fr/hal-01320331
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Comptes Rendus. Mathématique, 2016, Série I Mathémtiques, 354 (11), pp.1132-1138

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