Neural network regression for Bermudan option pricing

Bernard Lapeyre () and Jérôme Lelong ()
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Bernard Lapeyre: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique
Jérôme Lelong: DAO - Données, Apprentissage et Optimisation - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes

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Abstract: The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques on a finite dimensional vector space. In this work, we study neural networks approximations of conditional expectations. We prove the convergence of the well-known Longstaff and Schwartz algorithm when the standard least-square regression is replaced by a neural network approximation. We illustrate the numerical efficiency of neural networks as an alternative to standard regression methods for approximating conditional expectations on several numerical examples.

Keywords: Deep learning; Bermudan options; Regression methods; Optimal stopping; Neural networks; optimal stopping; regression methods; deep learning; neural networks (search for similar items in EconPapers)
Date: 2021-09
New Economics Papers: this item is included in nep-big and nep-cmp
Note: View the original document on HAL open archive server: https://hal.univ-grenoble-alpes.fr/hal-02183587v3
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Citations: View citations in EconPapers (6)

Published in Monte Carlo Methods and Applications, 2021, 27 (3), pp.227-247. ⟨10.1515/mcma-2021-2091⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02183587

DOI: 10.1515/mcma-2021-2091

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