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Neural network regression for Bermudan option pricing

Author

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  • Lapeyre Bernard

    (CERMICS, École des Ponts ParisTech, INRIA, 6 et 8 avenue Blaise-Pascal, Champs-sur-Marne, 77455Marne-la-Vallée, France)

  • Lelong Jérôme

    (LJK, Université Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000Grenoble, France)

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, assuming an efficient algorithm to compute this approximation. We illustrate the numerical efficiency of neural networks as an alternative to standard regression methods for approximating conditional expectations on several numerical examples.

Suggested Citation

  • Lapeyre Bernard & Lelong Jérôme, 2021. "Neural network regression for Bermudan option pricing," Monte Carlo Methods and Applications, De Gruyter, vol. 27(3), pages 227-247, September.
    • Handle: RePEc:bpj:mcmeap:v:27:y:2021:i:3:p:227-247:n:5
    DOI: 10.1515/mcma-2021-2091
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