Pricing Bermudan options using regression trees/random forests

Zineb El Filali Ech-Chafiq (zinebelfilaliechchafique@gmail.com), Pierre Henry Labordère and Jérôme Lelong (jerome.lelong@univ-grenoble-alpes.fr)
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Zineb El Filali Ech-Chafiq: 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, Natixis
Pierre Henry Labordère: Natixis
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 value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the exercise value is strictly greater than the continuation value. We can formulate this problem as a dynamic programming equation, where the main difficulty comes from the computation of the conditional expectations representing the continuation values at each time step. In (Longstaff and Schwartz, 2001), these conditional expectations were estimated using regressions on a finite-dimensional vector space (typically a polynomial basis). In this paper, we follow the same algorithm; only the conditional expectations are estimated using Regression trees or Random forests. We discuss the convergence of the LS algorithm when the standard least squares regression is replaced with regression trees. Finally, we expose some numerical results with regression trees and random forests. The random forest algorithm gives excellent results in high dimensions.

Keywords: Regression trees; Random forests; Bermudan options; Optimal stopping (search for similar items in EconPapers)
Date: 2023-12
Note: View the original document on HAL open archive server: https://hal.science/hal-03436046v2
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Citations: View citations in EconPapers (1)

Published in SIAM Journal on Financial Mathematics, 2023, 14 (4), pp.1113-1139. ⟨10.1137/21M1460648⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03436046

DOI: 10.1137/21M1460648

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