Pricing Bermudan options using regression trees/random forests
Autor: | El Filali Ech-Chafiq, Zineb, Henry-Labordere, Pierre, Lelong, Jérôme |
---|---|
Přispěvatelé: | Données, Apprentissage et Optimisation (DAO), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Natixis, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) |
Jazyk: | angličtina |
Rok vydání: | 2023 |
Předmět: |
History
050208 finance Polymers and Plastics Regression trees Probability (math.PR) 05 social sciences Computational Finance (q-fin.CP) Random forests [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP] Industrial and Manufacturing Engineering FOS: Economics and business [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Quantitative Finance - Computational Finance 0502 economics and business FOS: Mathematics Optimal stopping 050207 economics Business and International Management Bermudan options Mathematics - Probability |
Zdroj: | SIAM Journal on Financial Mathematics SIAM Journal on Financial Mathematics, In press |
ISSN: | 1945-497X |
Popis: | International audience; 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. |
Databáze: | OpenAIRE |
Externí odkaz: |