Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view

Bruno Bouchard (), Ki Chau, Arij Manai and Ahmed Sid-Ali
Additional contact information
Bruno Bouchard: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Ki Chau: CWI - Centrum voor Wiskunde en Informatica - CWI - Centrum Wiskunde & Informatica - Netherlands Organisation for Scientific Research
Arij Manai: UM - Le Mans Université
Ahmed Sid-Ali: ULaval - Université Laval [Québec]

Post-Print from HAL

Abstract: We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of [8]. Our numerical experiments show that approximating the discontinu-ous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results.

Keywords: Viscosity solution; Semilinear Black and Sc- holes partial differential equation; Semilinear Black and Sc-holes partial differential equation; American options; BSDE; Branching method (search for similar items in EconPapers)
Date: 2019
Note: View the original document on HAL open archive server: https://hal.science/hal-01666399v2
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in ESAIM: Proceedings and Surveys, 2019, 65, pp.294-308. ⟨10.1051/proc/201965294⟩

Downloads: (external link)
https://hal.science/hal-01666399v2/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01666399

DOI: 10.1051/proc/201965294

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().