Volume 65, 2019CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field
|Page(s)||294 - 308x|
|Published online||02 April 2019|
Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view
Université Paris-Dauphine, PSL University, CNRS, CEREMADE, Paris
2 Centrum Wiskunde & Informatica
3 Institut du Risque et de l’Assurance du Mans, Le Mans université
4 Université Laval, Département de mathématiques et de statistique, Québec, Canada
We extend the viscosity solution characterization proved in  for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear reaction/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching processes based algorithm of . Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results.
Key words: American options / Viscosity solution / Semilinear Black and Scholes partial differential equation / Branching method / BSDE
© EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.