| Issue |
ESAIM: ProcS
Volume 65, 2019
CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field
|
|
|---|---|---|
| Page(s) | 294 - 308x | |
| DOI | https://doi.org/10.1051/proc/201965294 | |
| Published online | 02 April 2019 | |
Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view
1
Université Paris-Dauphine, PSL University, CNRS, CEREMADE, Paris
e-mail: bouchard@ceremade.dauphine.fr
2
Centrum Wiskunde & Informatica
e-mail: K.W.Chau@cwi.nl
3
Institut du Risque et de l’Assurance du Mans, Le Mans université
e-mail: arijmanai@gmail.com
4
Université Laval, Département de mathématiques et de statistique, Québec, Canada
e-mail: ahmed.sid-ali.1@ulaval.ca
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 reaction/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 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
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