Geodesic
Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view
Bruno Bouchard1 ; Ki Wai Chau2 ; Arij Manai3 ; Ahmed Sid-Ali4
1 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
ESAIM. Proceedings, Tome 65 (2019), pp. 294-308x Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

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.
DOI : 10.1051/proc/201965294

Bruno Bouchard 1 ; Ki Wai Chau 2 ; Arij Manai 3 ; Ahmed Sid-Ali 4

1 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 
@article{EP_2019_65_a12,
     author = {Bruno Bouchard and Ki Wai Chau and Arij Manai and Ahmed Sid-Ali},
     title = {Monte-Carlo methods for the pricing of {American} options: a semilinear {BSDE} point of view},
     journal = {ESAIM. Proceedings},
     pages = {294--308x},
     year = {2019},
     volume = {65},
     doi = {10.1051/proc/201965294},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965294/}
}
TY  - JOUR
AU  - Bruno Bouchard
AU  - Ki Wai Chau
AU  - Arij Manai
AU  - Ahmed Sid-Ali
TI  - Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view
JO  - ESAIM. Proceedings
PY  - 2019
SP  - 294
EP  - 308x
VL  - 65
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201965294/
DO  - 10.1051/proc/201965294
LA  - en
ID  - EP_2019_65_a12
ER  - 
%0 Journal Article
%A Bruno Bouchard
%A Ki Wai Chau
%A Arij Manai
%A Ahmed Sid-Ali
%T Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view
%J ESAIM. Proceedings
%D 2019
%P 294-308x
%V 65
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201965294/
%R 10.1051/proc/201965294
%G en
%F EP_2019_65_a12
Bruno Bouchard; Ki Wai Chau; Arij Manai; Ahmed Sid-Ali. Monte-Carlo methods for the pricing of American options: a semilinear BSDE point of view. ESAIM. Proceedings, Tome 65 (2019), pp. 294-308x. doi: 10.1051/proc/201965294

Cité par Sources :