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.

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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 
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     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},
     publisher = {mathdoc},
     volume = {65},
     year = {2019},
     doi = {10.1051/proc/201965294},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965294/}
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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. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965294/

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