We consider the use of finite volume methods for the approximation of a parabolic variational inequality arising in financial mathematics. We show, under some regularity conditions, the convergence of the upwind implicit finite volume scheme to a weak solution of the variational inequality in a bounded domain. Some results, obtained in comparison with other methods on two dimensional cases, show that finite volume schemes can be accurate and efficient.
Keywords: american option, variational inequality, finite volume method, convergence of numerical scheme
@article{M2AN_2006__40_2_311_0,
author = {Berton, Julien and Eymard, Robert},
title = {Finite volume methods for the valuation of american options},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {311--330},
year = {2006},
publisher = {EDP Sciences},
volume = {40},
number = {2},
doi = {10.1051/m2an:2006011},
mrnumber = {2241825},
zbl = {1137.91427},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2006011/}
}
TY - JOUR AU - Berton, Julien AU - Eymard, Robert TI - Finite volume methods for the valuation of american options JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 311 EP - 330 VL - 40 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2006011/ DO - 10.1051/m2an:2006011 LA - en ID - M2AN_2006__40_2_311_0 ER -
%0 Journal Article %A Berton, Julien %A Eymard, Robert %T Finite volume methods for the valuation of american options %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 311-330 %V 40 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2006011/ %R 10.1051/m2an:2006011 %G en %F M2AN_2006__40_2_311_0
Berton, Julien; Eymard, Robert. Finite volume methods for the valuation of american options. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 2, pp. 311-330. doi: 10.1051/m2an:2006011
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