Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, p. 359-369

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

DOI : https://doi.org/10.1051/m2an:2004018
Classification:  49L25,  65M06,  65M12
Keywords: high-order compact finite differences, numerical convergence, viscosity solution, financial derivatives
@article{M2AN_2004__38_2_359_0,
author = {D\"uring, Bertram and Fourni\'e, Michel and J\"ungel, Ansgar},
title = {Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {38},
number = {2},
year = {2004},
pages = {359-369},
doi = {10.1051/m2an:2004018},
mrnumber = {2069151},
zbl = {1124.91031},
language = {en},
url = {http://www.numdam.org/item/M2AN_2004__38_2_359_0}
}

Düring, Bertram; Fournié, Michel; Jüngel, Ansgar. Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, pp. 359-369. doi : 10.1051/m2an:2004018. http://www.numdam.org/item/M2AN_2004__38_2_359_0/

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