This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of the numerical approximation of the Gamma of the option, previously obtained. Results are illustrated with numerical examples.
Mots-clés : nonlinear Black-Scholes equation, option pricing, numerical analysis, transaction costs
@article{M2AN_2009__43_6_1045_0,
author = {Company, Rafael and J\'odar, Lucas and Pintos, Jos\'e-Ram\'on},
title = {Consistent stable difference schemes for nonlinear {Black-Scholes} equations modelling option pricing with transaction costs},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1045--1061},
publisher = {EDP-Sciences},
volume = {43},
number = {6},
year = {2009},
doi = {10.1051/m2an/2009014},
mrnumber = {2588432},
zbl = {1175.91071},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2009014/}
}
TY - JOUR AU - Company, Rafael AU - Jódar, Lucas AU - Pintos, José-Ramón TI - Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 1045 EP - 1061 VL - 43 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009014/ DO - 10.1051/m2an/2009014 LA - en ID - M2AN_2009__43_6_1045_0 ER -
%0 Journal Article %A Company, Rafael %A Jódar, Lucas %A Pintos, José-Ramón %T Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 1045-1061 %V 43 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009014/ %R 10.1051/m2an/2009014 %G en %F M2AN_2009__43_6_1045_0
Company, Rafael; Jódar, Lucas; Pintos, José-Ramón. Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 6, pp. 1045-1061. doi : 10.1051/m2an/2009014. http://www.numdam.org/articles/10.1051/m2an/2009014/
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