Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 6, p. 1045-1061

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.

DOI : https://doi.org/10.1051/m2an/2009014
Classification:  35K55,  65M12,  39A10,  90A09
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {6},
     year = {2009},
     pages = {1045-1061},
     doi = {10.1051/m2an/2009014},
     zbl = {1175.91071},
     mrnumber = {2588432},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 6, pp. 1045-1061. doi : 10.1051/m2an/2009014. http://www.numdam.org/item/M2AN_2009__43_6_1045_0/

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