Geodesic
Finite difference schemes for a nonlinear Black-Scholes model with transaction cost and volatility risk
Sima Mashayekhi1 ; Jens Hugger1 ; Sima Mashayekhi ; Jens Hugger
1University of Copenhagen
Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 2, pp. 255-266 
Sima Mashayekhi; Jens Hugger; Sima Mashayekhi; Jens Hugger. Finite difference schemes for a nonlinear Black-Scholes model with transaction cost and volatility risk. Acta mathematica Universitatis Comenianae, Tome 84 (2015) no. 2, pp. 255-266. http://geodesic.mathdoc.fr/item/AMUC_2015_84_2_a6/
@article{AMUC_2015_84_2_a6,
     author = {Sima Mashayekhi and Jens Hugger and Sima Mashayekhi and Jens Hugger},
     title = { Finite difference schemes for a nonlinear {Black-Scholes} model with transaction cost and volatility risk},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {255--266},
     year = {2015},
     volume = {84},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2015_84_2_a6/}
}
TY  - JOUR
AU  - Sima Mashayekhi
AU  - Jens Hugger
AU  - Sima Mashayekhi
AU  - Jens Hugger
TI  - Finite difference schemes for a nonlinear Black-Scholes model with transaction cost and volatility risk
JO  - Acta mathematica Universitatis Comenianae
PY  - 2015
SP  - 255
EP  - 266
VL  - 84
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_2015_84_2_a6/
ID  - AMUC_2015_84_2_a6
ER  - 
%0 Journal Article
%A Sima Mashayekhi
%A Jens Hugger
%A Sima Mashayekhi
%A Jens Hugger
%T Finite difference schemes for a nonlinear Black-Scholes model with transaction cost and volatility risk
%J Acta mathematica Universitatis Comenianae
%D 2015
%P 255-266
%V 84
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2015_84_2_a6/
%F AMUC_2015_84_2_a6

Voir la notice de l'article provenant de la source Comenius University

Several nonlinear Black-Scholes models have been proposed to taketransaction cost, large investor performance and illiquid markets into account. Oneof the most comprehensive models was introduced by Barles and Soner in [4] andconsiders transaction cost in the hedging strategy and risk from an illiquid market.In this paper we compare several finite difference methods for the solution of thismodel with respect to precision and order of convergence. We conclude that standard explicit Euler comes out as the preferred explicit method and standard CrankNicolson with Rannacher time stepping as the preferred implicit method.