# Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs

Rafael Company; Lucas Jódar; José-Ramón Pintos

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

- Volume: 43, Issue: 6, page 1045-1061
- ISSN: 0764-583X

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topCompany, Rafael, Jódar, Lucas, and Pintos, José-Ramón. "Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs." ESAIM: Mathematical Modelling and Numerical Analysis 43.6 (2009): 1045-1061. <http://eudml.org/doc/250609>.

@article{Company2009,

abstract = {
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.
},

author = {Company, Rafael, Jódar, Lucas, Pintos, José-Ramón},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Nonlinear Black-Scholes equation; option pricing; numerical analysis; transaction costs.; nonlinear Black-Scholes equation; transaction costs},

language = {eng},

month = {6},

number = {6},

pages = {1045-1061},

publisher = {EDP Sciences},

title = {Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs},

url = {http://eudml.org/doc/250609},

volume = {43},

year = {2009},

}

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: Mathematical Modelling and Numerical Analysis

DA - 2009/6//

PB - EDP Sciences

VL - 43

IS - 6

SP - 1045

EP - 1061

AB -
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.

LA - eng

KW - Nonlinear Black-Scholes equation; option pricing; numerical analysis; transaction costs.; nonlinear Black-Scholes equation; transaction costs

UR - http://eudml.org/doc/250609

ER -

## References

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