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

Abstract

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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.

How to cite

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Company, 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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