Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation

Bertram Düring; Michel Fournié; Ansgar Jüngel

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 2, page 359-369
  • ISSN: 0764-583X

Abstract

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A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

How to cite

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Düring, Bertram, Fournié, Michel, and Jüngel, Ansgar. "Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation." ESAIM: Mathematical Modelling and Numerical Analysis 38.2 (2010): 359-369. <http://eudml.org/doc/194218>.

@article{Düring2010,
abstract = { A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides. },
author = {Düring, Bertram, Fournié, Michel, Jüngel, Ansgar},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {High-order compact finite differences; numerical convergence; viscosity solution; financial derivatives.; viscosity solutions; financial derivatives},
language = {eng},
month = {3},
number = {2},
pages = {359-369},
publisher = {EDP Sciences},
title = {Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation},
url = {http://eudml.org/doc/194218},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Düring, Bertram
AU - Fournié, Michel
AU - Jüngel, Ansgar
TI - Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 2
SP - 359
EP - 369
AB - A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.
LA - eng
KW - High-order compact finite differences; numerical convergence; viscosity solution; financial derivatives.; viscosity solutions; financial derivatives
UR - http://eudml.org/doc/194218
ER -

References

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