Convergence of a High-Order Compact Finite Difference Scheme for a Nonlinear Black-Scholes Equation

University of Konstanz Discussion Paper No. 04/02

16 Pages Posted: 26 Mar 2004

See all articles by Bertram Düring

Bertram Düring

University of Warwick - Mathematics Institute

Michel Fournie

Université Paul Sabatier Toulouse III

Ansgar Jüngel

Fachbereich Mathematik und Informatik, University of Mainz

Date Written: February 5, 2004

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.

Keywords: High-order compact finite differences, numerical convergence, viscosity solution, financial derivatives

JEL Classification: G13

Suggested Citation

Düring, Bertram and Fournie, Michel and Jüngel, Ansgar, Convergence of a High-Order Compact Finite Difference Scheme for a Nonlinear Black-Scholes Equation (February 5, 2004). University of Konstanz Discussion Paper No. 04/02, Available at SSRN: https://ssrn.com/abstract=520443 or http://dx.doi.org/10.2139/ssrn.520443

Bertram Düring (Contact Author)

University of Warwick - Mathematics Institute ( email )

Zeeman Building
Coventry, CV4 7AL
United Kingdom

Michel Fournie

Université Paul Sabatier Toulouse III ( email )

118 Route de Narbonne
Toulouse cedex 9, F-31062
France

Ansgar Jüngel

Fachbereich Mathematik und Informatik, University of Mainz ( email )

D-55099 Mainz
Germany

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