High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation

University of Konstanz Center of Finance and Econometrics Discussion Paper No. 01/07

28 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: November 24, 2001

Abstract

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. In particular, the compact schemes of Rigal are generalized. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

Keywords: Option pricing, transaction costs, parabolic equations, compact finite difference discretizations

JEL Classification: G13

Suggested Citation

Düring, Bertram and Fournie, Michel and Jüngel, Ansgar, High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation (November 24, 2001). University of Konstanz Center of Finance and Econometrics Discussion Paper No. 01/07, Available at SSRN: https://ssrn.com/abstract=520162 or http://dx.doi.org/10.2139/ssrn.520162

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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