This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

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

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Bertram Düring () (Department of Mathematics and Informatics, University of Mainz)
Michel Fournié (Laboratoire MIP, Université Paul Sabatier, Toulouse)
Ansgar Jüngel () (Department of Mathematics and Informatics, University of Mainz)

Additional information is available for the following registered author(s):

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.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://cofe.uni-konstanz.de/Papers/dp04_02.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 04-02.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 16 pages
Date of creation: Jan 2004
Date of revision:
Handle: RePEc:knz:cofedp:0402

Contact details of provider:
Postal: Fach D 147, D-78457 Konstanz
Phone: +49-7531-88-2204
Fax: +49-7531-88-4450
Web page: http://cofe.uni-konstanz.de
More information through EDIRC

Order Information:
Email:
Web: http://cofe.uni-konstanz.de

For technical questions regarding this item, or to correct its listing, contact: (Ingmar Nolte).

Related research
Keywords: High-order compact finite differences; numerical convergence; viscosity solution; financial derivatives;

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Gennotte, Gerard & Leland, Hayne, 1990. "Market Liquidity, Hedging, and Crashes," American Economic Review, American Economic Association, vol. 80(5), pages 999-1021, December. [Downloadable!] (restricted)
    Other versions:
  2. E. Platen & M. Schweizer, . "On Feedback Effects from Hedging Derivatives," Sonderforschungsbereich 373 1997-83, Humboldt Universitaet Berlin.
  3. George M. Constantinides & Thaleia Zariphopoulou, . "Bounds on Prices of Contingent Claims in an Intertemporal Economy with Proportional Transaction Costs and General Preferences," CRSP working papers 347, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    Other versions:
  4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  5. RØdiger Frey, 1998. "Perfect option hedging for a large trader," Finance and Stochastics, Springer, vol. 2(2), pages 115-141. [Downloadable!] (restricted)
  6. Jarrow, Robert A., 1992. "Market Manipulation, Bubbles, Corners, and Short Squeezes," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(03), pages 311-336, September. [Downloadable!]
  7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  8. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397. [Downloadable!] (restricted)
Full references

Statistics
Access and download statistics

Did you know? You can use IDEAS to provide links to papers and articles in your course syllabus.

This page was last updated on 2009-11-26.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.