IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v17y2010i1p59-81.html
   My bibliography  Save this article

Numerical Methods for Non-Linear Black-Scholes Equations

Author

Listed:
  • Pascal Heider

Abstract

In recent years non-linear Black-Scholes models have been used to build transaction costs, market liquidity or volatility uncertainty into the classical Black-Scholes concept. In this article we discuss the applicability of implicit numerical schemes for the valuation of contingent claims in these models. It is possible to derive sufficient conditions, which are required to ensure the convergence of the backward differentiation formula (BDF) and Crank-Nicolson scheme (CN) scheme to the unique viscosity solution. These stability conditions can be checked a priori and convergent schemes can be constructed for a large class of non-linear models and payoff profiles. However, if these conditions are not satisfied we show that the schemes are not convergent or produce spurious solutions. We study the practical implications of the derived stability criterions on relevant numerical examples.

Suggested Citation

  • Pascal Heider, 2010. "Numerical Methods for Non-Linear Black-Scholes Equations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(1), pages 59-81.
  • Handle: RePEc:taf:apmtfi:v:17:y:2010:i:1:p:59-81
    DOI: 10.1080/13504860903075670
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075670
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Karol Duris & Shih-Hau Tan & Choi-Hong Lai & Daniel Sevcovic, 2015. "Comparison of the analytical approximation formula and Newton's method for solving a class of nonlinear Black-Scholes parabolic equations," Papers 1511.05661, arXiv.org, revised Nov 2015.
    2. repec:eee:apmaco:v:251:y:2015:i:c:p:318-330 is not listed on IDEAS

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:17:y:2010:i:1:p:59-81. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.