Numerical Methods for Non-Linear Black-Scholes Equations
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Taylor and Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 17 (2010)
Issue (Month): 1 ()
Contact details of provider:
Web page: http://taylorandfrancis.metapress.com/link.asp?target=journal&id=100141
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Michael McNulty).
If references are entirely missing, you can add them using this form.