Analysis of the stability of the linear boundary condition for the Black–Scholes equation

Heath Windcliff, Peter A. Forsyth and Ken R.Vetzal

Journal of Computational Finance

Abstract: ABSTRACT The linear asymptotic boundary condition, which assumes that the second derivative of the value of the derivative security vanishes as the asset price becomes large, is commonly used in practice. To our knowledge there have been no rigorous studies of the stability of this method despite the fact that the discrete matrix equations obtained using this boundary condition lose diagonal dominance for large time steps. In this paper, we demonstrate that the discrete equations obtained using this boundary condition satisfy necessary conditions for stability for a finite-difference discretization. Computational experiments show that this boundary condition satisfies sufficient conditions for stability as well.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-of-computational-fina ... ack-scholes-equation (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rsk:journ0:2160483

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine ().