A semilinear Black and Scholes partial differential equation for valuing American options: approximate solutions and convergence
type: Item
instance of: scholarly article
title: A semilinear Black and Scholes partial differential equation for valuing American options: approximate solutions and convergence
zbMATH Open document ID: 1068.35190
DOI: 10.4171/IFB/106
author: Fred Espen Benth
author: Kenneth H. Karlsen
author: Kristin Reikvam
published in: Interfaces and Free Boundaries
publication date: 2005-03-21T00:00:00Z
review text: In [Finance Stoch. 7, No. 3, 277--298 (2003; Zbl 1064.60080)] the authors proved that the American (call/put) option valuation problem can be stated in terms of one single semilinear Black and Scholes partial differential equation set in a fixed domain. The semilinear Black and Scholes equation constitutes a starting point for designing and analyzing a variety of ``easy to implement'' numerical schemes for computing the value of an American option. To demonstrate this feature, the authors propose and analyze an upwind finite difference scheme of ``predicator-corrector type'' for the semilinear Black and Scholes equation. The authors prove that the approximate solutions generated by the predicator-corrector scheme respect the early exercise constraint and that they converge uniformly to the American option value. A numerical example is also presented. Besides the predictor-corrector schemes, other methods for constructing approximate solution sequences are discussed and analyzed.
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 65C30
zbMATH DE Number: 2148304
zbMATH Keywords: American call/put option valuation
zbMATH Keywords: upwind finite difference scheme of predicator-corrector type
zbMATH Keywords: approximate solutions
Wikidata QID: Q115212490
reviewed by: Stanisław Wedrychowicz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/ifb/106
OpenAlex ID: W2169882516
description: scientific article; zbMATH DE number 2148304