Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation

S. Wang, X. Q. Yang and K. L. Teo
Additional contact information
S. Wang: University of Western Australia
X. Q. Yang: Hong Kong Polytechnic University
K. L. Teo: Curtin University of Technology

Journal of Optimization Theory and Applications, 2006, vol. 129, issue 2, No 1, 227-254

Abstract: Abstract In this paper, we present a power penalty function approach to the linear complementarity problem arising from pricing American options. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown that the solution to the penalized equation converges to that of the variational inequality problem with an arbitrary order. This arbitrary-order convergence rate allows us to achieve the required accuracy of the solution with a small penalty parameter. A numerical scheme for solving the penalized nonlinear PDE is also proposed. Numerical results are given to illustrate the theoretical findings and to show the effectiveness and usefulness of the method.

Keywords: Power penalty functions; linear complementarity problems; partial differential equations; American options (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (23)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-006-9062-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:joptap:v:129:y:2006:i:2:d:10.1007_s10957-006-9062-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-006-9062-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().