Power penalty method for a linear complementarity problem arising from American option valuation

S. Wang, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

88 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)227-254
Number of pages28
JournalJournal of Optimization Theory and Applications
Volume129
Issue number2
DOIs
Publication statusPublished - 1 May 2006

Keywords

  • American options
  • Linear complementarity problems
  • Partial differential equations
  • Power penalty functions

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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