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.
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Communicated by F. Giannessi
This work was partially supported by a research grant from the University of Western Australia and the Research Grant Council of Hong Kong, Grants PolyU BQ475 and PolyU BQ493.
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Wang, S., Yang, X.Q. & Teo, K.L. Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation. J Optim Theory Appl 129, 227–254 (2006). https://doi.org/10.1007/s10957-006-9062-3
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DOI: https://doi.org/10.1007/s10957-006-9062-3