Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/20661
Title: Power penalty method for a linear complementarity problem arising from American option valuation
Authors: Wang, S
Yang, XQ 
Teo, KL
Keywords: American options
Linear complementarity problems
Partial differential equations
Power penalty functions
Issue Date: 2006
Publisher: Springer/Plenum Publishers
Source: Journal of optimization theory and applications, 2006, v. 129, no. 2, p. 227-254 How to cite?
Journal: Journal of Optimization Theory and Applications 
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.
URI: http://hdl.handle.net/10397/20661
ISSN: 0022-3239
DOI: 10.1007/s10957-006-9062-3
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