Year: 2009
Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 2 : pp. 202–223
Abstract
This paper aims to develop a power penalty method for a linear parabolic variational inequality (VI) in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant $\lambda > 1$ and a power parameter $k>0$. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order $O( \lambda^{-k/2}) $. A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-NMTMA-6022
Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 2 : pp. 202–223
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Complementarity problem option pricing penalty method finite volume method.