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Volume 2, Issue 2
A Power Penalty Approach to Numerical Solutions of Two-Asset American Options

K. Zhang, S. Wang, X. Q. Yang & K. L. Teo

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 202-223.

Published online: 2009-02

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  • 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.

  • Keywords

Complementarity problem, option pricing, penalty method, finite volume method.

  • AMS Subject Headings

65M12, 65M60, 91B28

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-202, author = {K. Zhang, S. Wang, X. Q. Yang and K. L. Teo}, title = {A Power Penalty Approach to Numerical Solutions of Two-Asset American Options}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6022.html} }
TY - JOUR T1 - A Power Penalty Approach to Numerical Solutions of Two-Asset American Options AU - K. Zhang, S. Wang, X. Q. Yang & K. L. Teo JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 202 EP - 223 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6022.html KW - Complementarity problem, option pricing, penalty method, finite volume method. AB -

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.

K. Zhang, S. Wang, X. Q. Yang and K. L. Teo. (2009). A Power Penalty Approach to Numerical Solutions of Two-Asset American Options. Numerical Mathematics: Theory, Methods and Applications. 2 (2). 202-223. doi:
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