TY - JOUR
T1 - A Power Penalty Approach to Numerical Solutions of Two-Asset American Options
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 - <p style="text-align: justify;">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 $\lambda &gt; 1$ and a power parameter $k&gt;0$. 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.</p>