| Abstrakt: |
In this paper, we consider the partial differential equations approach for valuing American style options on multiple assets. We develop and analyze a penalty method to solve the parabolic variational inequality that characterizes the American style option. Such a method is obtained by adding a non-linear penalty term to the Black–Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. The proposed penalty method is based on the reformulation of the original inequality in the form of a variational inequality without constraints, which includes a non-differentiable functional that has a different form for convex and non-convex payoff functions. The penalty operator is defined as the gradient of a differentiable approximation of this functional. It is shown that various well-known penalty operators can be obtained in a similar way. Under realistic assumptions about the regularity of the payoff function, error estimates of a penalty method in uniform and energy norm are established. [ABSTRACT FROM AUTHOR] |
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