A Power Penalty Approach to Numerical Solutions of Two-Asset American Options

A Power Penalty Approach to Numerical Solutions of Two-Asset American Options

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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.