Convergenceproperty of an interior penalty approach to pricing American option

Kai Zhang; Song Wang

doi:10.3934/jimo.2011.7.435

Article Contents

2011, Volume 7, Issue 2: 435-447. Doi: 10.3934/jimo.2011.7.435

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Convergence property of an interior penalty approach to pricing American option

Kai Zhang^1, and
Song Wang^2,

1.
Department of Finance, Business School, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong 518060
2.
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009

Received: February 2010

Revised: February 2011

Published: April 2011

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Abstract

This paper establishes a convergence theory for an interior penalty method for a linear complementarity problem governing American option valuation. By introducing an interior penalty term, we first transform the complementarity problem into a nonlinear degenerated Black-Scholes PDE. We then prove that the PDE is uniquely solvable and its solution converges to that of the original complementarity problem. Furthermore, we demonstrate the advantages of the interior penalty method over exterior penalty methods by comparing it with an existing exterior penalty method.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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