Convergence property of an interior penalty approach to pricing American option

Pages: 435 - 447, Volume 7, Issue 2, May 2011

doi:10.3934/jimo.2011.7.435       Abstract        References        Full Text (349.1K)       Related Articles

Kai Zhang - Department of Finance, Business School, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong 518060, China (email)
Song Wang - School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia (email)

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:  Complementarity problem, variational inequalities, option pricing, penalty method.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: February 2010;      Revised: February 2011;      Published: April 2011.

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