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Zbl 1219.91146
Zhang, Kai; Wang, Song
Convergence property of an interior penalty approach to pricing American option. (English)
[J] J. Ind. Manag. Optim. 7, No. 2, 435-447 (2011). ISSN 1547-5816; ISSN 1553-166X/e

Summary: 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.

MSC 2000:: *91G20
90C33 Complementarity problems
91G60

Keywords: complementarity problem; variational inequalities; option pricing; penalty method

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