Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/27190
Title: Augmented Lagrangian method applied to American option pricing
Authors: Zhang, K
Yang, XQ 
Teo, KL
Issue Date: 2006
Source: Automatica, 2006, v. 42, no. 8, p. 1407-1416
Abstract: The American option pricing problem is originally formulated as a stochastic optimal stopping time problem. It is also equivalent to a variational inequality problem or a complementarity problem involving the Black-Scholes partial differential operator. In this paper, the corresponding variational inequality problem is discretized by using a fitted finite volume method. Based on the discretized form, an algorithm is developed by applying augmented Lagrangian method (ALM) to the valuation of the American option. Convergence properties of ALM are considered. By empirical numerical experiments, we conclude that ALM is more effective than penalty method and Lagrangian method, and comparable with the projected successive overrelaxation method (PSOR). Furthermore, numerical results show that ALM is more robust in terms of computation time under changes in market parameters: interest rate and volatility.
Keywords: Complementarity problems
Computational methods
Finance
Publisher: Pergamon Press
Journal: Automatica 
ISSN: 0005-1098
DOI: 10.1016/j.automatica.2006.01.017
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