On the Solution of Complementarity Problems Arising in American Options Pricing
University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering
Northwestern University - Department of Industrial Engineering and Management Sciences
Jose Luis Morales
Instituto Tecnológico Autónomo de México (ITAM)
November 4, 2010
Optimization Methods and Software, Forthcoming
In the Black-Scholes-Merton model, as well as in more general stochastic models in finance, the price of an American option solves a parabolic variational inequality. When the variational inequality is discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution of these types of linear complementarity problems that is significantly faster than the methods currently used in practice. The new algorithm is a two-phase method that combines the active-set identification properties of the projected SOR iteration with the second-order acceleration of a (recursive) reduced-space phase. We show how to design the algorithm so that it exploits the structure of the linear complementarity problems arising in these financial applications and present numerical results that show the effectiveness of our approach.
Number of Pages in PDF File: 16
Keywords: American Options Pricing, Linear Complementarity, Projected SOR Method
JEL Classification: C61
Date posted: November 6, 2010
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