On the Solution of Complementarity Problems Arising in American Options Pricing

Optimization Methods and Software, Forthcoming

16 Pages Posted: 6 Nov 2010  

Liming Feng

University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering

Vadim Linetsky

Northwestern University - Department of Industrial Engineering and Management Sciences

Jose Luis Morales

Instituto Tecnológico Autónomo de México (ITAM)

Jorge Nocedal

Northwestern University

Date Written: November 4, 2010

Abstract

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.

Keywords: American Options Pricing, Linear Complementarity, Projected SOR Method

JEL Classification: C61

Suggested Citation

Feng, Liming and Linetsky, Vadim and Morales, Jose Luis and Nocedal, Jorge, On the Solution of Complementarity Problems Arising in American Options Pricing (November 4, 2010). Optimization Methods and Software, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1703199

Liming Feng

University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering ( email )

104 S. Mathews Avenue
Urbana, IL 61801
United States

Vadim Linetsky

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

Evanston, IL 60208-3119
United States

Jose Luis Morales

Instituto Tecnológico Autónomo de México (ITAM) ( email )

Av. Camino a Sta. Teresa 930
Col. Héroes de Padierna
Mexico City, D.F. 01000, Federal District 01080
Mexico

Jorge Nocedal (Contact Author)

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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