Pricing American Stock Options by Linear Programming

34 Pages Posted: 6 Dec 1997

See all articles by M. A. H. Dempster

M. A. H. Dempster

University of Cambridge - Centre for Financial Research; Cambridge Systems Associates Limited; University of Cambridge - Judge Business School

J.P. Hutton

Nomura Holdings, Inc. (NHI)

Date Written: October 24, 1996

Abstract

We investigate numerical solution of nine difference approximations to American option pricing problems, using a novel direct numerical method |simplex solution of a linear programming formulation. This approach is based on a new result extending to the parabolic case the equivalence between linear order complementarity problems and abstract linear programs known for certain elliptic operators. We test this method empirically, comparing simplex and interior point algorithms with the projected successive overrelaxation (PSOR) algorithm applied to the American vanilla put and lookback put. We conclude that simplex is roughly comparable with projected SOR on average (faster for fine discretisations, slower for coarse), but is more desirable for robustness of solution time under changes in parameters. Furthermore, signicant speed-ups are certainly possible over the results given here.

JEL Classification: G13

Suggested Citation

Dempster, M. A. H. and Hutton, J.P., Pricing American Stock Options by Linear Programming (October 24, 1996). Available at SSRN: https://ssrn.com/abstract=40870 or http://dx.doi.org/10.2139/ssrn.40870

M. A. H. Dempster (Contact Author)

University of Cambridge - Centre for Financial Research ( email )

Centre for Mathematical Sciences
Wilberforce Road
Cambridge, CB3 0WA
United Kingdom

Cambridge Systems Associates Limited ( email )

5-7 Portugal Place
Cambridge, CB5 8AF
United Kingdom

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

J.P. Hutton

Nomura Holdings, Inc. (NHI)

1 St. Martins-le-Grand
Nomura Research Inst Nomura House
London EC1A 4NP
United Kingdom
0171 521 2000 (Phone)

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