Pricing American perpetual warrants by linear programming
Author
Vanderbei, R.J.
Pinar, M. Ç.
Date
2009Source Title
SIAM Review
Print ISSN
0036-1445
Electronic ISSN
1095-7200
Publisher
Society for Industrial and Applied Mathematics
Volume
51
Issue
4
Pages
767 - 782
Language
English
Type
ArticleItem Usage Stats
101
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91
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Abstract
A warrant is an option that entitles the holder to purchase shares of a common stock at some prespecified price during a specified interval. The problem of pricing a perpetual warrant (with no specified interval) of the American type (that can be exercised any time) is one of the earliest contingent claim pricing problems in mathematical economics. The problem was first solved by Samuelson and McKean in 1965 under the assumption of a geometric Brownian motion of the stock price process. It is a well-documented exercise in stochastic processes and continuous-time finance curricula. The present paper offers a solution to this time-honored problem from an optimization point of view using linear programming duality under a simple random walk assumption for the stock price process, thus enabling a classroom exposition of the problem in graduate courses on linear programming without assuming a background in stochastic processes.
Keywords
PricingPerpetual warrant
American option
Linear programming, duality
Lynamic programming
Harmonic functions
Second-order difference equations