Option Pricing: A Simplified Approach†
John C. Cox Massachusetts Institute of Technology and Stanford University Stephen A. Ross Yale University Mark Rubinstein University of California, Berkeley
March 1979 (revised July 1979) (published under the same title in Journal of Financial Economics (September 1979)) [1978 winner of the Pomeranze Prize of the Chicago Board Options Exchange] [reprinted in Dynamic Hedging: A Guide to Portfolio Insurance, edited by Don Luskin (John Wiley and Sons 1988)] [reprinted in The Handbook of Financial Engineering, edited by Cliff Smith and Charles Smithson (Harper and Row 1990)] [reprinted in Readings in Futures Markets published by the Chicago Board of Trade, Vol. VI (1991)] [reprinted in Vasicek and Beyond: Approaches to Building and Applying Interest Rate Models, edited by Risk Publications, Alan Brace (1996)] [reprinted in The Debt Market, edited by Stephen Ross and Franco Modigliani (Edward Lear Publishing 2000)] [reprinted in The International Library of Critical Writings in Financial Economics: Options Markets edited by G.M. Constantinides and A..G. Malliaris (Edward Lear Publishing 2000)]

Abstract This paper presents a simple discrete-time model for valuing options. The fundamental economic principles of option pricing by arbitrage methods are particularly clear in this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black-Scholes model, which has previously been derived only by much more difficult methods. The basic model readily lends itself to generalization in many ways. Moreover, by its very construction, it gives rise to a simple and efficient numerical procedure for valuing options for which premature exercise may be optimal.
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Our best thanks go to William Sharpe, who first suggested to us the advantages of the discrete-time