Journal

of Financial

Economics

7 (1979) 229-263.

0 North-Holland

Publishing

Company

OPTION

PRICING:

A SIMPLIFIED John C. COX

APPROACH*

Massachusetts

Institute

of Technology, Cambridge, MA 02139, USA

Stanford University, Stanford, CA 94305, USA

Stephen
Yale University,

A. ROSS
USA

New Haven, CT06520,

Mark

RUBINSTEIN

University of Califorma, Berkeley, CA 94720, USA Received March 1979, revised version received July 1979

This paper presents a simple discrete-time model for valumg optlons. The fundamental econonuc 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-&holes 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 constructlon, it gives rise to a simple and efficient numerical procedure for valumg optlons for which premature exercise may be optimal.

1. Introduction An option is a security which gives its owner the right to trade in a fixed number of shares of a specified common stock at a fixed price at any time on or before a given date. The act of making this transaction is referred to as exercising the option. The fixed price is termed the striking price, and the given date, the expiration date. A call option gives the right to buy the shares; a put option gives the right to sell the shares. Options have been traded for centuries, but they remained relativelv obscure financial instruments until the introduction of a listed options exchange in 1973. Since then, options trading has enjoyed an expansion unprecedented in American securities markets. Option pricing theory has a long and illustrious history, but it also underwent a revolutionary change in 1973. At that time, Fischer Black and
*Our best thanks go to William