Encyclopedia of Financial Models I

No-Arbitrage Price Relations for Options

ROBERT E. WHALEY, PhD

Valere Blair Potter Professor of Management and Co-Director of the Financial Markets Research Center, Owen Graduate School of Management, Vanderbilt University

Abstract: For derivative instruments, in the absence of costless arbitrage price relations can be developed. In the case of options (calls and puts), there are three types of price relations that can be obtained. The first is the lower bound on the option’s price. The second, and perhaps most important, no-arbitrage price relation is the one between the price of a put and the price of a call. This relation is called the put-call parity relation and arises from simultaneous trades in the call, the put, and the asset. The third price relation is the intermarket relation, which is the link between the prices of asset options and the prices of futures options. The price relations exist for European-style and American-style options and under both the continuous rate and discrete flow net cost of carry assumptions. Price relations are important for risk management strategies using options. Option pricing models go beyond these price relations to provide a fair value for an option.

The purpose of this entry is to develop no-arbitrage price relations for option contracts assuming that two perfect substitutes have the same price. In the absence of costless arbitrage opportunities, options have three types of no-arbitrage price relations—lower bounds, put-call parity ...