No-Arbitrage Price Relations for Forwards, Futures, and Swaps

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: The three key factors that drive the valuation of a financial asset are risk, return, and timing of cash flows. A fundamental assumption in valuation is that in the absence of costless arbitrage opportunities, if two investments whose risk, return, and timing of cash flow properties are exactly the same are identified, they must have the same price in the marketplace. Otherwise, market participants can make free money by simultaneously selling the more expensive one and buying the cheaper one. This principle allows for the development of no-arbitrage price relations for forwards, futures, and swaps. The price of a futures contract is identical to the price of a forward contract in an environment in which short-term interest rates are known. In addition, a swap contract is nothing more than a portfolio of forward contracts. Hence, if a forward contract can be valued, a swap can be valued. The forward price and the underlying spot price are inextricably linked by the net cost of carry relation.

Exchange-traded and over-the-counter (OTC) derivatives contracts are traded worldwide. Of these, the lion’s share is plain-vanilla forwards, futures, and swaps. The purpose of this entry is to develop no-arbitrage price relations for forwards, ...

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