An Introduction to Financial Markets

Chapter Twelve Forward and Futures Contracts

Forward and futures contracts are classified as linear derivatives, unlike options, which are characterized by nonlinear payoffs. We have already introduced forward and futures contracts related with interest rates and fixed-income assets in Chapters 3 and 4. There, we used no-arbitrage arguments to find forward rates and to evaluate forward rate agreements. In Section 4.3, we have also pointed out that forward and futures rates need not be the same, because of the potential interaction of interest rate movements with daily marking-to-market of futures contracts. As we know from Section 1.2.6, a further difference between forward and futures is standardization, which has the effect of making perfect hedging impossible in practice.

In this chapter, we consider forward and futures contracts on equity and foreign currencies. Under stylized assumptions, we show in Section 12.1 how no-arbitrage arguments immediately lead to a fair forward price, which is the only price such that the initial value of the contract is zero. On the contrary, applying the idea to derivatives written on commodities is more troublesome, as commodities cannot be included in a financial portfolio, and they also raise issues with storage costs as well as limitations to short-selling. Finding the fair futures price is less trivial, due to the presence of daily cash flows. Nevertheless, as we show in Section 12.2, forward and futures prices would actually be the ...