## Introduction

A derivative security is a security whose payoff is explicitly tied to the value of some other variable In practice, however, this broad definition is often restricted to securities whose payoffs are explicitly tied to the price of some other financial security. A hypothetical example of such a derivative security is a certificate that can be redeemed in 6 months for an amount equal to the price, then, of a share of IBM stock The certificate is a derivative security since its payoff depends on the future price of IBM Most real derivatives are fashioned to have important risk control features, and the payoff relation is more subtle than that of the hypothetical certificate example A more realistic example is a forward contract to purchase 2,000 pounds of sugar at 12 cents per pound in 6 weeks. There is no reference to a payoff:—the contract just guarantees the purchase of sugar—but in fact a payoff is implied. The payoff is determined by the price of sugar in 6 weeks. If the price of sugar then were, say, 13 cents per pound, the contract would have a value of 1 cent per pound, or \$20, since the owner of the contract could buy sugar at 12 cents according to the contract and then turn around and sell that sugar in the sugar market at 13 cents. The contract is a derivative security because its value is derived from the price of sugar Another realistic example is a contract that gives one the right, but not the obligation, to purchase 100 shares of GM stock for \$60 per share in exactly 3 months This is an option to buy GM The payoff of this option will be determined in 3 months by the price of GM stock at that time If GM is selling then for \$70, the option will be worth \$1,000 because the owner of the option could at that time purchase 100 shares of GM for \$60 per share according to the option contract, and immediately sell those shares for \$70 each. As a final example of a derivative security, suppose you take out a mortgage whose interest rate is adjusted periodically according to a weighted average of the rates on new mortgages offered by major banks Your mortgage is a derivative security since its value at later times is determined by other financial prices, namely, prevailing interest rates

As mentioned earlier, the payoff of a derivative security is usually based on the price of some other financial security In the foregoing examples these were the price of IBM shares, the price of sugar, the price of GM shares, and the prevailing interest rates The security that determines the value of a derivative security is called the underlying security. However, according to the broad definition, derivatives may have payoffs that are functions of nonfinancial variables, such as the weather or the outcome of an election, The main point is that the payments derived from a derivative security are deterministic functions of some other variable whose value will be revealed before or at the time of the payoff.

The main types of derivative securities ate forward contracts, futures contracts, options, options on futures, and swaps.1 Such securities play an important role in everyday commerce, since they provide effective tools for hedging risks involving the underlying variables For example, a business that deals with a lot of sugars— perhaps a sugar producer, a processor, a marketeer, or a commercial user—typically faces substantial risks associated with possible sugar price fluctuations, Such users can control that risk through die use of derivative securities (in this case mainly through the use of sugar futures contracts)., Indeed, the primary function of derivative securities in a portfolio—for businesses, institutions, or individuals—is to control risk.

This third part of the text addresses several aspects of derivative securities. First, these chaptets explain what these different types of securities are; that is, how forwards, futures, swaps, and options are structured Second, these chapters show, through theory and example, how derivative securities are used to control risk; that is, how derivatives can enhance the overall structure of a portfolio that contains risky components. Third, these chapters present the special pricing theory that applies to derivative securities, This is the aspect that receives the most attention in the text. Finally, an important technical subject presented in this part of the text is concerned with how to model security price fluctuations. This is the primary topic of the next chapter. This current chapter is devoted to forward and futures contracts, which are among the simplest and most useful derivative securities

Before starting this topic, we offer a small warning and a suggestion. This chapter is not difficult page by page, but it contains many new concepts. You may find that your progress through the chapter is slower than in other chapters. Since the next three chapters do not depend on this one, one reading strategy is to scan the chapter briefly and then skip to Chapter 1 i, returning to this one later., However, the study of forwards, futures, and swaps is both practical and fascinating, so this chapter should be studied in depth at some point

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