Below you will find a brief overview of the content of each chapter.

Chapter 1: Introduction: Overview
This chapter begins by defining a derivative instrument and distinguishing financial derivatives from derivatives in general.  As the word implies, a derivative instrument is one whose value depends on the value of something else.

The major derivatives considered in this book are forward contracts, futures contracts, options contracts, options on futures, and swap contracts. This chapter briefly introduces each of these instruments and explains their key features. Later chapters consider each instrument in detail.

After introducing forwards, futures, options, options on futures, and swaps, this chapter gives a brief explanation of why financial derivatives  are so critically important in finance today. As we will see throughout this text, these instruments have grown from trivial importance to play a key role in virtually all financial markets.  Compared with the fundamental securities on which they are based, financial derivatives afford numerous benefits to both speculators and risk managers.  In addition, derivatives offer some surprising advantages in reducing transaction costs and other forms of trading efficiency.

Throughout this text, we will be concerned with the principles that determine the prices of the financial derivatives we consider. The text consistently employs a no-arbitrage principle to illuminate the pricing principles for each instrument. An arbitrage opportunity is a chance to make a riskless profit with no investment. In essence, finding an arbitrage opportunity is like finding free money, as we explain in more detail later in this chapter.  The no-arbitrage principle states that any rational price for a financial instrument must exclude arbitrage opportunities. This is a minimal requirement for a feasible or rational price for any financial instrument.  As we will see in detail in the chapters that follow, this no-arbitrage principle is extremely powerful in helping to understand what prices can reasonably prevail for forwards, futures, options, options on futures, and swaps. The chapter then turns to explain how the text is organized.

A computer program called OPTION! accompanies this text. OPTION! allows the user to compute option prices with ease and provides modules for pricing swaps.

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Chapter 2: Futures Markets: Overview
This chapter lays the foundations that are essential to understanding how futures markets function. Futures markets originated to trade agricultural commodities, and it is only in the last 20 years that financial futures have come to play an important role in these markets.  Accordingly, this chapter considers financial futures in the broad context of the futures markets, while later chapters focus on financial futures more exclusively.

We focus on futures markets in the United States, where they are currently the most complete and provide the widest range of trading opportunities. Futures markets, as they now exist in the United States, are a fairly recent development, but understanding their origins helps us understand both the role these markets play today and likely future changes in that role.

Before entering the arena of the futures market, a prospective trader must understand the organizational form of the futures exchanges, the types of contracts that are traded, and the ways in which futures exchanges compete with each other for business.

The chapter discusses the purposes that futures markets serve and the participants in the markets. Because regulation is important in determining whether futures markets can serve their social function and the interests of the trading parties, the chapter next discusses the regulatory framework, closing with a description of the taxation of futures markets.

The futures industry is large and growing. Such a large industry requires specialization among brokers, trading advisors, and other professionals. In this chapter, we examine some of these specialized functions to show more completely how futures trading functions.

Futures were once a virtual U.S. monopoly. In the 1980s, the industry moved toward true international status. Foreign exchanges developed rapidly, and exchanges around the world began to trade commodities associated with other countries. This process of internationalization is reshaping the futures industry today and for the years to come. Internationalization is intimately tied to electronic trading. Today, electronic systems allow traders in New York to trade Japanese markets as if they were sitting in Tokyo. The chapter explores this trend toward globalization and the impact of electronic trading.

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Chapter 3: Futures Prices: Overview
Having explored the basic institutional features of the futures market in Chapter 2, we now consider futures prices. In an important sense, the study of the prices in a market provides the essential key to understanding all features of the market. Prices and the factors that determine those prices will ultimately influence every use of the market.

This chapter examines the fundamental factors that affect futures prices. There is little doubt that the determinants of foreign exchange futures prices and orange juice futures prices, for example, are very different. We must also recognize, however, that a common thread of understanding links futures contracts of all types. This chapter follows that common thread, while subsequent chapters explore the individual factors that affect prices for financial futures. Perhaps the most basic and most common factor affecting futures prices is the way in which their prices are quoted. Our discussion of futures prices begins with reading the price quotations which are available every day in The Wall Street Journal.

Futures market prices bear economically important relationships to other observable prices as well. An important goal of this chapter is to develop an understanding of those relationships. The futures price for the delivery of coffee in three months, for example, must be related to the spot price, or the current cash price of coffee at a particular physical location. The spot price is the price of a good for immediate delivery. In a restaurant, for example, you buy a cup of coffee at the spot price. The spot price is also called the cash price or the current price.

This important difference between the cash price and the futures price is called the basis. Likewise, the futures price for delivery of coffee in three months must be related in some fashion to the futures price for delivery of coffee in six months. The difference in price for two futures contract expirations on the same commodity is an intracommodity spread. As we will see, the time spread can also be an economically important variable.

Because futures contracts call for the delivery of some good at a particular time in the future, we can be sure that the expectations of market participants help to determine futures prices. If people believe that gold will sell for $50 per ounce in three months, then the price of the futures contact for delivery of gold in three months cannot be $100. The connection between futures prices and expected future spot prices is so strong that some market observers believe that they must be, or at least should be, equal.

Similarly, the price for storing the good underlying the futures contract helps determine the relationships among futures prices and the relationship between the futures price and the spot price. By storing goods, it is possible, in effect to convert corn received in March into corn that can be delivered in June. The difference in price between the March corn futures and the June corn futures must, therefore, be related to the cost of storing corn.

All of these futures pricing issues are interconnected. The basis, the spreads, the expected future spot price, and the cost of storage all form a system of related concepts. This chapter describes the linkages among these concepts that are common to all futures contracts. The discussion begins with the futures prices themselves.

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Chapter 4: Using Futures Markets: Overview
In the two preceding chapters, we discussed the institutional setting of futures markets and the determination of futures prices. This chapter explores three different ways that futures markets serve different elements of society. As we have already noted, futures markets provide a means of price discovery. Second, futures markets provide a means for transferring risk, or hedging. This chapter explores each of these contributions of futures markets.

First we will analyze the function of price discovery-the revelation of information about the prices of commodities in the future. Because prices in the futures markets provide information that is not readily available elsewhere, the markets serve societal needs. We note that price discovery is open to everyone, the first group of beneficiaries from these markets.

Speculators comprise the second major group to benefit from futures markets. A speculator is a trader who enters the futures market in pursuit of profit, thereby accepting an increase in risk. It may seem strange to list an opportunity for speculation as a service to society, but consider the following examples. Casinos provide speculative opportunities for citizens, and that might be reckoned as a public service. Professional and college sports teams also provide a way for people to speculate by betting, illegally in some states and legally in others.

Clearly, sports teams do not exist so that people can bet on them, but the chance to bet is a side effect, and perhaps a side benefit, of the existence of sports. The situation is similar in the futures markets. Futures markets do not exist in order to provide the chance to speculate, but they do provide speculative opportunities. Less obvious is the way in which speculators themselves contribute to the smooth functioning of the futures market. As we show, the speculator pursues profit. As a side effect, the speculator provides liquidity to the market that helps the market function more effectively.

Hedgers are a third major group of futures market users. A hedger is a trader with a preexisting risk who enters the futures market in order to reduce that risk. For example, a wheat farmer has price risk associated with the future price of wheat at harvest. By trading in the futures market, the farmer may be able to reduce that preexisting risk. The opportunity to transfer risk is perhaps the greatest contribution of futures markets to society. In many cases, businesses face risks that result from the ordinary conduct of business. Often these risks are undesired, and the futures market provides a way in which risk may be transferred to other individuals willing to bear it. If people know that unwanted risks may be avoided by transacting in the futures market at a reasonable cost, then they will not be afraid to make decisions that will expose them initially to certain risk. They know that they can hedge that risk.

From the point of view of society, hedging has important advantages. Enterprises that are profitable, but that involve more risk than their principals wish to bear, can still be pursued. The unwanted risk can then be transferred in the futures market, and society benefits economically. This is the strongest argument for the existence of futures markets. By providing an efficient way of transferring risk to those individuals in society willing to bear it cheaply, futures markets contribute to the economy.

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Chapter 5: Interest Rate Futures: Introduction: Overview
This chapter explores one of the most successful and exciting innovations in the history of futures markets-the emergence of interest rate futures contracts. Since the first contracts were traded on October 20, 1975, the market has expanded rapidly. In spite of a number of relatively unsuccessful contracts that have been introduced, such as commercial paper and Certificate Delivery GNMA contracts, the market has been a huge success. By fall 1998, open interest exceeded $5.6 trillion (face value) of underlying financial instruments, up from just $800 billion in 1990 and $300 billion in 1987. From inception, the interest rate futures market has come to represent about one-half of the entire futures market, and most industry observers expect the continued growth of the futures market to center around financial instruments.

Almost all of the activity in the U.S. interest rate futures is concentrated in two exchanges, the Chicago Board of Trade (BOT) and the International Monetary Market (IMM) of the Chicago Mercantile Exchange (CME). The Board of Trade specializes in contracts at the longer end of the maturity spectrum, with active contracts on long-term Treasury bonds and ten-year, five-year, and two-year Treasury notes. In addition, CBOT trades a municipal bond contract. By contrast, the International Monetary Market has successful contracts with very short maturities, trading contracts for three-month Treasury bills, and Eurodollar deposits. While this chapter discusses features of many different contracts, we focus on the seven most important contracts: the T-bond contract, three T-note contracts, and the municipal bond contract traded on the CBOT, along with the T-bill and Eurodollar contracts traded on the IMM of the CME. For the most part, these are highly active contracts that differ widely in their contract terms and the maturities of the underlying instruments. Figure 5.1 presents price quotations for key contracts.

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Chapter 6: Interest Rate Futures: Refinements: Overview
Chapter 6 builds on the foundation of Chapter 5. Having already explored the fundamental features of interest rate futures, we now turn to refining our understanding of these important markets. Thus, Chapter 6 considers more closely some of the same issues addressed in Chapter 5. In addition, we examine some new issues, such as the informational efficiency of the interest rate futures market.

The T-bond contract is perhaps the most important futures contract ever devised. It also happens to be one of the most complicated. We begin this chapter with a detailed analysis of the T-bond contract. This analysis lays the foundation for a richer understanding of how to apply interest rate futures to speculate and to manage risk. Next, we consider the informational efficiency of the interest rate futures markets. A market is efficient with respect to some set of information if prices in the market fully reflect the information contained in that set. There have been many studies of informational efficiency for interest rate futures, and we review the results of those studies.

In Chapter 5 we saw that interest rate futures should be full carry markets. However, this conclusion requires some qualifications. Taking the T-bond contract as a model, we analyze the special features of the contract and show how those features can make full carry difficult to measure. For example, the seller's options have important implications for the theoretically correct futures price.

Many traders use interest rate futures to manage risk. The techniques for risk management are quite diverse and increasingly sophisticated.   Essentially, two different sets of techniques apply, depending upon the nature of the risk. Therefore, we consider applications for short-term interest rate futures first, and then conclude the chapter by examining the applications of long-term interest rate futures.

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Chapter 7: Stock Index Futures: Introduction: Overview
Everyone who follows the financial news hears predictions about the future of the stock market. Usually these predictions refer to the future movement of some stock market index. With the advent of stock index futures trading in 1982, these pundits can now trade to take advantage of their insights. (Perhaps they should be required to do so.) In addition to providing a chance to speculate, stock index futures also have a role in hedging various kinds of portfolio risk.

Currently, dramatic changes in stock index futures are under way. Previously successful contracts have greatly diminished in importance, while new contracts have begun to gain ascendancy. This chapter begins our exploration of stock index futures and the indexes upon which they are based.  We focus on four stock market indexes and the futures contracts that are based on them. These indexes are: the Dow Jones Industrial Average, the Standard and Poor's 500 (S&P 500), the New York Stock Exchange (NYSE) composite index, and the Nikkei index. There are other popular indexes traded around the world, but we can explore the salient features of these markets by focusing on these indexes that dominate the U.S. exchanges.

Successful trading of the index contracts requires a thorough understanding of the construction of the indexes. When the differences and interrelationships among the indexes are understood, it is easier to understand the differences among the futures contracts that are based on those indexes. The differences among the indexes should not be exaggerated, however. The kinds of risk and the expected changes in the levels of the indexes are predicted by the capital asset pricing model (CAPM). The CAPM expresses the relationship between the returns of individual stocks and partially diversified portfolios, on the one hand, and the broad indexes on the other.

As is the case with all futures contracts, the exact construction of the contracts is very important for the trader. No-arbitrage conditions constrain the possible deviations between the price of the futures contract and the level of the underlying index. Cash-and-carry strategies keeps the futures price from being too low relative to stock prices. In other words, potential arbitrage strategies constrain the basis for stock index futures as these strategies do for other types of futures contracts.

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Chapter 8: Stock Index Futures: Refinements: Overview
In Chapter 7, we saw that stock index futures prices are governed by the cost-of-carry model. Because stocks often pay dividends, we saw how to tailor the cost-of-carry model to reflect the dividends on the stocks that underlie the stock index futures. In this chapter, we explore some of the empirical evidence on the relationship between theoretical and observed market prices. As in any violation of cost-of-carry principles, arbitrage opportunities should be possible if stock index futures prices do not correspond to theoretically determined prices.

Index arbitrage is the specific name given to attempts to exploit discrepancies between theoretical and actual stock index futures prices. As we also discussed in Chapter 7, index arbitrage usually proceeds through program trading. With the advent of program trading, there has been some evidence of a link between high index price variability and the style of trading used by program traders. This chapter considers some of the evidence on volatility and explores the market concern about volatility.

Because of the perception that futures trading is responsible for stock market volatility, new concern has focused on trading practices in the futures market, leading changes in trading rules. This chapter also considers some of the new trading practices rules recently implemented in the S&P 500 futures pit.

Chapter 7 considered some speculative and hedging applications of stock index futures. This chapter explores some more sophisticated techniques for using stock index futures that are becoming an important tool in portfolio management. By trading stock index futures in conjunction with a stock portfolio, a portfolio manager can tailor the risk characteristics of the entire portfolio. These strategies have aspects of both speculation and hedging. Two of the most notable of these are asset allocation and portfolio insurance, which we consider in some detail.

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Chapter 9: Foreign Currency Futures
Foreign currencies are traded in both a highly active forward market and a futures market. The foreign exchange market is the only one in which a successful futures market has grown up in the face of a robust forward market. The forward market for foreign exchange has existed for a long time, but the foreign exchange futures market developed only in the early 1970s, with trading beginning on May 16, 1972, on the International Monetary Market (IMM) of the Chicago Mercantile Exchange (CME). Without doubt, the presence of such a strong and successful forward market retarded the development of a futures market for foreign exchange. This dual market system means that the futures market cannot be understood in isolation from the forward market. The conceptual bond arises both from the similarity of the two markets and from the fact that the forward market continues to be much larger than the futures market. Because many traders are active in both markets, familiar cash-and-carry and reverse cash-and-carry strategies ensure that the proper price relationships between the two markets are maintained.

As discussed in Chapter 3, forward and futures markets for a given commodity are similar in many respects. Because of this similarity, specific price relationships must hold between the two markets to prevent arbitrage opportunities. While any observer might be impressed by the similarities in the two markets, the forward and futures markets differ in several key respects. Particularly important are the differences in the cash flow patterns (due to daily resettlement in the futures market) and the different structure of the contracts with respect to their maturities.

To understand foreign exchange futures trading, this chapter begins with a brief discussion of the markets for foreign exchange: the spot, forward, and futures markets. Next, we review the most important factors in determining exchange rates between two currencies, including the exchange rate regimes of fixed versus floating rates, the question of devaluation, and the influence of balance-of-payments. Against this institutional background, we analyze no-arbitrage pricing relationships, such as the interest rate parity (IRP) theorem and the purchasing power parity (PPP) theorem. These theorems essentially express the pricing relationship of the cost-of-carry model. We also examine the relationship between forward and futures prices and the accuracy of foreign exchange forecasting. As always in the futures market, the twin issues of speculation and hedging play an important role, and we consider them in detail.

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Chapter 10: The Options Market: Overview
As we discussed in Chapter 1, options can be either call options or put options. A call option is a financial instrument that gives its owner the right to purchase an underlying good at a specified price for a specified time. A put option is a financial instrument that gives its owner the right to sell the underlying good at a specified price for a specified time. This chapter considers the options exchanges and the well-defined options contracts that trade on these exchanges.

In modern options trading, an individual can contact a broker and trade an option on an exchange in a matter of moments. This chapter explains how orders flow from an individual to the exchange, and it shows how the order is executed and confirmed for the trader. At first, the options exchanges only traded options on stocks. Now exchanges trade options on a wide variety of underlying goods, such as bonds, futures contracts, and foreign currencies. The chapter concludes with a brief consideration of these diverse types of options.

The importance of options goes well beyond the profit-motivated trading that is most visible to the public. Today, sophisticated institutional traders use options to execute extremely complex strategies. For instance, large pension funds and investment banking firms trade options in conjunction with stock and bond portfolios to control risk and capture additional profits. Corporations use options to execute their financing strategies and to hedge unwanted risks that they could not avoid in any other way. Option research has advanced in step with the exploding option market. Scholars have found that there is an option way of thinking that allows many financial decisions to be analyzed using an option framework. Together, these developments constitute an options revolution.

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Chapter 11: Option Payoffs and Option Strategies: Overview
This chapter considers the factors that determine the value of an option at expiration and introduces the principal strategies used in options trading. When an option is about to expire, it is relatively easy to determine its value. Thus, we begin our analysis by considering option values at expiration. When we say that an option is at expiration, we mean that the owner has a simple choice: exercise the option immediately or allow it to expire as worthless. As we will see, the value of an option at expiration depends only on the stock price and the exercise price. We also give rules for whether an owner should exercise an option or allow it to expire.

With all assets, we consider either the value of the asset or the profit or loss incurred from trading the asset. The value of an asset equals its market price. As such, the value of an asset does not depend on the purchase price. However, the profit or loss on the purchase and sale of an asset depends critically on the purchase price. In considering options, we keep these two related ideas strictly distinct. We present graphs for both the value of options and the profits from trading options, but we want to be sure not to confuse the two. By graphing the value of options and the profits or losses from options at expiration, we develop our grasp of option pricing principles. To focus on the principles of pricing we ignore commissions and other transaction costs in this chapter.

Option traders often trade options with other options and with other assets, particularly stocks and bonds. This chapter analyzes the payoffs from combining different options and from combining options with the underlying stock. Many of these combinations have colorful names such as spreads, straddles, and strangles. Beyond the terminology, these combinations interest us because they offer special profit and loss characteristics. We also explore the particular payoff patterns that traders can create by trading options in conjunction with stocks and bonds.

We can use OPTION!, the software that accompanies this book, to explore the concepts we develop in this chapter. The first module of OPTION! analyzes the values, profits and losses of all the combinations we explore in this chapter. Detailed instructions for using OPTION! appear at the end of this book.

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Chapter 12: Bounds on Option Prices: Overview
This chapter continues to use no-arbitrage conditions to explore option pricing principles. In the last chapter, we considered the prices options could have at expiration, consistent with no-arbitrage conditions. In this chapter, we consider option prices before expiration. Extending our analysis to options with time remaining until expiration brings new factors into consideration.

The value of an option before expiration depends on five factors: the price of the underlying stock, the exercise price of the option, the time remaining until expiration, the risk-free rate of interest, and the possible price movements on the underlying stock.¹ For stocks with dividends, the potential dividend payments during an option's life can also influence the value of the option. In this chapter, we focus on the intuition underlying the relationship between put and call prices and these factors. The next chapter builds on these intuitions to specify these relationships more formally.

We first consider how option prices respond to changes in the stock price, the time remaining until expiration, and the exercise price of the option. These factors set general boundaries for possible option prices. Later in the chapter, we discuss the influence of interest rates on options prices, and we consider how the riskiness of the stock affects the price of the option.

¹ The price of an option depends on these five factors when the underlying stock pays no dividends. As we will discuss in Chapter 14, if the underlying stock pays a dividend, the dividend is a sixth factor that we must consider. back

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Chapter 13: European Option Pricing: Overview
In Chapter 12, we showed how to compute call and put prices assuming that stock prices behave in a highly specified manner. Specifically, we assumed that stock prices could rise by a certain percentage or fall by a certain percentage for a single period. After that single period, we assumed that the option expired. Under these unrealistic and highly restrictive assumptions, we found that calls and puts must each have a unique price; any other price leads to arbitrage. In this chapter, we develop similar option pricing models, but we use more realistic models of stock price movement.

To develop a more realistic option pricing model, this chapter first analyzes option pricing under the simple percentage change model of stock price movements. Now, however, we show how to find the unique prices that the no-arbitrage conditions imply. This framework is the single-period binomial model. Analyzing the single-period model leads to more realistic models of stock price movements. One of these more realistic models is the multi-period binomial model. By considering several successive models of stock price changes, we eventually come to one of the most elegant models in all of finance - the Black-Scholes option pricing model.

Throughout this chapter, we focus on European options. Later, in Chapter 15, we consider American option pricing and the complications arising from the potential for early exercise. At the beginning of this chapter, we focus on stocks with no dividends. Later in this chapter, we consider the complications that dividends bring in evaluating the prices of European options.

OPTION! provides support for the diverse models that we study in this chapter. With OPTION!, we can make virtually all of the computations discussed in this chapter, including the single period and multi-period binomial model call and put values and Black-Scholes model prices. In each case, using the software can save considerable computational labor.

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Chapter 14: Option Sensitivities and Option Hedging: Overview
Chapter 13 developed the principles of pricing for European options. There we analyzed option pricing within the framework of the binomial model and extended the discussion to encompass the Black-Scholes model, which gives a closed-form solution for the price of a European option on a non-dividend stock. We also considered the Merton model, which provides a solution for the price of a European option on a stock paying a continuous dividend.

In this chapter, we continue our exploration of these models by focusing on the response of option prices to the factors that determine the price. Specifically, we noted in Chapter 13 that the price of a European option depends on the price of the underlying stock, the exercise price, the interest rate, the volatility of the underlying stock, and the time until expiration. This chapter analyzes the sensitivity of option prices to these factors and shows how a knowledge of these relationships can direct trading strategies and can improve option hedging techniques.

With OPTION!, we can compute all of the sensitivity measures that we consider in this chapter. Also, OPTION! can graph the response of the option price to the different factors.

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Chapter 15: American Option Pricing: Overview
Chapter 13 considered the principles of pricing for European options-those that can be exercised only at the expiration of the option. There we considered the binomial model and saw how it could be extended logically to the Black-Scholes model. Strictly speaking, the Black-Scholes model holds only for European options on non-dividend paying stocks. However, we saw that it is possible to extend the Black-Scholes model to account for dividends by several adjustment procedures, such as known dividend adjustment and Merton's model, which accounts for continuous dividends. In addition, we saw that the binomial model can price options on stocks that pay dividends, either in the form of a proportional dividend or an actual dollar dividend. Therefore, the tools for pricing European options are quite robust. However, all of the models considered in Chapter 13 pertain strictly to European options.

This chapter focuses on American options-those that can be exercised at any time during the option's life. Most options that are publicly traded are American options, so it is important to develop techniques for pricing these instruments. However, the early exercise feature of American options brings with it substantial complexity. As we will see, there are no general closed-form pricing models for American options that would parallel the Black-Scholes model for European options.

This chapter begins by analyzing the differences between American and European options. It then turns to consider some attempts to estimate the value of American options. Also, we consider a special case in which these is an exact option pricing formula. Later in the chapter, we return to the binomial model and show how it can be used to price American options with a high degree of accuracy. OPTION! can compute prices for all of the option models considered in this chapter.

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Chapter 16: Options on Stock Indexes, Foreign Currency, and Futures: Overview
This chapter considers three different kinds of options: options on stock indexes, options on foreign currency, and options on futures. We consider these different types of options together because the principles that determine the price of these options are almost identical. In essence, the three types of options considered in this chapter are united by the fact that the good underlying each option can be treated as paying a continuous dividend. The pricing of these options is further unified by the conceptual connections among the different options. For example, we will consider options on stock index futures as well as options on stock indexes themselves, and we analyze options on foreign currency futures as well as options on foreign currencies alone.

While there may be common principles for the pricing of these three types of options, the markets for each of these options are quite large and have their own features. These were explored in Chapter 10. Consequently, this chapter begins by analyzing the pricing principles for these options. As noted above, the underlying instruments may all be treated as paying continuous dividend-particularly when we think of a dividend as a leakage of value from the instrument paying the dividend. For a stock index, the continuous dividend really is a dividend-the aggregate dividends on the stock represented in the index. For a foreign currency, we may treat the foreign interest rate as a continuous dividend. For a futures, the cost of financing and storing the underlying good (a bond, 5,000 bushels of wheat, or the proverbial pork bellies) is a leakage of value from the commodity.

Because the underlying good pays a continuous dividend, we know that the Merton model, which was discussed in Chapter 13, pertains directly to pricing these three types of European options. Also, the binomial model directly applies as well. For American options, discussed in Chapter 17, two approaches are clearly applicable. First, the analytic approximation technique works extremely well in pricing the types of options discussed in this chapter. Second, we can also apply the binomial model under the assumption of continuous dividends.

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Chapter 17: The Options Approach to Corporate Securities: Overview
In this chapter, we apply the concepts developed in this book to the analysis of corporate securities such as stocks and bonds. We see that virtually all securities have option features, and the options approach can help us understand these securities more fully.

Since the Black-Scholes model first appeared in the early 1970s, research on options has expanded rapidly. Option theory had given insight into several areas of finance, one of the most fruitful being corporate finance. In this chapter, we explore the insights that option theory brings to understanding corporate securities. By thinking of corporate securities as embracing options, we can build a deeper understanding of the value of securities such as stocks and bonds ¹.

The chapter begins by considering a firm with a simple capital structure of equity and a single pure discount bond. We show that the equity of the firm can be regarded as a call option on the entire firm with an exercise price equal to the obligation to the bondholders. Similarly, we can analyze the bond as involving an option as well. For this simple case, we show that the corporate bond can be regarded as consisting of a risk-free bond plus a short position in a put option. Of course, most firms have a more complex financial structure, but considering this simple case introduces the option dimension of most corporate securities.

In more realistic situations, the options embedded in corporate securities are more complex. In many firms, some debt is subordinated to more senior debt, meaning that the firm pays on the junior debt only after the senior debt claims have been satisfied. We show that the options approach to junior and senior debt analyzes these bonds as involving different exercise prices. When a firm has equity and coupon bonds, the analysis of the equity shows that the stock owners have a series of options. As another example, convertible debt includes a specific option-the option to convert the debt instrument into shares of the firm.  The option to convert debt to equity is an option purchased by and held by the bond owner. Most corporate bonds are callable, so the issuer of the bond is entitled to retire the bond under specified circumstances. This call feature gives the issuer of the bond options with specified exercise prices. Understanding the option features of these different debt instruments gives a clearer understanding of their pricing. As we will see, these option features of corporate bonds have value, and they definitely affect the value of the bonds in which they are embedded.

A warrant is a security that gives the owner the option to convert the warrant into a new share of the issuing firm by paying a state exercise price. This definition shows that a warrant is very similar to an option. However, there is an important difference. An option has an existing share as its underlying good. By contrast, the exercise warrant requires that the firm issue a new share of stock. As we will see, the difference leads to a slight difference in the valuation of options and warrants.

¹ Of course, the original Black-Scholes paper, "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, 81, 1973, pp. 637-59, already focused on the option characteristics of stocks and bonds. back

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Chapter 18: Exotic Options: Overview
In recent years, financial engineers have created a variety of complex options that are collectively known as exotic options. The payoffs on these options are considerably more diverse than the payoffs on the straightforward options that we have considered to this point. For example, a payoff on a lookback call option depends on the minimum stock price experienced during some past period. Other exotic options have different and more complicated payoff structures. This chapter explores the pricing and uses of these exotic options.

We approach these exotic options by contrasting them with the plain vanilla options explored earlier in this book. For a plain vanilla option, the value of an option at any particular moment depends only upon the current price of the underlying good, the exercise price, the risk-free rate of interest, the volatility of the underlying good, the time until expiration, and the dividend rate on the underlying good. Further, there is a fixed underlying good, a fixed and state exercise price, a known time to expiration, and no special conditions on any of the option parameters.

With respect to the price of the underlying good, it is important to emphasize that the price of a plain vanilla option depends only on the current price of the underlying good, so the price of the option is independent of the price path followed by the underlying good. As we will see in this chapter, many exotic options exhibit path dependence-the price of the option today depends on the previous or future price path followed by the underlying good.  For example, the price of a lookback call option depends on the minimum price reached by the underlying good over some past period. Further, the price of an average price option depends upon the future average price of the underlying good. Thus, to price a path-dependent option, it is not enough to know the current price of the underlying good. Instead, we must have information about the previous path that the price of the underlying good traversed. ¹

This chapter considers nine classes of exotic options: forward-start options, compound options, chooser options, barrier options, binary options, lookback options, average price options, exchange options, and rainbow options. Because of the complexity of these options, we focus on European options, emphasizing cases in which closed-form solutions are available. Thus, all of the exotic options are analyzed as extended instances of the Merton continuous dividend model. In their working paper, "Exotic Option," Mark Rubinstein and Eric Reiner have presented a unified and comprehensive treatment of these exotic options, and this chapter relies largely on this excellent work. ²  We also refer to other studies and original contributions for each of the types of exotic options.

This chapter explores each type of exotic option in a separate section that discussed the payoff structure of the option, presents the valuation formula for the option, and shows a calculation example. The OPTION! software that accompanies this book can compute the value of all of the exotic options discussed in this chapter.

¹ For a good introduction to the idea od path dependence in option pricing, see W. Hunter and S. Stowe, "Path-Dependent Options: Valuation and Applications," Economic Review, Federal Reserve Bank of Atlanta, July/August 1992, pp. 30-43. back

² Mark Rubinstein and Eric Reiner, "Exotic Options," Working paper, University of California at Berkeley, 1995. back

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Chapter 19: Interest Rate Options: Overview
This chapter explores interest rate options-options on financial assets whose prices are sensitive to changing interest rates. Prior to this chapter, we have assumed that interest rates are constant in the application of our various pricing models. For instance, the Black-Scholes model explicitly assumes that interest rates are constant over the life of the option. This assumption has worked well on the whole, allowing us to value options while keeping mathematical complexity under control. However, the value of many instruments is tied very directly to interest rates, and for some instruments, prices fluctuated primarily due to changes in interest rates.

We begin by examining the market for interest rate options. As we will see, the main classes of interest rate options are options on interest rate futures contracts, over-the-counter options that are traded on a wide variety of instruments, and interest rate options that are embedded in debt instruments, such as bonds and mortgages.

Key to pricing interest rate options is a basic understanding of the term structure of interest rates and the yield curve. We discuss the relationship between the yield curve for coupon bearing instruments, the zero-coupon yield curve, and the forward yield curve. These three measures of the relationship between maturity and yield are intimately connected, and we show how to move from one kind of yield measure to another using a method called bootstrapping. We also consider an explicit market in forward rates of interest.

After surveying the yield curve, we explore some analytical tools for valuing interest rate options. First of these is the option adjusted spread (OAS). In this kind of spread analysis, an instrument with an embedded interest rate option is compared to a similar instrument with no such option. The difference in yields between the instruments, the yield spread, provides a measure of the value of the embedded option.

Central to the evaluation of interest rate options is the Black model. We have already introduced the Black model in Chapter 16. There we saw how to use the Black model to value options on futures, including interest rate futures. In this chapter, we show why the Black model works even for options on interest rate futures. We also evaluate the Black model in more detail and show how to use it to value more explicit interest rate options. For example, the Black model can be used to value European options on coupon bearing bonds. In addition, we explore the active market in interest rate options based on LIBOR (London Interbank Offered Rate).

These options based on LIBOR are known as "calls on LIBOR" and "puts on LIBOR." We explore the application of the Black model to create interest rate caps, floors, and collars. These are powerful interest rate risk management tools that can also be valued using the Black model.

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Chapter 20: The Swaps Market: Introduction: Overview
This chapter provides a basic introduction to the swaps market.¹ As we will see, the swaps market has grown rapidly in the last few years because it provides firms that face financial risks with a flexible way to manage that risk. We will explore the risk management motivation that has led to this phenomenal growth in some detail.

In essence a swap is an agreement between two parties, called counterparties, to exchange a sequence of cash flows on the same or different currencies. The most important kinds of swaps are interest rate swaps and foreign currency swaps. In an interest rate swap, one party might pay interest based on a floating rate, while the other party would pay at a fixed rate. In a foreign currency swap, one party might pay in dollars at a floating rate, while the other would pay in Japanese yen at a fixed rate. Changes in interest rates determine the winners and losers in an interest rate swap. For a foreign currency swap, changes in interest rates in both countries and changes in the exchange rate between the two currencies determine the winners and losers, as we will see in some detail.

Participants in the swaps market have various motivations, covering the game from speculation and arbitrage to hedging. However, the basic motivation for swaps, and the basic purpose of the swap market, is for businesses to shape and manage the interest rate and foreign currency risk inherent in their commercial operations.

A significant industry has arisen to facilitate swap transactions. This chapter considers the role of swap facilitators-economic agents who help counterparties consummate swap transactions. Swap facilitators may serve as brokers or dealers. In the early days of the swap market, brokers were much in evidence, functioning as agents who identified and brought prospective counterparties into contact with each other without participating in the swap itself. Swap dealers are in the business of making a market in swaps and serving as counterparties to those seeking to complete swaps. In today's swap market, swap dealers predominate.

The chapter focuses largely on simpler interest rate and currency swaps known as plain vanilla swaps. We briefly consider how prices for these swaps are set and how they can be employed for business purposes. Chapters 21 and 22 extend the discussions of pricing and applications, respectively.

By taking part in swap transactions, swap dealers expose themselves to financial risk. This risk can be serious, because it is exactly the risk that the swap counterparties are trying to avoid. Therefore, the swap dealer has two key problems. First, the swap dealer must price the swap to provide a reward for his services in bearing risk. Second, the swap dealer essentially has a portfolio of swaps that results from his numerous transactions in the swaps market. Therefore, the swap dealer has the problem of managing a swap portfolio. We explore how swap dealers price their swap transactions and how swap dealers manage the risks inherent in their swap portfolios.

The chapter concludes with a survey of swaps that go beyond plain vanilla interest rate and currency swaps. These include many more complicated interest rate and foreign currency swap structures. Also, there are other types of swaps based on commodity and equity indexes. In summary, this chapter provides an overview of the swap market and indicates how swaps are priced and used to manage business risk.

¹ I wish to acknowledge the special contribution to these swaps chapters, Chapters 20-22, made by Gerald W. Beutow of James Madison University and Donald J. Smith of Boston University. Both Jeff and Don read an commented on earlier versions of these chapters. Of course, I am responsible for any remaining deficiencies. The material for this chapter and the next draws heavily from Interest Rate and Currency Swaps: A Tutorial, by Keith C. Brown and Donald J. Smith, Charlottesville, VA: The Research Foundation of the Institute of Chartered Financial Analystst, 1995. back

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Chapter 21: Swaps: Economic Analysis and Pricing: Overview
In this chapter, we explore two closely related themes, the economic analysis of swaps and the principles of swap pricing. The economic analysis of swaps shows how swaps may be interpreted in terms of other financial instruments. In a number of instances, this chapter shows that a portfolio of nonswap instruments can exactly replicated the cash flows on a swap. When that exact replication is possible, we have a greater insight into swap pricing. The price of a swap must be identical to a portfolio of other instruments with cash flows on the swap.

The chapter begins by showing how a plain vanilla interest rate swap can be replicated by two bonds, one of which is a regular coupon bond and the other a bond that pays a floating rate. A fixed-for-fixed currency swap and a plain vanilla currency swap are also show to be equivalent to two-bond portfolios. The same principles of analyzing plain vanilla swaps apply to more complicated swaps, as we demonstrate for a forward and a seasonal interest rate swap. Interest rate swaps are also shown to be analyzable as a portfolio of forward interest rate contracts, while a fixed-for-fixed currency swap is equivalent to a portfolio of foreign exchange forward contracts. An interest rate swap is also closely related to a portfolio of Eurodollar futures contracts. Finally, an interest rate swap is shown to be equivalent to a portfolio of calls and puts on LIBOR.

Having explored the relationship between swaps and other financial instruments, the chapter turns to the pricing of swaps, considering interest rate and currency swaps in turn. The plain vanilla interest rate swap always pays LIBOR as the floating rate, so pricing an interest rate swap essentially requires finding the correct fixed rate for the swap. The chapter shows how to find the one fixed rate that prevents arbitrage, which is also the one fixed rate that does not disadvantage either party. Pricing currency swaps is closely related to pricing interest rate swaps, except that a currency swap involves two currencies. Therefore, currency swap pricing must be responsible to the term structure of interest rates in the two currencies and the term structure of exchange rates as well. The chapter concludes by showing how to find the no-arbitrage fixed rate for currency swaps.

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Chapter 22: Swaps: Applications: Overview
In this chapter, we explore a variety of applications and extensions to the discussion of swaps in the preceding two chapters. We have already briefly considered some possible simple applications of swap in these earlier chapters; this chapters extends those examples to more realistic situations. The swap applications presented in this chapter range from the relatively simpler examples to more complex. The application examples including pricing applications and solutions to more practical business problems for interest rate and currency swaps, as well as some more esoteric swap structures.

We begin by considering a parallel loan, a loan designed to evade currency restrictions that was popular in the late 1970s and early 1980s and which led directly to the development of the swaps market. We then show how to create a variety of synthetic securities by using swaps. A useful technique for comparing complex financing alternatives is the all-in cost. The technique considers all of the cash flows on two or more financing alternatives and uses internal rate of return techniques to find the cheapest alternative. We next consider a historical interest rate swap example-a swap between B. F. Goodrich and a Dutch bank, Rabobank. This provides an opportunity to use the all-in cost to compare alternatives that these companies faced.

In discussing hedging with interest rate futures earlier in this text, we saw that duration was an important concept. This chapter explores the duration of interest rate swaps and shows how to apply duration techniques with swaps to manage the interest rate risk that firms face. As we will see, the firm can take a duration-based approach to eliminating, decreasing, or increasing interest rate risk, to suit the firm's risk preferences.

Structured notes are debt instruments with peculiar payoff characteristics, such as  a floating rate that moves inversely with market rates. Firms typically issue structured notes to appeal to investor tasted, and then combine those notes with swaps to give the issuer a simpler and more traditional total debt obligation. This chapter shows how to create them synthetically from simple securities combined with swaps.

The chapter also shows how to price flavored interest rate and currency swaps. This discussion extend the pricing techniques introduced in Chapter 21. This chapter shows how to price equity swaps and how to use equity swaps to control equity market risk. We considered swaptions in Chapter 20. This chapter explains how to price swaptions using the Black model of Chapter 19. The chapter gives examples of pricing and using swaptions to create cancelable and extendable swaps.

Finally, the chapter explains day count conventions that are used in actual market pricing of swaps. Money market instruments and bonds are priced under varying assumptions about the number of days in a year. These assumptions affect actual cash flows on swaps. The chapter concludes by showing how to take these conventions into account, and illustrates swap pricing under realistic conventions.

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