ROBERT E.WHALEY+ DERIVATIVES Abstract The area of derivatives is arguably the most fascinating area within financial economics during the past thirty years.This chapter reviews the evolution of derivatives contract markets and derivatives research over the past thirty years.The chapter has six complementary sections. The first contains a brief history of contract markets.The most important innovations occurred in the 1970s and 1980s,when contracts written on financial contracts were introduced.Concurrent with these important industry innovations was the development of modern-day option valuation theory,which is reviewed in the second and third sections.The key contribution is seminal theoretical framework of the Black-Scholes (1973)and Merton (1973)("BSM")model.The key economic insight of their model is that a risk-free hedge can be formed between a derivatives contract and its underlying asset.This implies that contract valuation is possible under the assumption of risk-neutrality without loss of generality. The final three sections summarize the three main strands of empirical work in the derivatives area.In the first group are studies that focus on testing no-arbitrage pricing relations that link the prices of derivatives contracts with their underling asset and with each other.The second group contains studies that evaluate option empirical performance of option valuation models.The approaches used include investigating the in-sample properties of option values by examining pricing errors or patterns in implied volatilities,examining the performance of different option valuation models by simulating a trading strategy based on under-and over- pricing,and examining the informational content of the volatility implied by option prices.The final group focuses on the social costs and/or benefits that arise from derivatives trading.The main conclusion that can be drawn from the empirical work is that the BSM model is one of the most resilient in the history of financial economics. Latest revision:August 27,2002 Keywords:derivatives,options forwards,futures,swaps JEL codes:G100,G120,G130,G140 *T.Austin Finch Foundation Professor of Business Administration,Fuqua School of Business,Duke University,Durham,NC 27706,E-mail:whaley@duke.edu.Prepared for the Handbook of the Economics of Finance,edited by George Constantinides,Milton Harris,and Rene Stulz.Comments and suggestions by Nick Bollen,George Constantinides,Jeff Fleming,Tom Smith,Rene Stulz,and Seth Wechsler are gratefully acknowledged. Copyright 2002 by Robert E.Whaley.All rights are reserved
ROBERT E. WHALEY* DERIVATIVES Abstract The area of derivatives is arguably the most fascinating area within financial economics during the past thirty years. This chapter reviews the evolution of derivatives contract markets and derivatives research over the past thirty years. The chapter has six complementary sections. The first contains a brief history of contract markets. The most important innovations occurred in the 1970s and 1980s, when contracts written on financial contracts were introduced. Concurrent with these important industry innovations was the development of modern-day option valuation theory, which is reviewed in the second and third sections. The key contribution is seminal theoretical framework of the Black-Scholes (1973) and Merton (1973) (“BSM”) model. The key economic insight of their model is that a risk-free hedge can be formed between a derivatives contract and its underlying asset. This implies that contract valuation is possible under the assumption of risk-neutrality without loss of generality. The final three sections summarize the three main strands of empirical work in the derivatives area. In the first group are studies that focus on testing no-arbitrage pricing relations that link the prices of derivatives contracts with their underling asset and with each other. The second group contains studies that evaluate option empirical performance of option valuation models. The approaches used include investigating the in-sample properties of option values by examining pricing errors or patterns in implied volatilities, examining the performance of different option valuation models by simulating a trading strategy based on under- and overpricing, and examining the informational content of the volatility implied by option prices. The final group focuses on the social costs and/or benefits that arise from derivatives trading. The main conclusion that can be drawn from the empirical work is that the BSM model is one of the most resilient in the history of financial economics. Latest revision: August 27, 2002 Keywords: derivatives, options forwards, futures, swaps JEL codes: G100, G120, G130, G140 *T. Austin Finch Foundation Professor of Business Administration, Fuqua School of Business, Duke University, Durham, NC 27706, E-mail: whaley@duke.edu. Prepared for the Handbook of the Economics of Finance, edited by George Constantinides, Milton Harris, and Rene Stulz. Comments and suggestions by Nick Bollen, George Constantinides, Jeff Fleming, Tom Smith, Rene Stulz, and Seth Wechsler are gratefully acknowledged. Copyright © 2002 by Robert E. Whaley. All rights are reserved
DERIVATIVES Arguably the most fascinating area within financial economics during the past thirty years is derivatives.With virtually no derivatives contracts written on financial assets at the beginning of the 1970s,the industry has grown to a level exceeding $100 trillion.This growth would not have been possible without the powerful theoretical contributions of Black-Scholes (1973)and Merton(1973).Their concept of forming a risk-free hedge between a derivatives contract and its underlying asset serves as the foundation for valuing an enormous array of different contract structures. The purpose of this chapter is to provide an overview of the key contributions to the derivatives literature over the past thirty years.This review has six complementary sections.The first section contains a brief history of derivatives contracts and contract markets.Although the origin of derivatives use dates back thousands of years,the most important innovations occurred only recently,in the 1970s and 1980s.Not coincidently, these two decades are also the most important in terms of theoretical developments in the derivatives literature. The second section is the first of two that focus on derivative contract valuation. The key assumption in the development of the valuation results presented in this section is the law of one price-two perfect substitutes will have the same price in a rationally- functioning marketplace.Under this seemingly innocuous assumption,a myriad of pricing relations can be developed for derivatives contracts including forwards,futures options and swaps. The third section focuses particularly on the valuation of contingent claims.To value such claims,it is necessary to know the character of the asset price distribution at time(s)in the future as well as the appropriate discount rate to apply in bringing the expected future cash flows of the derivatives contract (which,of course,depend on the asset price distribution)back to the present.It is this style of claim that underlies the seminal theoretical framework of the Black-Scholes(1973)and Merton(1973)("BSM") model.The key economic insight of their model is that a risk-free hedge can be formed between an option and its underlying asset.This implies that option valuation is possible
DERIVATIVES Arguably the most fascinating area within financial economics during the past thirty years is derivatives. With virtually no derivatives contracts written on financial assets at the beginning of the 1970s, the industry has grown to a level exceeding $100 trillion. This growth would not have been possible without the powerful theoretical contributions of Black-Scholes (1973) and Merton (1973). Their concept of forming a risk-free hedge between a derivatives contract and its underlying asset serves as the foundation for valuing an enormous array of different contract structures. The purpose of this chapter is to provide an overview of the key contributions to the derivatives literature over the past thirty years. This review has six complementary sections. The first section contains a brief history of derivatives contracts and contract markets. Although the origin of derivatives use dates back thousands of years, the most important innovations occurred only recently, in the 1970s and 1980s. Not coincidently, these two decades are also the most important in terms of theoretical developments in the derivatives literature. The second section is the first of two that focus on derivative contract valuation. The key assumption in the development of the valuation results presented in this section is the law of one price—two perfect substitutes will have the same price in a rationallyfunctioning marketplace. Under this seemingly innocuous assumption, a myriad of pricing relations can be developed for derivatives contracts including forwards, futures options and swaps. The third section focuses particularly on the valuation of contingent claims. To value such claims, it is necessary to know the character of the asset price distribution at time(s) in the future as well as the appropriate discount rate to apply in bringing the expected future cash flows of the derivatives contract (which, of course, depend on the asset price distribution) back to the present. It is this style of claim that underlies the seminal theoretical framework of the Black-Scholes (1973) and Merton (1973) (“BSM”) model. The key economic insight of their model is that a risk-free hedge can be formed between an option and its underlying asset. This implies that option valuation is possible 1
without knowing investor risk preferences,hence the risk-free rate of interest can be used as the appropriate discount rate to apply to the expected future cash flows.To develop the expectations of future cash flows,BSM assume that the underlying asset price follows geometric Brownian motion with constant volatility.Among other things,this implies that,at any point in time in the future,the asset price will be log-normally distributed, eliminating the prospect of negative asset prices that had plagued earlier work.Not only did this framework provide BSM with the ability to value standard call and put options,it has provided other researchers with the ability to value thousands of differently structured agreements including caps,collars,floors,binary options,and quantos.Many of these contributions,as well as other extensions to the BSM model,are summarized. The fourth through sixth sections of this chapter summarize empirical work that investigates the pricing and valuation of derivatives contracts and the efficiency of the markets within which they trade.The studies are divided into three groups.In the first group are studies that focus on testing no-arbitrage pricing conditions.These are contained in section 4.A review of tests of the no-arbitrage price relations between forwards and futures and their underlying assets as well as tests lower price bounds and put-call parity in the options markets is provided. The second group contains studies that attempt to evaluate option empirical performance of option valuation models.Approaches differ.Some investigate the in- sample properties of option values by examining pricing errors or patterns in implied volatilities.Others examine the performance of different option valuation models by simulating a trading strategy based on under-and over-pricing.Yet others examine the informational content of the volatility implied by option prices.Discussions of each approach of study are included in Section 5. The third and final group of studies focuses on the social costs and/or benefits that arise from derivatives trading.One sub-group examines whether the introduction of derivatives trading disrupts the market for the underlying asset by generating abnormal price movements and/or increased volatility.A second sub-group examines whether the expiration of derivatives groups disrupts the underlying asset market.A final sub-group examines the inter-temporal relation of price movements in the derivatives and asset 2
without knowing investor risk preferences, hence the risk-free rate of interest can be used as the appropriate discount rate to apply to the expected future cash flows. To develop the expectations of future cash flows, BSM assume that the underlying asset price follows geometric Brownian motion with constant volatility. Among other things, this implies that, at any point in time in the future, the asset price will be log-normally distributed, eliminating the prospect of negative asset prices that had plagued earlier work. Not only did this framework provide BSM with the ability to value standard call and put options, it has provided other researchers with the ability to value thousands of differently structured agreements including caps, collars, floors, binary options, and quantos. Many of these contributions, as well as other extensions to the BSM model, are summarized. The fourth through sixth sections of this chapter summarize empirical work that investigates the pricing and valuation of derivatives contracts and the efficiency of the markets within which they trade. The studies are divided into three groups. In the first group are studies that focus on testing no-arbitrage pricing conditions. These are contained in section 4. A review of tests of the no-arbitrage price relations between forwards and futures and their underlying assets as well as tests lower price bounds and put-call parity in the options markets is provided. The second group contains studies that attempt to evaluate option empirical performance of option valuation models. Approaches differ. Some investigate the insample properties of option values by examining pricing errors or patterns in implied volatilities. Others examine the performance of different option valuation models by simulating a trading strategy based on under- and over-pricing. Yet others examine the informational content of the volatility implied by option prices. Discussions of each approach of study are included in Section 5. The third and final group of studies focuses on the social costs and/or benefits that arise from derivatives trading. One sub-group examines whether the introduction of derivatives trading disrupts the market for the underlying asset by generating abnormal price movements and/or increased volatility. A second sub-group examines whether the expiration of derivatives groups disrupts the underlying asset market. A final sub-group examines the inter-temporal relation of price movements in the derivatives and asset 2
markets to ascertain,among other things,where private information is being traded first. All of these discussions are contained in Section 6. The final section contains a brief summary. 1.BACKGROUND Derivatives,while seemingly new,have been used for thousands of years.In his treatise,Politics,'Aristotle tells the story of Thales,a philosopher (and reasonably good meteorologist).Based on studying the winter sky,Thales predicted an unusually large olive harvest.He was so confident of his prediction that he bought rights to rent all of the olive presses in the region for the following year.The fall arrived,and the harvest was unusually plentiful.The demand and price for the use of olive presses soared. Thales'call options were early examples of over-the-counter (OTC)derivatives. OTC derivatives are private contracts negotiated between parties.Thales bought,and the olive press owners sold,call options.The prices of the options were negotiated,and Thales paid for them in the form of cash deposits.The chief advantage of OTC derivatives markets is limitless flexibility in contract design.The underlying asset can be anything,the size of the contract can be any amount,and the delivery can be made at any time and at any location.The only requirement of an OTC contract is a willing buyer and seller. Among the disadvantages of OTC markets,however,is that willing buyers and sellers must spend time identifying each other.Thousands of years ago,before the advent of high-speed communication and computer technology,such searches were costly.Consequently,centralized markets evolved.The Romans organized commodity markets with specific locations and fixed times for trading.Medieval fairs in England and France during the 12th and 13th centuries served the same purpose.While centralized commodity markets were originally developed to facilitate immediate cash transactions,the practice of contracting for future delivery (i.e.,forward transactions) was also introduced. I See Politics by Aristotle (350 BC,Book 1,Part XI). 3
markets to ascertain, among other things, where private information is being traded first. All of these discussions are contained in Section 6. The final section contains a brief summary. 1. BACKGROUND Derivatives, while seemingly new, have been used for thousands of years. In his treatise, Politics, 1 Aristotle tells the story of Thales, a philosopher (and reasonably good meteorologist). Based on studying the winter sky, Thales predicted an unusually large olive harvest. He was so confident of his prediction that he bought rights to rent all of the olive presses in the region for the following year. The fall arrived, and the harvest was unusually plentiful. The demand and price for the use of olive presses soared. Thales’ call options were early examples of over-the-counter (OTC) derivatives. OTC derivatives are private contracts negotiated between parties. Thales bought, and the olive press owners sold, call options. The prices of the options were negotiated, and Thales paid for them in the form of cash deposits. The chief advantage of OTC derivatives markets is limitless flexibility in contract design. The underlying asset can be anything, the size of the contract can be any amount, and the delivery can be made at any time and at any location. The only requirement of an OTC contract is a willing buyer and seller. Among the disadvantages of OTC markets, however, is that willing buyers and sellers must spend time identifying each other. Thousands of years ago, before the advent of high-speed communication and computer technology, such searches were costly. Consequently, centralized markets evolved. The Romans organized commodity markets with specific locations and fixed times for trading. Medieval fairs in England and France during the 12th and 13th centuries served the same purpose. While centralized commodity markets were originally developed to facilitate immediate cash transactions, the practice of contracting for future delivery (i.e., forward transactions) was also introduced. 1 See Politics by Aristotle (350 BC, Book 1, Part XI). 3
Another disadvantage of OTC derivatives is credit risk,that is,the risk that a counterparty will renege on his contractual obligation.Perhaps the most colorful example of this type of risk involves forward and option contracts on tulip bulbs.In what can be characterized as a speculative bubble,rare and beautiful tulips became collectors'items for the upper class in Holland in the early 17hcentury.Prices soared to incredible levels.2 Homes,jewels,livestock-nothing was too precious that it could not be sacrificed for the purchase of tulips.In an attempt to cash-in on this craze,it was not uncommon for tulip bulb dealers to sell bulbs for future delivery.They did so based on call options provided by tulip bulb growers.In this way,if bulb prices rose significantly prior to delivery,the dealers would simply exercise their options and acquire the bulbs to be delivered on the forward commitments at a fixed (lower)price. The tulip bulb growers also engaged in risk management by buying put options from the dealers.In this way,if prices fell,the growers could exercise their puts and sell their bulbs at a price higher than that prevailing in the market.In retrospect,both the tulip bulb dealers and growers were managing the risk of their positions quite sensibly. Everything could have worked out fine,except that the bubble burst in the winter of 1637 when a gathering of bulb merchants could not get the usual inflated prices for their bulbs.Panic ensued.Prices sank to levels of 1/100th of what they had once been. This set off an unfortunate chain of events.Individuals who had agreed to buy bulbs from dealers did not do so.Consequently,dealers did not have the cash necessary to buy the bulbs when the growers attempted to exercise their puts.Some legal attempts were made to enforce the contracts,however,the attempts were unsuccessful.These contract defaults left an indelible mark on OTC derivatives trading. By the 1800s,the pendulum had swung from undisciplined derivatives trading in OTC markets toward more structured trading on organized exchanges.The first derivatives exchange in the U.S.was the Chicago Board of Trade(CBT).While the CBT was originally formed in 1848 as a centralized marketplace for exchanging grain,forward contracts were also negotiated.The earliest recorded forward contract trade was made on March 13,1851 and called for 3,000 bushels of corn to be delivered in June at a price of 2 Garber (2000)provides a detailed recount of tulip bulb price levels during this period. 4
Another disadvantage of OTC derivatives is credit risk, that is, the risk that a counterparty will renege on his contractual obligation. Perhaps the most colorful example of this type of risk involves forward and option contracts on tulip bulbs. In what can be characterized as a speculative bubble, rare and beautiful tulips became collectors’ items for the upper class in Holland in the early 17th century. Prices soared to incredible levels.2 Homes, jewels, livestock—nothing was too precious that it could not be sacrificed for the purchase of tulips. In an attempt to cash-in on this craze, it was not uncommon for tulip bulb dealers to sell bulbs for future delivery. They did so based on call options provided by tulip bulb growers. In this way, if bulb prices rose significantly prior to delivery, the dealers would simply exercise their options and acquire the bulbs to be delivered on the forward commitments at a fixed (lower) price. The tulip bulb growers also engaged in risk management by buying put options from the dealers. In this way, if prices fell, the growers could exercise their puts and sell their bulbs at a price higher than that prevailing in the market. In retrospect, both the tulip bulb dealers and growers were managing the risk of their positions quite sensibly. Everything could have worked out fine, except that the bubble burst in the winter of 1637 when a gathering of bulb merchants could not get the usual inflated prices for their bulbs. Panic ensued. Prices sank to levels of 1/100th of what they had once been. This set off an unfortunate chain of events. Individuals who had agreed to buy bulbs from dealers did not do so. Consequently, dealers did not have the cash necessary to buy the bulbs when the growers attempted to exercise their puts. Some legal attempts were made to enforce the contracts, however, the attempts were unsuccessful. These contract defaults left an indelible mark on OTC derivatives trading. By the 1800s, the pendulum had swung from undisciplined derivatives trading in OTC markets toward more structured trading on organized exchanges. The first derivatives exchange in the U.S. was the Chicago Board of Trade (CBT). While the CBT was originally formed in 1848 as a centralized marketplace for exchanging grain, forward contracts were also negotiated. The earliest recorded forward contract trade was made on March 13, 1851 and called for 3,000 bushels of corn to be delivered in June at a price of 2 Garber (2000) provides a detailed recount of tulip bulb price levels during this period. 4
one cent per bushel below the March 13h spot price.3 Forward contracts had their drawbacks,however.They were not standardized according to quality or delivery time. In addition,like in the case of the tulip bulb fiasco,merchants and traders often did not fulfill their forward commitments. In 1865,the CBT made three important changes to the structure of their grain trading market.First,they introduced the use of standardized contracts called futures contracts.Unlike forwards contracts in which the parties are free to choose the terms of the contract,the terms of futures contracts are set by the exchange and are standardized with respect to quality,quantity,and time and place of delivery for the underlying commodity.By concentrating hedging and speculative demands on fewer contracts,the depth and liquidity of the market are enhanced.This facilitates position unwinding.If a party to a trade wants to exit his position prior to the delivery date of the contract,he need only execute an opposite trade(i.e.,reverse his trade)in the same contract.There is no need to seek out the counterparty of the original trade and attempt to negotiate the contract's termination. The second and third changes were made in an effort to promote market integrity. The second was the introduction of a clearinghouse to stand between the buyer and the seller and guarantee the performance of each party.This crucial step eliminated the counterparty risk that had plagued OTC trading.In the event a buyer defaults,the clearinghouse"makes good"on the seller's position,and then holds the buyer's clearing firm liable for the consequences.The buyer's clearing firm,in turn,passes the liability onto the buyer's broker,and ultimately the buyer.Note that,at any point in time,the clearinghouse has no net position since there are as many long contracts outstanding as there are short.The third was the introduction of a margining system.When the buyer and seller enter a futures position,they are both required to deposit good-faith collateral designed to show that they can fulfill the terms of the contract. From the late 1800s through the early 1980s,the majority of derivatives trading took place on exchanges.Futures contracts were the dominant contract design,and agricultural commodities were the dominant underlying asset.The list of contracts that 3 See Chicago Board of Trade(1994,ch.1,p.14) 5
one cent per bushel below the March 13th spot price.3 Forward contracts had their drawbacks, however. They were not standardized according to quality or delivery time. In addition, like in the case of the tulip bulb fiasco, merchants and traders often did not fulfill their forward commitments. In 1865, the CBT made three important changes to the structure of their grain trading market. First, they introduced the use of standardized contracts called futures contracts. Unlike forwards contracts in which the parties are free to choose the terms of the contract, the terms of futures contracts are set by the exchange and are standardized with respect to quality, quantity, and time and place of delivery for the underlying commodity. By concentrating hedging and speculative demands on fewer contracts, the depth and liquidity of the market are enhanced. This facilitates position unwinding. If a party to a trade wants to exit his position prior to the delivery date of the contract, he need only execute an opposite trade (i.e., reverse his trade) in the same contract. There is no need to seek out the counterparty of the original trade and attempt to negotiate the contract’s termination. The second and third changes were made in an effort to promote market integrity. The second was the introduction of a clearinghouse to stand between the buyer and the seller and guarantee the performance of each party. This crucial step eliminated the counterparty risk that had plagued OTC trading. In the event a buyer defaults, the clearinghouse “makes good” on the seller’s position, and then holds the buyer’s clearing firm liable for the consequences. The buyer’s clearing firm, in turn, passes the liability onto the buyer’s broker, and ultimately the buyer. Note that, at any point in time, the clearinghouse has no net position since there are as many long contracts outstanding as there are short. The third was the introduction of a margining system. When the buyer and seller enter a futures position, they are both required to deposit good-faith collateral designed to show that they can fulfill the terms of the contract. From the late 1800s through the early 1980s, the majority of derivatives trading took place on exchanges. Futures contracts were the dominant contract design, and agricultural commodities were the dominant underlying asset. The list of contracts that 3 See Chicago Board of Trade (1994, ch.1, p.14). 5
have been active for more than a century include the CBT's corn,oats,and wheat futures launched in 1865,the New York Cotton Exchange's cotton futures launched in 1870,the Chicago Produce Exchange(which later became the Chicago Mercantile Exchange)was formed by a group of agricultural dealers to trade futures on butter and egg futures launched in 1874,and the Coffee Exchange's coffee futures launched in 1882.3 The move to non-agricultural commodities was slow.Indeed,51 years elapsed before the Commodity Exchange(COMEX)in New York was formed to trade the first metals contract-silver futures.The New York Mercantile Exchange (NYMEX)followed with platinum futures in December 1956 and palladium futures in January 1968.The introduction of futures on livestock occurred in the 1960s.The Chicago Mercantile Exchange(CME)launched pork belly futures in September 1961,live cattle futures in November 1964,and live hog futures in February 1966.Futures contracts on energy products did not emerge until November 1978,at which time the NYMEX introduced the heating oil futures contract. The pace of innovation in derivatives markets increased remarkably in the 1970s Many of the important events occurring during this decade,as well as the next,are summarized in Table 1.The first major innovation occurred in February 1972,when the CME began trading futures on currencies in its International Monetary Market (IMM) division.This marked the first time a futures contract was written on anything other than a physical commodity.The second was in April 1973,when the CBT formed the Chicago Board Options Exchange(CBOE)to trade options on common stocks.This marked the first time an option was traded on an exchange.The third major innovation occurred in October 1975,when the CBT introduced the first futures contract on an interest rate instrument-Government National Mortgage Association futures.In January 1976,the 4The Chicago Produce Exchange aso traded futures on other perishable commodities.In 198.the butter and egg dealers withdrew to form their own market,the Chicago Butter and Egg Board.In 1919,it was reorganized to trade other commodity futures and was renamed the Chicago Mercantile Exchange. 5 In 1914,the Coffee Exchange expanded to include sugar futures,and,in 1916,it changed its name to the New York Coffee and Sugar Exchange.In 1979,it merged with the New York Cocoa Exchange to form today's Coffee,Sugar Cocoa Exchange. Initially,only call options were listed in the U.S.Put option trading were not listed until June 1977,and, even then,only on an experimental basis. 6
have been active for more than a century include the CBT’s corn, oats, and wheat futures launched in 1865, the New York Cotton Exchange’s cotton futures launched in 1870, the Chicago Produce Exchange4 (which later became the Chicago Mercantile Exchange) was formed by a group of agricultural dealers to trade futures on butter and egg futures launched in 1874, and the Coffee Exchange’s coffee futures launched in 1882.5 The move to non-agricultural commodities was slow. Indeed, 51 years elapsed before the Commodity Exchange (COMEX) in New York was formed to trade the first metals contract—silver futures. The New York Mercantile Exchange (NYMEX) followed with platinum futures in December 1956 and palladium futures in January 1968. The introduction of futures on livestock occurred in the 1960s. The Chicago Mercantile Exchange (CME) launched pork belly futures in September 1961, live cattle futures in November 1964, and live hog futures in February 1966. Futures contracts on energy products did not emerge until November 1978, at which time the NYMEX introduced the heating oil futures contract. The pace of innovation in derivatives markets increased remarkably in the 1970s. Many of the important events occurring during this decade, as well as the next, are summarized in Table 1. The first major innovation occurred in February 1972, when the CME began trading futures on currencies in its International Monetary Market (IMM) division. This marked the first time a futures contract was written on anything other than a physical commodity. The second was in April 1973, when the CBT formed the Chicago Board Options Exchange (CBOE) to trade options on common stocks.6 This marked the first time an option was traded on an exchange. The third major innovation occurred in October 1975, when the CBT introduced the first futures contract on an interest rate instrument—Government National Mortgage Association futures. In January 1976, the 4 The Chicago Produce Exchange also traded futures on other perishable commodities. In 1898, the butter and egg dealers withdrew to form their own market, the Chicago Butter and Egg Board. In 1919, it was reorganized to trade other commodity futures and was renamed the Chicago Mercantile Exchange. 5 In 1914, the Coffee Exchange expanded to include sugar futures, and, in 1916, it changed its name to the New York Coffee and Sugar Exchange. In 1979, it merged with the New York Cocoa Exchange to form today’s Coffee, Sugar & Cocoa Exchange. 6 Initially, only call options were listed in the U.S. Put option trading were not listed until June 1977, and, even then, only on an experimental basis. 6
CME launched Treasury bill futures and,in August 1977,the CBT launched Treasury bond futures. The 1980s brought yet another round of important innovations.The first was the use of cash settlement.In December 1981,the IMM launched the first cash settlement contracts,the 3-month Eurodollar futures.At expiration,the Eurodollar futures is settled in cash based on the interest rate prevailing for a three-month Eurodollar time deposit.? Cash settlement made feasible the introduction of derivatives on stock index futures,the second major innovation of the 1980s.In February 1982,the Kansas City Board of Trade (KCBT)listed futures on the Value Line Composite stock index,and,in April 1982,the CME listed futures on the S&P 500.These contract introductions marked the first time that futures contracts were written on stock indexes.The third major innovation of the 1980s was the introduction of exchange-traded option contracts written on"underlyings" other than individual common stocks.The CBOE and AMEX listed interest rate options in October 1982 and the Philadelphia Stock Exchange(PHLX)listed currency options in December 1982.In the same year,options on futures appeared for the first time.In October 1982,the CBT began to list Treasury bond futures options,and the Coffee, Sugar,and Cocoa Exchange(CSCE)began to list options on sugar and gold futures.In January 1983,the CME and the New York Futures Exchange (NYFE)began to list options directly on stock index futures,and,in March 1983,the CBOE began to list options on stock indexes. These two decades of innovation have transformed the nature of derivatives trading activity on exchanges.While derivatives exchanges were originally developed to help market participants manage the price risk of physical commodities,today's trading activity is focused on hedging the financial risks associated with unanticipated price movements in stocks,bonds,and currencies. 7A Eurodollar time deposit is a U.S.dollar deposit in London bank,and the interest rate uoted onsuch deposits is called the London Interbank Offer Rate (i.e..the L/BOR rate).Since different banks may offer different rates on deposits of the same maturity,the settlement rate is based on an average of rates across banks. 8 From this point forward,the term"underlying"refers to the asset or instrument that underlies the derivative contract. For a comprehensive review of these new option introductions and therconmpurposes Stoll and Whaley (1985)
CME launched Treasury bill futures and, in August 1977, the CBT launched Treasury bond futures. The 1980s brought yet another round of important innovations. The first was the use of cash settlement. In December 1981, the IMM launched the first cash settlement contracts, the 3-month Eurodollar futures. At expiration, the Eurodollar futures is settled in cash based on the interest rate prevailing for a three-month Eurodollar time deposit.7 Cash settlement made feasible the introduction of derivatives on stock index futures, the second major innovation of the 1980s. In February 1982, the Kansas City Board of Trade (KCBT) listed futures on the Value Line Composite stock index, and, in April 1982, the CME listed futures on the S&P 500. These contract introductions marked the first time that futures contracts were written on stock indexes. The third major innovation of the 1980s was the introduction of exchange-traded option contracts written on “underlyings”8 other than individual common stocks.9 The CBOE and AMEX listed interest rate options in October 1982 and the Philadelphia Stock Exchange (PHLX) listed currency options in December 1982. In the same year, options on futures appeared for the first time. In October 1982, the CBT began to list Treasury bond futures options, and the Coffee, Sugar, and Cocoa Exchange (CSCE) began to list options on sugar and gold futures. In January 1983, the CME and the New York Futures Exchange (NYFE) began to list options directly on stock index futures, and, in March 1983, the CBOE began to list options on stock indexes. These two decades of innovation have transformed the nature of derivatives trading activity on exchanges. While derivatives exchanges were originally developed to help market participants manage the price risk of physical commodities, today’s trading activity is focused on hedging the financial risks associated with unanticipated price movements in stocks, bonds, and currencies. 7 A Eurodollar time deposit is a U.S. dollar deposit in a London bank, and the interest rate quoted on such deposits is called the London Interbank Offer Rate (i.e., the LIBOR rate). Since different banks may offer different rates on deposits of the same maturity, the settlement rate is based on an average of rates across banks. 8 From this point forward, the term “underlying” refers to the asset or instrument that underlies the derivative contract. 9 For a comprehensive review of these new option introductions and their economic purposes, see Stoll and Whaley (1985). 7
The 1980s also saw the re-emergence of OTC derivatives trading.As derivatives on financial assets became increasingly popular,investment banks began to think of new ways to tailor contracts to meet customer needs.Some innovations were minor changes in the standard terms of exchange-traded derivatives contracts on financial instruments(e.g., modifications to the expiration date and/or the contract denomination).In 1980,for example,the first OTC Treasury bond option was traded.Other contracts were new and seemingly different.They fall under the generic heading of"swaps."A swap contract is a contract to"swap"a series of periodic future cash flows,where the terms of the swap are usually set such that the up-front payment is zero.The first interest rate swap was in 1981,when the Student Loan Marketing Association(i.e.,"Sallie Mae")swapped interest payments on intermediate-term fixed rate debt for floating-rate payments indexed to the three-month Treasury bill rate.The cash flows of the two legs of a swap can be linked to virtually any asset or index.A basis rate swap,for example,is an exchange of floating rate payments where the two floating rates are linked to,say,a three-month Treasury bill rate and a three-month Eurodollar time deposit rate.A currency swap is an exchange of interest payments (either fixed or floating)in one currency for payments (either fixed or floating)in another.An equity swap involves the exchange of an interest rate payment and a payment based on the performance of a stock index,while an equity basis swap involves an exchange of payments on two different indexes.Swap agreements may appear different from standard forward and option contracts,but they are not.Every swap can be decomposed into a portfolio of forwards and options.The benefit a swap provides is that several transactions are bundled into a single product. 2.NO-ARBITRAGE PRICING RELATIONS A great deal can be learned about valuing derivatives under minimal assumptions. The sole necessary assumption is the law of one price (LOP).Stated simply,the LOP says that two perfect substitutes must have the same price.If they do not,a costless arbitrage profit can be earned by simultaneously buying the cheaper asset and selling the 8
The 1980s also saw the re-emergence of OTC derivatives trading. As derivatives on financial assets became increasingly popular, investment banks began to think of new ways to tailor contracts to meet customer needs. Some innovations were minor changes in the standard terms of exchange-traded derivatives contracts on financial instruments (e.g., modifications to the expiration date and/or the contract denomination). In 1980, for example, the first OTC Treasury bond option was traded. Other contracts were new and seemingly different. They fall under the generic heading of “swaps.” A swap contract is a contract to “swap” a series of periodic future cash flows, where the terms of the swap are usually set such that the up-front payment is zero. The first interest rate swap was in 1981, when the Student Loan Marketing Association (i.e., “Sallie Mae”) swapped interest payments on intermediate-term fixed rate debt for floating-rate payments indexed to the three-month Treasury bill rate. The cash flows of the two legs of a swap can be linked to virtually any asset or index. A basis rate swap, for example, is an exchange of floating rate payments where the two floating rates are linked to, say, a three-month Treasury bill rate and a three-month Eurodollar time deposit rate. A currency swap is an exchange of interest payments (either fixed or floating) in one currency for payments (either fixed or floating) in another. An equity swap involves the exchange of an interest rate payment and a payment based on the performance of a stock index, while an equity basis swap involves an exchange of payments on two different indexes. Swap agreements may appear different from standard forward and option contracts, but they are not. Every swap can be decomposed into a portfolio of forwards and options. The benefit a swap provides is that several transactions are bundled into a single product. 2. NO-ARBITRAGE PRICING RELATIONS A great deal can be learned about valuing derivatives under minimal assumptions. The sole necessary assumption is the law of one price (LOP). Stated simply, the LOP says that two perfect substitutes must have the same price. If they do not, a costless arbitrage profit can be earned by simultaneously buying the cheaper asset and selling the 8
more expensive one.Because the same asset is bought and sold simultaneously,the position is risk-free.This is the key attribute of an arbitrage strategy.The fact that the strategy involves no initial cash outlay makes it costless.The absence of costless arbitrage opportunities is fundamental in derivatives contract valuation. A second assumption is that markets are frictionless.Frictionless markets have a number of attributes including: a)No trading costs. b)No differential tax rates. c)Unlimited borrowing and lending at the risk-free rate of interest. d)Freedom to sell(short),with full use of any proceeds. e)Can trade at any time and in any quantity. The frictionless market assumption is made largely for convenience.By ignoring market frictions,pricing relations can more easily be identified.In most cases,the impact of considerations such as trading costs,taxes,and divergent borrowing and lending rates can be and have been introduced into the valuation framework straightforwardly.Indeed,the very presence of these market restrictions has caused many derivatives markets to thrive. The focus of this section is to describe some important no-arbitrage relations for derivative contract prices. 2.1 Carrying costs Derivative contracts are written on four types of assets-stocks,bonds,foreign currencies and commodities.The derivatives literature contains seemingly independent developments of derivative valuation principles for each asset category.Generally speaking,however,the valuation principles are not asset-specific.The only distinction among assets is how carry costs are modeled.12 10 This"law of one price"argument is the fundamental theoretical underpinning to the Nobel prize-winning corporate finance theory of Modigliani/Miller(1958)and Miller/Modigliani(1961). 1The termarbitrage,is frequently misapplied.Risk arbitrage,for example,refers to a trading strategyin which the shares of a firm rumored to be on the verge of being acquired are purchased and the shares of the acquiring firm are simultaneously purchased.Since the merger may or may not take place and the stock prices may change,this activity is not arbitrage 1 See,for example,Stoll and Whaley (1986). 9
more expensive one.10 Because the same asset is bought and sold simultaneously, the position is risk-free. This is the key attribute of an arbitrage strategy.11 The fact that the strategy involves no initial cash outlay makes it costless. The absence of costless arbitrage opportunities is fundamental in derivatives contract valuation. A second assumption is that markets are frictionless. Frictionless markets have a number of attributes including: a) No trading costs. b) No differential tax rates. c) Unlimited borrowing and lending at the risk-free rate of interest. d) Freedom to sell (short), with full use of any proceeds. e) Can trade at any time and in any quantity. The frictionless market assumption is made largely for convenience. By ignoring market frictions, pricing relations can more easily be identified. In most cases, the impact of considerations such as trading costs, taxes, and divergent borrowing and lending rates can be and have been introduced into the valuation framework straightforwardly. Indeed, the very presence of these market restrictions has caused many derivatives markets to thrive. The focus of this section is to describe some important no-arbitrage relations for derivative contract prices. 2.1 Carrying costs Derivative contracts are written on four types of assets—stocks, bonds, foreign currencies and commodities. The derivatives literature contains seemingly independent developments of derivative valuation principles for each asset category. Generally speaking, however, the valuation principles are not asset-specific. The only distinction among assets is how carry costs are modeled.12 10 This “law of one price” argument is the fundamental theoretical underpinning to the Nobel prize-winning corporate finance theory of Modigliani/Miller (1958) and Miller/Modigliani (1961). 11 The term, arbitrage, is frequently misapplied. Risk arbitrage, for example, refers to a trading strategy in which the shares of a firm rumored to be on the verge of being acquired are purchased and the shares of the acquiring firm are simultaneously purchased. Since the merger may or may not take place and the stock prices may change, this activity is not arbitrage. 12 See, for example, Stoll and Whaley (1986). 9
