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