fundamentals of futures and options markets - pdfuni.com

N I N T H E D I T I O N

FUNDAMENTALS OFFUTURES AND OPTIONS

MARKETS

John C. Hull

Maple Financial Group Professor of Derivatives and Risk ManagementJoseph L. Rotman School of Management

University of Toronto

Boston Columbus Indianapolis New York San Francisco

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Library of Congress Cataloging-in-Publication Data

Hull, John, author.

Fundamentals of futures and options markets / John C. Hull.

Ninth edition. Boston: Pearson, [2017]. Includes index.

2015039251 j 01340832451. Futures market. 2. Options (Finance). I. Title.

HG6024.A3 H84 2017

332.64/52–dc23

LC record available at http://lccn.loc.gov/2015039251

10 9 8 7 6 5 4 3 2 1

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To My Students

CONTENTS IN BRIEF

Preface .................................................................................................................... xv

1. Introduction...............................................................................................................1

2. Futures markets and central counterparties ................................................................... 24

3. Hedging strategies using futures .................................................................................. 49

4. Interest rates ............................................................................................................ 81

5. Determination of forward and futures prices............................................................... 107

6. Interest rate futures ................................................................................................. 136

7. Swaps ................................................................................................................... 161

8. Securitization and the credit crisis of 2007 .................................................................. 190

9. Mechanics of options markets .................................................................................. 205

10. Properties of stock options ....................................................................................... 227

11. Trading strategies involving options ........................................................................... 249

12. Introduction to binomial trees .................................................................................. 268

13. Valuing stock options: the Black–Scholes–Merton model ............................................. 293

14. Employee stock options ........................................................................................... 318

15. Options on stock indices and currencies ..................................................................... 328

16. Futures options and Black’s model ............................................................................ 344

17. The Greek letters .................................................................................................... 359

18. Binomial trees in practice ......................................................................................... 391

19. Volatility smiles ...................................................................................................... 413

20. Value at risk and expected shortfall ........................................................................... 428

21. Interest rate options ................................................................................................ 458

22. Exotic options and other nonstandard products .......................................................... 477

23. Credit derivatives .................................................................................................... 496

24. Weather, energy, and insurance derivatives ................................................................. 515

25. Derivatives mishaps and what we can learn from them................................................. 523

Answers to quiz questions ........................................................................................ 535

Glossary of terms ................................................................................................... 559

DerivaGem software................................................................................................ 577

Major exchanges trading futures and options .............................................................. 581

Tables for NðxÞ....................................................................................................... 582Index .................................................................................................................... 585

iv

BUSINESS SNAPSHOTS

1.1 The Lehman Bankruptcy ............................................................................... 41.2 Systemic Risk .............................................................................................. 51.3 Hedge Funds ............................................................................................. 121.4 SocGen’s Big Loss in 2008........................................................................... 192.1 The Unanticipated Delivery of a Futures Contract........................................... 262.2 Long-Term Capital Management’s Big Loss ................................................... 343.1 Hedging by Gold Mining Companies ............................................................ 553.2 Metallgesellschaft: Hedging Gone Awry ......................................................... 714.1 Orange County’s Yield Curve Plays............................................................... 944.2 Liquidity and the 2007–2009 Financial Crisis................................................. 1005.1 Kidder Peabody’s Embarrassing Mistake....................................................... 1125.2 A Systems Error?....................................................................................... 1175.3 The CME Nikkei 225 Futures Contract ........................................................ 1195.4 Index Arbitrage in October 1987.................................................................. 1206.1 Day Counts Can Be Deceptive .................................................................... 1376.2 The Wild Card Play................................................................................... 1436.3 Asset–Liability Management by Banks......................................................... 1527.1 Extract from Hypothetical Swap Confirmation............................................... 1687.2 The Hammersmith and Fulham Story .......................................................... 1828.1 The Basel Committee ................................................................................. 2019.1 Gucci Group’s Large Dividend.................................................................... 2149.2 Tax Planning Using Options ....................................................................... 22210.1 Put–Call Parity and Capital Structure .......................................................... 23811.1 Losing Money with Box Spreads ................................................................. 25711.2 How to Make Money from Trading Straddles................................................ 26313.1 Mutual Fund Returns Can be Misleading ..................................................... 29813.2 What Causes Volatility?.............................................................................. 30114.1 Employee Stock Options and Dilution.......................................................... 32415.1 Can We Guarantee that Stocks Will Beat Bonds in the Long Run?................... 33717.1 Dynamic Hedging in Practice ...................................................................... 38017.2 Was Portfolio Insurance to Blame for the Crash of 1987?................................ 38619.1 Making Money from Foreign Currency Options............................................. 41619.2 Crashophobia ........................................................................................... 41820.1 How Bank Regulators Use VaR .................................................................. 42921.1 Put–Call Parity for Caps and Floors............................................................ 46721.2 Swaptions and Bond Options ...................................................................... 47022.1 Hypothetical Confirmation for Nonstandard Swap ......................................... 48622.2 Hypothetical Confirmation for Compounding Swap........................................ 48722.3 Hypothetical Confirmation for an Equity Swap.............................................. 48922.4 Procter and Gamble’s Bizarre Deal .............................................................. 49123.1 Who Bears the Credit Risk? ........................................................................ 49723.2 The CDS Market ...................................................................................... 49925.1 Big Losses by Financial Institutions ............................................................. 52425.2 Big Losses by Nonfinancial Organizations..................................................... 525

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Contents

Preface ......................................................................................................................... xv

Chapter 1: Introduction .................................................................................................. 1

1.1 Futures Contracts ......................................................................................... 1

1.2 History of Futures Markets ........................................................................... 2

1.3 The Over-the-Counter Market........................................................................ 4

1.4 Forward Contracts ........................................................................................ 6

1.5 Options........................................................................................................ 7

1.6 History of Options Markets......................................................................... 10

1.7 Types of Trader .......................................................................................... 11

1.8 Hedgers ..................................................................................................... 11

1.9 Speculators................................................................................................. 14

1.10 Arbitrageurs ............................................................................................... 17

1.11 Dangers ..................................................................................................... 18

Summary ................................................................................................... 18

Further Reading ......................................................................................... 20

Quiz .......................................................................................................... 20

Practice Questions ....................................................................................... 20

Further Questions ....................................................................................... 22

Chapter 2: Futures Markets and Central Counterparties .................................................. 24

2.1 Opening and Closing Futures Positions ........................................................ 24

2.2 Specification of a Futures Contract............................................................... 25

2.3 Convergence of Futures Price to Spot Price .................................................. 28

2.4 The Operation of Margin Accounts.............................................................. 29

2.5 OTC Markets ............................................................................................. 32

2.6 Market Quotes ........................................................................................... 35

2.7 Delivery ..................................................................................................... 37

2.8 Types of Trader and Types of Order ............................................................ 38

2.9 Regulation.................................................................................................. 39

2.10 Accounting and Tax ................................................................................... 40

2.11 Forward vs. Futures Contracts ..................................................................... 42

Summary ................................................................................................... 44

Further Reading ......................................................................................... 45

Quiz .......................................................................................................... 45

Practice Questions ....................................................................................... 46


vii

Chapter 3: Hedging Strategies Using Futures .................................................................. 49

3.1 Basic Principles ........................................................................................... 49

3.2 Arguments for and Against Hedging ............................................................ 52

3.3 Basis Risk .................................................................................................. 55

3.4 Cross Hedging ............................................................................................ 59

3.5 Stock Index Futures .................................................................................... 63

3.6 Stack and Roll ............................................................................................ 69

Summary.................................................................................................... 70

Further Reading.......................................................................................... 72

Quiz........................................................................................................... 72Practice Questions ....................................................................................... 73


Appendix: Review of Key Concepts in Statistics and the CAPM .................... 76

Chapter 4: Interest Rates .............................................................................................. 81

4.1 Types of Rates ............................................................................................ 81

4.2 Swap Rates................................................................................................. 83

4.3 The Risk-Free Rate ..................................................................................... 84

4.4 Measuring Interest Rates ............................................................................. 85

4.5 Zero Rates.................................................................................................. 87

4.6 Bond Pricing .............................................................................................. 884.7 Determining Zero Rates .............................................................................. 89

4.8 Forward Rates ............................................................................................ 93

4.9 Forward Rate Agreements ........................................................................... 95

4.10 Theories of the Term Structure of Interest Rates ........................................... 97

Summary.................................................................................................. 100

Further Reading........................................................................................ 101

Quiz......................................................................................................... 101

Practice Questions ..................................................................................... 102

Further Questions ..................................................................................... 103

Appendix: Exponential and Logarithmic Functions..................................... 105

Chapter 5: Determination of Forward and Futures Prices ............................................... 107

5.1 Investment Assets vs. Consumption Assets .................................................. 107

5.2 Short Selling ............................................................................................. 108

5.3 Assumptions and Notation ........................................................................ 109

5.4 Forward Price for an Investment Asset ....................................................... 110

5.5 Known Income ......................................................................................... 113

5.6 Known Yield ............................................................................................ 115

5.7 Valuing Forward Contracts ........................................................................ 115

5.8 Are Forward Prices and Futures Prices Equal? ............................................ 118

5.9 Futures Prices of Stock Indices .................................................................. 118

5.10 Forward and Futures Contracts on Currencies............................................. 121

5.11 Futures on Commodities............................................................................ 124

5.12 The Cost of Carry..................................................................................... 127

5.13 Delivery Options ....................................................................................... 127

5.14 Futures Prices and Expected Spot Prices ..................................................... 128Summary.................................................................................................. 130

Further Reading........................................................................................ 131

viii Contents

Quiz .........................................................................................................132Practice Questions ......................................................................................132Further Questions ......................................................................................134

Chapter 6: Interest Rate Futures...................................................................................136

6.1 Day Count and Quotation Conventions.......................................................1366.2 Treasury Bond Futures...............................................................................1396.3 Eurodollar Futures.....................................................................................1436.4 Duration ...................................................................................................1486.5 Duration-Based Hedging Strategies Using Futures........................................152

Summary ..................................................................................................156Further Reading ........................................................................................157Quiz .........................................................................................................157Practice Questions ......................................................................................158Further Questions ......................................................................................159

Chapter 7: Swaps .......................................................................................................161

7.1 Mechanics of Interest Rate Swaps ...............................................................1627.2 Day Count Issues ......................................................................................1677.3 Confirmations............................................................................................1677.4 The Comparative-Advantage Argument .......................................................1687.5 Valuation of Interest Rate Swaps ................................................................1717.6 How the Value Changes through Time ........................................................1747.7 Fixed-for-Fixed Currency Swaps .................................................................1757.8 Valuation of Fixed-for-Fixed Currency Swaps ..............................................1787.9 Other Currency Swaps ...............................................................................180

7.10 Credit Risk ...............................................................................................1817.11 Credit Default Swaps .................................................................................1827.12 Other Types of Swaps ................................................................................183


Chapter 8: Securitization and the Credit Crisis of 2007 ..................................................190

8.1 Securitization.............................................................................................1908.2 The U.S. Housing Market ..........................................................................1948.3 What Went Wrong? ...................................................................................1988.4 The Aftermath...........................................................................................200


Chapter 9: Mechanics of Options Markets ....................................................................205

9.1 Types of Option ........................................................................................2059.2 Option Positions ........................................................................................2089.3 Underlying Assets......................................................................................2109.4 Specification of Stock Options ....................................................................211

Contents ix

9.5 Trading .................................................................................................... 2159.6 Commissions............................................................................................. 2169.7 Margin Requirements ................................................................................ 2179.8 The Options Clearing Corporation ............................................................. 2199.9 Regulation ................................................................................................ 220

9.10 Taxation................................................................................................... 2209.11 Warrants, Employee Stock Options, and Convertibles .................................. 2219.12 Over-the-Counter Options Markets............................................................. 222

Summary.................................................................................................. 223Further Reading........................................................................................ 223Quiz......................................................................................................... 224Practice Questions ..................................................................................... 224Further Questions ..................................................................................... 225

Chapter 10: Properties of Stock Options ...................................................................... 227

10.1 Factors Affecting Option Prices ................................................................ 22710.2 Assumptions and Notation....................................................................... 23110.3 Upper and Lower Bounds for Option Prices.............................................. 23210.4 Put–Call Parity ....................................................................................... 23510.5 Calls on a Non-Dividend-Paying Stock ..................................................... 23910.6 Puts on a Non-Dividend-Paying Stock ...................................................... 24110.7 Effect of Dividends.................................................................................. 243

Summary ................................................................................................ 244Further Reading...................................................................................... 245Quiz ....................................................................................................... 245Practice Questions.................................................................................... 246Further Questions.................................................................................... 247

Chapter 11: Trading Strategies Involving Options .......................................................... 249

11.1 Principal-Protected Notes......................................................................... 24911.2 Strategies Involving a Single Option and a Stock ....................................... 25111.3 Spreads................................................................................................... 25311.4 Combinations.......................................................................................... 26111.5 Other Payoffs .......................................................................................... 264


Chapter 12: Introduction to Binomial Trees .................................................................. 268

12.1 A One-Step Binomial Model and a No-Arbitrage Argument....................... 26812.2 Risk-Neutral Valuation ............................................................................ 27212.3 Two-Step Binomial Trees ......................................................................... 27412.4 A Put Example ....................................................................................... 27712.5 American Options ................................................................................... 27812.6 Delta ...................................................................................................... 27912.7 Determining u and d ............................................................................... 28012.8 Increasing the Number of Time Steps ....................................................... 28112.9 Using DerivaGem.................................................................................... 282

x Contents

12.10 Options on Other Assets...........................................................................282Summary.................................................................................................287Further Reading.......................................................................................287Quiz........................................................................................................287Practice Questions ....................................................................................288Further Questions ....................................................................................289Appendix: Derivation of the Black–Scholes–Merton Option Pricing

Formula from Binomial Tree ....................................................291

Chapter 13: Valuing Stock Options: The Black–Scholes–Merton Model ..........................293

13.1 Assumptions about How Stock Prices Evolve.............................................29413.2 Expected Return ......................................................................................29713.3 Volatility .................................................................................................29813.4 Estimating Volatility from Historical Data .................................................299

13.5 Assumptions Underlying Black–Scholes–Merton .......................................30113.6 The Key No-Arbitrage Argument..............................................................30213.7 The Black–Scholes–Merton Pricing Formulas............................................30413.8 Risk-Neutral Valuation.............................................................................30613.9 Implied Volatilities ...................................................................................307

13.10 Dividends ................................................................................................309Summary.................................................................................................311Further Reading.......................................................................................312Quiz........................................................................................................313Practice Questions ....................................................................................313Further Questions ....................................................................................315Appendix: The Early Exercise of American Call Options on

Dividend-Paying Stocks ...........................................................316

Chapter 14: Employee Stock Options ...........................................................................318

14.1 Contractual Arrangements ........................................................................31814.2 Do Options Align the Interests of Shareholders and Managers?...................32014.3 Accounting Issues ....................................................................................32114.4 Valuation.................................................................................................32314.5 Backdating Scandals.................................................................................324

Summary.................................................................................................325Further Reading.......................................................................................326Quiz........................................................................................................326Practice Questions ....................................................................................327Further Questions ....................................................................................327

Chapter 15: Options on Stock Indices and Currencies.....................................................328

15.1 Options on Stock Indices..........................................................................32815.2 Currency Options.....................................................................................33115.3 Options on Stocks Paying Known Dividend Yields.....................................33315.4 Valuation of European Stock Index Options ..............................................33515.5 Valuation of European Currency Options ..................................................33815.6 American Options ....................................................................................339

Summary.................................................................................................340Further Reading.......................................................................................341Quiz........................................................................................................341

Contents xi

Practice Questions.................................................................................... 341Further Questions.................................................................................... 343

Chapter 16: Futures Options and Black’s Model............................................................ 344

16.1 Nature of Futures Options ....................................................................... 34416.2 Reasons for the Popularity of Futures Options .......................................... 34616.3 European Spot and Futures Options ......................................................... 34716.4 Put–Call Parity ....................................................................................... 34716.5 Bounds for Futures Options ..................................................................... 34916.6 A Futures Price as an Asset Providing a Yield........................................... 34916.7 Black’s Model for Valuing Futures Options............................................... 35016.8 Using Black’s Model Instead of Black–Scholes–Merton............................. 35016.9 Valuation of Futures Options Using Binomial Trees................................... 351

16.10 American Futures Options vs. American Spot Options............................... 35416.11 Futures-Style Options .............................................................................. 354


Chapter 17: The Greek Letters.................................................................................... 359

17.1 Illustration .............................................................................................. 35917.2 Naked and Covered Positions ................................................................... 36017.3 Greek Letter Calculation.......................................................................... 36217.4 Delta ...................................................................................................... 36317.5 Theta...................................................................................................... 36917.6 Gamma .................................................................................................. 37117.7 Relationship Between Delta, Theta, and Gamma ....................................... 37417.8 Vega....................................................................................................... 37817.9 Rho........................................................................................................ 377

17.10 The Realities of Hedging.......................................................................... 37917.11 Scenario Analysis .................................................................................... 37917.12 Extension of Formulas............................................................................. 38017.13 Creating Options Synthetically for Portfolio Insurance ............................... 38217.14 Stock Market Volatility............................................................................ 385


Chapter 18: Binomial Trees in Practice ........................................................................ 391

18.1 The Binomial Model for a Non-Dividend-Paying Stock.............................. 39118.2 Using the Binomial Tree for Options on Indices, Currencies, and Futures

Contracts ................................................................................................ 39818.3 The Binomial Model for a Dividend-Paying Stock ..................................... 40118.4 Extensions of the Basic Tree Approach ..................................................... 40518.5 Alternative Procedure for Constructing Trees ............................................. 40718.6 Monte Carlo Simulation .......................................................................... 407

xii Contents


Chapter 19: Volatility Smiles .......................................................................................413

19.1 Foreign Currency Options.........................................................................41319.2 Equity Options ........................................................................................41619.3 The Volatility Term Structure and Volatility Surfaces..................................41819.4 When a Single Large Jump Is Anticipated .................................................420

Summary.................................................................................................421Further Reading.......................................................................................422Quiz........................................................................................................423Practice Questions ....................................................................................423Further Questions ....................................................................................424Appendix: Why the Put Volatility Smile is the Same as the Call

Volatility Smile........................................................................426

Chapter 20: Value at Risk and Expected Shortfall .........................................................428

20.1 The VaR and ES Measures.......................................................................42820.2 Historical Simulation................................................................................43120.3 Model-Building Approach.........................................................................43620.4 Generalization of Linear Model ................................................................43920.5 Quadratic Model ......................................................................................44420.6 Estimating Volatilities and Correlations......................................................44620.7 Comparison of Approaches.......................................................................45120.8 Back Testing ............................................................................................452


Chapter 21: Interest Rate Options ................................................................................458

21.1 Exchange-Traded Interest Rate Options .....................................................45821.2 Embedded Bond Options..........................................................................46021.3 Black’s Model..........................................................................................46021.4 European Bond Options ...........................................................................46221.5 Interest Rate Caps....................................................................................46421.6 European Swap Options ...........................................................................46921.7 Term Structure Models.............................................................................472


Chapter 22: Exotic Options and Other Nonstandard Products .........................................477

22.1 Exotic Options.........................................................................................47722.2 Agency Mortgage-Backed Securities ..........................................................484

Contents xiii

22.3 Nonstandard Swaps................................................................................. 485Summary ................................................................................................ 492Further Reading...................................................................................... 492Quiz ....................................................................................................... 493Practice Questions.................................................................................... 493Further Questions.................................................................................... 494

Chapter 23: Credit Derivatives..................................................................................... 496

23.1 Credit Default Swaps............................................................................... 49723.2 Valuation of Credit Default Swaps............................................................ 50123.3 Total Return Swaps ................................................................................. 50523.4 CDS Forwards and Options ..................................................................... 50623.5 Credit Indices.......................................................................................... 50723.6 The Use of Fixed Coupons ...................................................................... 50723.7 Collateralized Debt Obligations ................................................................ 509


Chapter 24: Weather, Energy, and Insurance Derivatives ................................................ 515

24.1 Weather Derivatives................................................................................. 51524.2 Energy Derivatives................................................................................... 51624.3 Insurance Derivatives............................................................................... 519

Summary ................................................................................................ 520Further Reading...................................................................................... 520Quiz ....................................................................................................... 521Practice Questions.................................................................................... 521Further Question ..................................................................................... 522

Chapter 25: Derivatives Mishaps and What We Can Learn From Them........................... 523

25.1 Lessons for All Users of Derivatives ......................................................... 52325.2 Lessons for Financial Institutions ............................................................. 52725.3 Lessons for Nonfinancial Corporations ..................................................... 532

Summary ................................................................................................ 534Further Reading...................................................................................... 534

Answers to Quiz Questions ............................................................................................ 535

Glossary of Terms........................................................................................................ 559

DerivaGem Software .................................................................................................... 577

Major Exchanges Trading Futures and Options ............................................................... 581

Table for NðxÞ When x 6 0 ........................................................................................... 582

Table for NðxÞ When x > 0 ........................................................................................... 583

Index .......................................................................................................................... 585

xiv Contents

Preface

I was originally persuaded to write this book by colleagues who liked my book Options,Futures, and Other Derivatives, but found the material a little too advanced for theirstudents. Fundamentals of Futures and Options Markets covers some of the same groundas Options, Futures, and Other Derivatives, but in a way that readers who have hadlimited training in mathematics find easier to understand. One important differencebetween the two books is that there is no calculus in this book. Fundamentals is suitablefor undergraduate and graduate elective courses offered by business, economics, andother faculties. In addition, many practitioners who want to improve their under-standing of futures and options markets will find the book useful.

Instructors can use this book in a many different ways. Some may choose to coveronly the first 12 chapters, finishing with binomial trees. For those who want to do more,there are many different sequences in which Chapters 13 to 25 can be covered. FromChapter 18 onward, each chapter has been designed so that it is independent of theothers and can be included in or omitted from a course without causing problems.I recommend finishing a course with Chapter 25, which students always find interestingand entertaining.

What ’s New in This Edition?

Many changes have been made to update material and improve the presentation. Thederivatives markets’ move toward OIS discounting has continued since the eighth editionwas written. This has allowed me to streamline the material in the first seven chapters ofFundamentals. LIBOR discounting is no longer presented as a way to value instrumentssuch as swaps and forward rate agreements. The valuation of these instruments requires(a) forward rates for the rate used to calculate payments (usually LIBOR) and (b) thezero-coupon risk-free zero curve used for discounting (usually the OIS zero curve). Mostinstructors will find the new presentation appealing and more logical. It can be extendedto situations where payments are dependent on any risky rate. Other changes include:

1. More on the new regulations concerning the trading and clearing of OTC derivatives.

2. A major revision of the swaps chapter (Chapter 7) to improve the presentation ofmaterial and reflect the derivative markets’ move to OIS discounting.

3. A fuller description of the impact of daily settlement when futures contracts are usedfor hedging.

4. More details on the calculation and use of Greek letters.

5. More discussion of the expected shortfall measure, reflecting its increasingimportance.

xv

6. A new version of the software DerivaGem, tailored to the needs of readers of this

book.

Other Points of Distinction

SoftwareDerivaGem Fundamentals 4.00 (DG400f) is included with this book. This consists of

two Excel applications: the Options Calculator and the Applications Builder. The

Options Calculator consists of easy-to-use software for valuing many of the derivatives

discussed in this book. The Applications Builder consists of a number of Excel functions

from which users can build their own applications. It includes some sample applications

and enables students to explore the properties of options and numerical procedures. It

also allows more interesting assignments to be designed.

The software is described more fully at the end of the book. Updates to the software

can be downloaded from my website:

www-2.rotman.utoronto.ca/�hull

End-of-Chapter ProblemsAt the end of each chapter (except the last) there are seven quiz questions, which

students can use to provide a quick test of their understanding of the key concepts. The

answers to these are given at the end of the book. In addition, there are a multitude of

practice questions and further questions in the book.

Solutions Manual and Study GuideAnswers to the practice questions and advice to readers on how each chapter should be

studied are in the Solutions Manual and Study Guide (ISBN 0-13-408365-2), which is

published by Pearson and can be purchased separately from this book.

For the Instructor

At the Instructor Resource Center, www.pearsonhighered.com/irc, instructors can

easily register to gain access to a variety of instructor resources available with this text

in downloadable format.

If assistance is needed, Pearson’s dedicated technical support team is ready to help

with the media supplements that accompany this text. Visit http://247.pearsoned.com

for answers to frequently asked questions and toll-free user support phone numbers.

The following supplements are available with this text:

. PowerPoint Presentations (adopting instructors can adapt the slides to meet theirneeds)

. Instructors Manual (including answers to both practice questions and furtherquestions)

. Test Bank (20 multiple choice questions per chapter)

xvi Preface

Acknowledgments

Many people have played a part in the development of successive editions of this book.Indeed, the list of people who have provided mewith feedback on the book is now so longthat it is not possible to mention everyone. I have benefited from the advice of manyacademics who have taught from the book and from the comments of many derivativespractitioners. I would like to thank the students on my courses at the University ofToronto, who have made many suggestions on how the material can be improved. EddieMizzi of the Geometric Press did a fine job handling the page composition.

Alan White, a colleague at the University of Toronto, deserves a special acknowledg-ment. Alan and I have been carrying out joint research and consulting in the areas ofderivatives and risk management for about 30 years. During that time, we have spentmany hours discussing key issues. Many of the new ideas in this book, and many of thenew ways used to explain old ideas, are as much Alan’s as mine. Alan has done most ofthe development work on the DerivaGem software.

Special thanks are due to many people at Pearson for their enthusiasm, advice, andencouragement. I would particularly like to mention Donna Battista, Neeraj Bhalla,and Alison Kalil. I welcome comments on the book from readers. My email address is:

[email protected]

John Hull

About the Author

John Hull is the Maple Financial Professor of Derivatives and Risk Management at theJoseph L. Rotman School of Management, University of Toronto. He is an internation-ally recognized authority on derivatives and risk management with many publications inthis area. His work has an applied focus. In 1999 he was voted Financial Engineer of theYear by the International Association of Financial Engineers. He has acted as con-sultant to many North American, Japanese, and European financial institutions. He haswon many teaching awards, including University of Toronto’s prestigious Northrop Fryeaward.

Preface xvii

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Introduction

Derivatives markets have become increasingly important in the world of finance and

investments. It is now essential for all finance professionals to understand how these

markets work, how they can be used, and what determines prices in them. This book

addresses these issues.

Derivatives are traded on exchanges and in what are termed ‘‘over-the-counter’’

(OTC) markets. The two main products trading on exchanges are futures and options.

In the over-the counter markets forwards, swaps, options, and a wide range of other

derivatives transactions are agreed to. Prior to the crisis which started in 2007, the OTC

derivatives market was relatively free from regulation. This has now changed. As we will

explain, OTC market participants are now subject to rules requiring that trades be

reported, that collateral be provided, and that trading platforms be used.

This opening chapter starts by providing an introduction to futures markets and

futures exchanges. It then compares exchange-traded derivatives markets with OTC

derivatives markets and discusses forward contracts, which are the OTC counterpart of

futures contracts. After that, it introduces options and outlines the activities of hedgers,

speculators, and arbitrageurs in derivatives markets.

1.1 FUTURES CONTRACTS

A futures contract is an agreement to buy or sell an asset at a certain time in the future

for a certain price. There are many exchanges throughout the world trading futures

contracts. These include the CME Group (www.cmegroup.com), the Intercontinental

Exchange (ICE; www.intercontinentalexchange.com), Euronext (www.euronext.

com), Eurex (www.eurexchange.com), BM&FBOVESPA (www.bmfbovespa.com.br),

the National Stock Exchange of India (www.nse-india.com), the Tokyo Financial

Exchange (www.tfx.co.jp), and the China Financial Futures Exchange (www.cffex.

com.cn). A table at the end of this book gives a more complete list.

Futures exchanges allow people who want to buy or sell assets in the future to trade

with each other. In June, a trader in New York might contact a broker with instructions

to buy 5,000 bushels of corn for September delivery. The broker would immediately

communicate the client’s instructions to the CME Group. At about the same time,

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1C H A P T E R

another trader in Kansas might instruct a broker to sell 5,000 bushels of corn for

September delivery. These instructions would also be passed on to the CME Group.A price would be determined and the deal would be done.

The trader in New York who agreed to buy has what is termed a long futures position;the trader in Kansas who agreed to sell has what is termed a short futures position. The

price is known as the futures price. We will suppose the price is 400 cents per bushel.

This price, like any other price, is determined by the laws of supply and demand. If at aparticular time more people wish to sell September corn than to buy September corn,

the price goes down. New buyers will then enter the market so that a balance betweenbuyers and sellers is maintained. If more people wish to buy September corn than to sell

September corn, the price goes up—for similar reasons.

Issues such as margin requirements, daily settlement procedures, trading practices,

commissions, bid–offer spreads, and the role of the exchange clearing house will be

discussed in Chapter 2. For the time being, we can assume that the end result of theevents just described is that the trader in New York has agreed to buy 5,000 bushels of

corn for 400 cents per bushel in September and the trader in Kansas has agreed to sell

5,000 bushels of corn for 400 cents per bushel in September. Both sides have enteredinto a binding contract. The contract is illustrated in Figure 1.1.

A futures price can be contrasted with the spot price. The spot price is for immediate,or almost immediate, delivery. The futures price is the price for delivery at some time in

the future. The two are not usually equal. As we will see in later chapters, the futures

price may be greater than or less than the spot price.

1.2 HISTORY OF FUTURES MARKETS

Futures markets can be traced back to the Middle Ages. They were originally developedto meet the needs of farmers and merchants. Consider the position of a farmer in June of

a certain year who will harvest a known amount of corn in September. There is

uncertainty about the price the farmer will receive for the corn. In years of scarcity itmight be possible to obtain relatively high prices, particularly if the farmer is not in a

hurry to sell. On the other hand, in years of oversupply the corn might have to be

disposed of at fire-sale prices. The farmer and the farmer’s family are clearly exposed to agreat deal of risk.

Consider next a company that has an ongoing requirement for corn. The company isalso exposed to price risk. In some years an oversupply situation may create favorable

prices; in other years scarcity may cause the prices to be exorbitant. It can make sense

for the farmer and the company to get together in June (or even earlier) and agree on a

June:

September: Trader must buy 5,000 bushels of cornfor $20,000

Trader takes a long position in a Septemberfutures contract on corn at 400 cents per bushel

Figure 1.1 A futures contract (assuming it is held to maturity)

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price for the farmer’s estimated production of corn in September. This involves themnegotiating a type of futures contract. The contract provides a way for each side toeliminate the risk it faces because of the uncertain future price of corn.

We might ask what happens to the company’s requirements for corn during the rest ofthe year. Once the harvest season is over, the corn must be stored until the next season. Ifthe farmer stores the corn, the company and the farmer both face risks associated withthe future corn price, and again there is a clear role for futures contracts.

The Chicago Board of Trade

The Chicago Board of Trade (CBOT) was established in 1848 to bring farmers andmerchants together. Initially, its main task was to standardize the quantities andqualities of the grains that were traded. Within a few years, the first futures-typecontract was developed. It was known as a to-arrive contract. Speculators soon becameinterested in the contract and found trading the contract to be an attractive alternativeto trading the grain itself. The CBOT developed futures contracts on many differentunderlying assets, including corn, oats, soybeans, soybean meal, soybean oil, wheat,Treasury bonds, and Treasury notes. It became part of the CME Group in 2007.

The Chicago Mercantile Exchange

In 1874 the Chicago Produce Exchange was established, providing a market for butter,eggs, poultry, and other perishable agricultural products. In 1898 the butter and eggdealers withdrew from the exchange to form the Chicago Butter and Egg Board. In 1919,this was renamed the Chicago Mercantile Exchange (CME) and was reorganized forfutures trading. Since then, the exchange has provided a futures market for manycommodities, including pork bellies (1961), live cattle (1964), live hogs (1966), and feedercattle (1971). In 1982 it introduced a futures contract on the Standard & Poor’s (S&P)500 Stock Index.

The Chicago Mercantile Exchange started futures trading in foreign currenciesin 1972. The currency futures traded now include the euro, British pound, Canadiandollar, Japanese yen, Swiss franc, Australian dollar, Mexican peso, Brazilian real,South African rand, New Zealand dollar, Russian rouble, Chinese renminbi, Swedishkrona, Czech koruna, Hungarian forint, Israeli shekel, Korean won, Polish złoty, andTurkish lira. The Chicago Mercantile Exchange developed the very popular Eurodollarfutures contract. (As later chapters will explain, this is a contract on the future value ofa short-term interest rate.) It has also introduced futures contracts on weather and realestate.

The CMEGroup now includes the Chicago Board of Trade, the New YorkMercantileExchange, and the Kansas City Board of Trade.

Electronic Trading

Traditionally futures have been traded using what is known as the open-outcry system.This involves traders physically meeting on the floor of the exchange, known as the‘‘trading pit,’’ and using a complicated set of hand signals to indicate the trades theywould like to carry out. In the example we considered earlier, one floor trader wouldrepresent the person in New York who wanted to buy September corn and anotherfloor trader would represent the person in Kansas who wanted to sell September corn.

Introduction 3

Futures exchanges throughout the world have largely replaced the open outcry systemby electronic trading, where traders enter their required trades at a keyboard and acomputer is used to match buyers and sellers. Electronic trading has led to a growth inhigh-frequency and algorithmic trading, which involve the use of computer programs toinitiate trades, often without human intervention.

1.3 THE OVER-THE-COUNTER MARKET

Futures contracts are very popular exchange-traded contracts. Options, which areintroduced later in this chapter, also trade very actively on exchanges. But not alltrading of derivatives is on exchanges. Many trades take place in the over-the-counter(OTC) market. Banks, other large financial institutions, fund managers, and corpora-tions are the main participants in OTC derivatives markets. The number of derivativestransactions per year in OTC markets is smaller than in exchange-traded markets, butthe average size of the transactions is much greater.

Business Snapshot 1.1 The Lehman Bankruptcy

On September 15, 2008, Lehman Brothers filed for bankruptcy. This was the largestbankruptcy in US history and its ramifications were felt throughout derivativesmarkets. Almost until the end, it seemed as though there was a good chance thatLehman would survive. A number of companies (e.g., the Korean DevelopmentBank, Barclays Bank in the UK, and Bank of America) expressed interest in buyingit, but none of these was able to close a deal. Many people thought that Lehman was‘‘too big to fail’’ and that the US government would have to bail it out if no purchasercould be found. This proved not to be the case.

How did this happen? It was a combination of high leverage, risky investments,and liquidity problems. Commercial banks that take deposits are subject to regula-tions on the amount of capital they must keep. Lehman was an investment bank andnot subject to these regulations. By 2007, its leverage ratio had increased to 31:1,which means that a 3–4% decline in the value of its assets would wipe out its capital.Dick Fuld, Lehman’s Chairman and Chief Executive, encouraged an aggressive deal-making, risk-taking culture. He is reported to have told his executives: ‘‘Every day isa battle. You have to kill the enemy.’’ The Chief Risk Officer at Lehman wascompetent, but did not have much influence and was even removed from the executivecommittee in 2007. The risks taken by Lehman included large positions in theinstruments created from subprime mortgages, which will be described in Chapter 8.Lehman funded much of its operations with short-term debt. When there was a lossof confidence in the company, lenders refused to roll over this funding, forcing it intobankruptcy.

Lehman was very active in the over-the-counter derivatives markets. It had over amillion transactions outstanding with about 8,000 different counterparties. Lehman’scounterparties were often required to post collateral and this collateral had in manycases been used by Lehman for various purposes. Litigation attempting to deter-mine who owes what to whom has continued for many years after the bankruptcyfiling.

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