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FUNDAMENTALS OF

DerivativesMarkets

Robert L McDonaldNorthwestern University

Kellogg School of Management

Boston San Francisco New YorkLondon Toronto Sydney Tokyo Singapore Madrid

Mexico City Munich Paris Cape Town Hong Kong Montreal

Preface xix

Chapter 1

Introduction to Derivatives 11.1 What Is a Derivative? 21.2 An Overview of Financial Markets 2

Trading of Financial Assets 3Measures of Market Size and Activity 4Stock and Bond Markets 5Derivatives Markets 6

1.3 The Role of Financial Markets 11Financial Markets and the Averages 11Risk Sharing 12

1.4 Ways to Think about Derivatives 14Uses of Derivatives 15Perspectives on Derivatives 16Financial Engineering and Security Design 16

1.5 Buying and Short-Selling Financial Assets 17Transaction Costs and the Bid-Ask Spread 17Ways to Buy or Sell 18Short-Selling 19The Lease Rate of an Asset 21

Chapter Summary 22Further Reading 23Problems 23

IX

I Contents

PART ONEInsurance, Hedging, and Simple Strategies 27

Chapter 2An Introduction to Forwards and Options 29

2.1 Forward Contracts 29The Payoff on a Forward Contract 31Graphing the Payoff on a Forward Contract 33Comparing a Forward and Outright Purchase 34Zero-Coupon Bonds in Payoff and Profit Diagrams 36Cash Settlement Versus Delivery 38Credit Risk 38

2.2 Call Options 39Option Terminology 40Payoff and Profit for a Purchased Call Option 42Payoff and Profit for a Written Call Option 44

2.3 Put Options 46Payoff and Profit for a Purchased Put Option 47Payoff and Profit for a Written Put Option 48The "Moneyness" of an Option 50

2.4 Summary of Forward and Option Positions 51Long Positions 51Short Positions 52

2.5 Options Are Insurance 54Homeowner's Insurance Is a Put Option 54But I Thought Insurance Was Prudent and Put Options Were Risky . . . 55Call Options Are Also Insurance 56

Chapter Summary 56Further Reading 57Problems 58

Chapter 3Insurance, Collars, and Other Strategies 61

3.1 Basic Insurance Strategies 61Insuring a Long Position: Floors 61Insuring a Short Position: Caps 65Selling Insurance 66

3.2 Using Options to Create Synthetic Forwards 68Put-Call Parity 70

Contents . I xi

3.3 Spreads and Collars 72Bull and Bear Spreads 73Box Spreads 74Ratio Spreads 75Collars 76

3.4 Speculating on Volatility 79Straddles 79Butterfly Spreads 82

3.5 Application: Equity-Linked CDs 84Graphing the Payoff on the CD 85Economics of the CD 85Why Equity-Linked CDs? 86

Chapter Summary 87Further Reading 89Problems 89

Chapter 4Introduction to Risk Management 93

4.1 Basic Risk Management: The Producer's Perspective 93Hedging with a Forward Contract 94Insurance: Guaranteeing a Minimum Price with a Put Option 96Insuring by Selling a Call 97Adjusting the Amount of Insurance 99

4.2 Basic Risk Management: The Buyer's Perspective 100Hedging with a Forward Contract 101Insurance: Guaranteeing a Maximum Price with a Call Option 101

4.3 Why Do Firms Manage Risk? 103Reasons to Hedge 104Reasons Not to Hedge 106Empirical Evidence on Hedging 107

4.4 Golddiggers Revisited 108Selling the Gain: Collars 109Other Collar Strategies 113Paylater Strategies 113

4.5 Basis Risk 114Hedging Jet Fuel with Crude Oil 115Stack and Strip Hedges 115

Chapter Summary 117Further Reading 118Problems 119

xn

PART T W OForwards, Futures, and Swaps 123

Chapter 5Financial Forwards and Futures 125

5.1 Alternative Ways to Buy a Stock 1255.2 Prepaid Forward Contracts on Stock 127

Pricing the Prepaid Forward by Analogy 127Pricing the Prepaid Forward by Discounted Present Value 127Pricing the Prepaid Forward by Arbitrage 128Pricing Prepaid Forwards with Dividends 129

5.3 Forward Contracts on Stock 132Creating a Synthetic Forward Contract 133Synthetic Forwards in Market-Making and Arbitrage 135No-Arbitrage Bounds with Transaction Costs 136Quasi-Arbitrage 137Does the Forward Price Predict the Future Price? 137An Interpretation of the Forward Pricing Formula 139

5.4 Futures Contracts 139The S&rP 500 Futures Contract 140

i Margins and Marking-to-Market 142Comparing Futures and Forward Prices 145

5.5 Uses of Index Futures 145Asset Allocation 146Cross-Hedging with Index Futures 147

Chapter Summary 150Further Reading 151Problems 152

Chapter 6The Wide World of Futures Contracts 157

6.1 Currency Contracts 157Currency Prepaid Forward 157Currency Forward 159Covered Interest Arbitrage 159

6.2 Eurodollar Futures 1606.3 An Introduction to Commodity Futures 164

Seasonality and Storage Costs 164The Forward Price and the Expected Commodity Price 166The Commodity Lease Rate 166

Contents i xiii

6.4 Energy Futures 168Electricity 168Natural Gas 169Crude Oil 171

6.5 Weather and Housing Futures 173Weather Derivatives 174Housing Futures 175

Chapter Summary 177Further Reading 178Problems 179

Chapter 7Interest Rate Forwards and Futures 183

7.1 Bond Basics 183Zero-Coupon Bonds 185Implied Forward Rates 186Coupon Bonds 188Zeros from Coupons 189Interpreting the Coupon,Rate 190Continuously Compounded Yields 191

7.2 Forward Rate Agreements, Eurodollars, and Hedging 192Forward Rate Agreements 193Synthetic FRAs 194Eurodollar Futures versus FRAs 196Interest Rate Strips and Stacks 197

7.3 Duration and Convexity 198Duration 198Duration Matching 201Convexity .202

7.4 Treasury-Bond and Treasury-Note Futures 2047.5 Repurchase Agreements 207Chapter Summary 209Further Reading 210Problems 210 .7.A Interest Rate and Bond Price Conventions 214

Bonds 215Bills 216

Chapter 8Swaps 219

8.1 An Example of a Commodity Swap 220Physical Versus Financial Settlement 221Why Is the Swap Price Not $20.50? 222

xiv ' I Contents

The Swap Counterparty 223The Market Value of a Swap 225

8.2 Interest Rate Swaps 227A Simple Interest Rate Swap 227Pricing and the Swap Counterparty 229Computing the Swap Rate in General 230Deferred Swaps 232The Swap Curve 233Amortizing and Accreting Swaps 234

8.3 Currency Swaps 235Currency Swap Formulas 238Other Currency Swaps 239

8.4 Swaptions 2408.5 Total Return Swaps 241Chapter Summary 244Further Reading 244Problems 245

PART THREEOptions 247

Chapter 9Parity and Other Option Relationships 249

9.1 Put-Call Parity 250Options on Stocks 251Options on Currencies 254Options on Bonds 254

9.2 Generalized Parity and Exchange Options 255Options to Exchange Stock 256What Are Calls and Puts? 257Currency Options 258

9.3 Comparing Options with Respect to Style, Maturity, and Strike ' 260European Versus American Options 260Maximum and Minimum Option Prices 261Early Exercise for American Options 262Time to Expiration 264Different Strike Prices 265

Chapter Summary 270Further Reading 271Problems 272

Contents I I XV

Chapter 10Binomial Option Pricing 277

10.1 A One-Period Binomial Tree 277Computing the Option Price 278The Binomial Solution 280Arbitraging a Mispriced Option 282A Graphical Interpretation of the Binomial Formula 283Pricing with Dividends 283Risk-Neutral Pricing 285Constructing a Binomial Tree 286Another One-Period Example 287Summary 288

10.2 Two or More Binomial Periods 288A Two-Period European Call 289Many Binomial Periods 291

10.3 Put Options 293European.Put 293American Put 294

10.4 American Options 29410.5 Options on Other Assets 295

Option on a Stock Index 295Options on Currencies 297Options on Futures Contracts 297Summary 299

Chapter Summary 301Further Reading 301Problems 30110.A Lognormality and the Binomial Model 30410.B Alternative Binomial Pricing Models 307

The Cox-Ross-Rubinstein Binomial Tree 307The Jarrow-Rudd Tree 308

Chapter 11The Black-Scholes Formula 309

11.1 Introduction to the Black-Scholes Formula 309Call Options 310Put Options 313 . 'What Assumptions Underlie the Black-Scholes Formula? 314

11.2 Applying the Formula to Other Assets 314Options on Stocks with Discrete Dividends 315Options on Currencies 316Options on Futures 316

xvi IH Contents

11.3 Option Greeks 317Definition of the Greeks 317Greek Measures for Portfolios 324Option Elasticity 325

11.4 Delta-Hedging 330Option Risk in the Absence of Hedging 330An Example of Delta-Hedging 331Interpreting Market-Maker Profit 333

11.5 Volatility 335Historical Volatility 335Implied Volatility 336Trading Volatility 339

• Chapter Summary 341Further Reading 342Problems 342

PART FOURFinancial Engineering and Applications 347

s

Chapter 12Financial Engineering and Security Design 349

12.1 The Modigliani-Miller Theorem 34912.2 Structured Notes Without Options 350

Zero-Coupon Bonds Paying Cash 351Coupon Bonds Paying Cash 351Equity-Linked Bonds 352Commodity-Linked Bonds 355Currency-Linked Bonds 357

12.3 Structured Notes with Options 358Coupon Bonds with Options 358Equity-Linked Notes with Options 359

Valuing and Structuring ah Equity-Linked CD 361Alternative Structures 363Application: Variable Prepaid Forwards 364

12;4 Engineered Solutions for Golddiggers 366Gold-Linked Notes 366Notes with Embedded Options 367

Contents 111 xvii

12.5 Credit Structures 369Collateralized Debt Obligations 370Credit Default Swaps 373CDS Indexes 376

Chapter Summary 378Further Reading 379Problems 379,

Chapter 13Corporate Applications 383

13.1 Equity, Debt, and Warrants 383Debt and Equity as Options 383Valuing Credit Guarantees 386Leverage and the Expected Return on Debt and Equity 388Multiple Debt Issues 392Warrants 393Convertible Bonds 394Callable Bonds 397Bond Valuation Based on the Stock Price 401

" Put Warrants 40213.2 Compensation Options 403

Whose Valuation? 406Valuation Inputs 406Level 3 Communications 409

13.3 The Use of Collars in Acquisitions 412The Northrop Grumman-TRW Merger 413

Chapter Summary 417Further Reading 417Problems 418

Chapter 14Real Options 423

14.1 DCF and Option Valuation for a Single Cash Flow 424Project 1 424

. Project 2 428Project 3 431Summary 432

14.2 Multiperiod Valuations 433Project 1 434Project 2 436

xviii 1 Contents

Project 3 437.Summary 437

14.3 Examples of Real Options in Practice 438Commodity Extraction 438Peak-Load Electricity Generation 442Pharmaceutical Research and Development 446

Chapter Summary 448Further Reading 448Problems 44914.A The Relationship Between DCF and Risk-Neutral Valuation 451

Appendix AThe Greek Alphabet 453

Appendix BContinuous Compounding 455

B.I The Language of Interest Rates 455B.2 The Logarithmic and Exponential Functions 456

Changing Interest Rates 457Symmetry for Increases and Decreases 458

Problems 459

Glossary 461

References 473

Index 481