List of Symbols

α

A0, AT

AI, AIt, AIT

b, bt, bT

B

β, βs, βf, βT, βy

B0, BT

B0(ti)

C

C1, C2, C3

C(S0,T,X)

Ce(S0,T,X)

Ca(S0,T,X)

C(f0,T,X)

Ce(f0,T,X)

Ca(f0,T,X)

Cu, Cd, Cu2, Cud, Cd2

χ

CIt

CovΔS,Δf

CovrS ,rf

ρΔS,Δf

CPt

CF

CF(t), CF(T)

c

Δ

ΔB, ΔM, ΔS, Δf, ΔyB, Δyf

δc

d

d1 , d2

¼ alpha, unsystematic return

¼ market value of firm assets at time 0 and T

¼ accrued interest today, at time t, and at time T

¼ basis today, at time t, and at expiration, T

¼ market value of bond portfolio

¼ beta, beta of spot asset or portfolio, beta of futures, target

beta, and yield beta

¼ market value of firm debt at time 0 and T

¼ price of zero coupon bond observed at time 0, matures in

ti days

¼ (abbreviated) price of call

¼ (abbreviated) price of call for exercise prices X1, X2, X3

¼ price of either European or American call on asset with

price S0, expiration T, and exercise price X

¼ price of European call on asset with price S0, expiration T,

and exercise price X

¼ price of American call on asset with price S0, expiration T,

and exercise price X

¼ price of either European or American call on futures with

price f0, expiration T, and exercise price X

¼ price of European call on futures with price f0, expiration T,

and exercise price X

¼ price of American call on futures with price f0, expiration T,

and exercise price X

¼ call price sequence in binomial model

¼ convenience yield

¼ coupon interest paid at time t

¼ covariance of the change in the spot price and change in

the futures price

¼ covariance of the rate of return on the spot and futures

¼ correlation of the change in the spot price and change in

the futures price

¼ cash payment (principal or interest) on bond at time t

¼ conversion factor on CBOT T-bond contract

¼ conversion factor on CBOT T-bond contracts deliverable

at times t and T

¼ coupon rate

¼ delta of an option

¼ change in bond price, change in market portfolio value,

change in spot price, change in futures price, change in

bond yield, change in futures yield

¼ dividend yield

¼ (without subscript) 1.0 + downward return on stock in

binomial model

¼ variables in Black-Scholes-Merton model

¼ present value of dividends to time 0, present value of dividends

¼ dividend paid at time j or time t

¼ compound future value of reinvested dividends

¼ Macaulay’s duration

¼ standard normal random variable in Monte Carlo simulation

¼ expected value of the argument x

¼ measure of hedging effectiveness

¼ (abbreviated) futures price at time 0, t, and T, value of futures

position

f0(T), ft(T), fT(T) ¼ futures price or futures exchange rate today, at time t, and at

expiration T

f0(T)(a)‡ ¼ critical futures price for early exercise of American option on

futures

F ¼ fixed rate on FRAs or continuously compounded forward rate

F(0,T) ¼ forward price for contracts written today 0, expiring at T

FV ¼ face value of bond

g ¼ days elapsed in FRA

Γ ¼ gamma of an option

h ¼ number of days in FRA when originated

hC, hS ¼ hedge ratios based on Black-Scholes-Merton model

h, hu, hd ¼ hedge ratios in binomial model

i ¼ interest rate for storage problem

J ¼ number of observations in sample

j ¼ counter in summation procedure

K ¼ parameter in break forward contract

k ¼ discount rate (required rate) on stock

LIBOR ¼ London Interbank Offer Rate, a Eurodollar rate

ln(x) ¼ natural log of the argument x

Lt(h) ¼ h-day LIBOR at t

m ¼ number of days associated with interest rate

M ¼ value of market portfolio of all risky assets

MDB, MDf, MDT ¼ modified duration of bond portfolio, modified duration of futures

contract, target modified duration

MOS ¼ number of months in computing CBOT conversion factor

MOS* ¼ number of months in computing CBOT conversion factor

rounded down to nearest quarter

N ¼ total number in summation procedure

N1, N2, N3 ¼ quantity of options

N(d1), N(d2) ¼ cumulative normal probabilities in Black-Scholes-Merton model

Nf* ¼ optimal hedge ratio

NPV ¼ net present value

NB, NC, NP, NS, Nf ¼ number of bonds, calls, puts, shares of stock, and futures held

in a position

NP, NP€, NP$ ¼ notional principle, euros, dollars

D0, D

Dj, Dt

DT

DURB

ε

E(x)

e*

f0, ft, fT, f

An Introduction to Derivatives

and Risk Management

EIGHTH EDITION

DON M. CHANCE

Louisiana State University

ROBERT BROOKS

University of Alabama

Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

An Introduction to Derivatives and Risk

Management, Eighth edition

Don M. Chance, Robert Brooks

Vice President of Editorial, Business: Jack

W. Calhoun

Publisher: Joe Sabatino

© 2010, 2007 South-Western, Cengage Learning

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Brief Contents

Preface

CHAPTER

1

xvi

Introduction

1

PART I Options

23

CHAPTER

2

Structure of Options Markets 24

CHAPTER

3

Principles of Option Pricing

CHAPTER

4

Option Pricing Models: The Binomial Model

CHAPTER

5

Option Pricing Models: The Black-Scholes-Merton Model

CHAPTER

6

Basic Option Strategies

CHAPTER

7

Advanced Option Strategies

57

95

127

183

221

PART II Forwards, Futures, and Swaps

253

CHAPTER

8

The Structure of Forward and Futures Markets 254

CHAPTER

9

Principles of Pricing Forwards, Futures, and Options on Futures

CHAPTER

10

Futures Arbitrage Strategies

CHAPTER

11

Forward and Futures Hedging, Spread, and Target Strategies

CHAPTER

12

Swaps

327

355

407

PART III Advanced Topics

447

CHAPTER

13

Interest Rate Forwards and Options

448

CHAPTER

14

Advanced Derivatives and Strategies

483

CHAPTER

15

Financial Risk Management Techniques and Applications

CHAPTER

16

Managing Risk in an Organization

Appendix A

Appendix B

Appendix C

287

List of Formulas 588

References 594

Solutions to Concept Checks

Glossary 620

Index 643

521

563

608

iii

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi

CHAPTER 1

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

Derivative Markets and Instruments

Options 2

Forward Contracts 3

Futures Contracts 3

Swaps and Other Derivatives 4

The Underlying Asset

2

4

Important Concepts in Financial and Derivative Markets

Risk Preference 5

Short Selling 5

Repurchase Agreements 6

Return and Risk 7

Market Efficiency and Theoretical Fair Value 8

Making the Connection

Risk and Return and Arbitrage

5

9

Fundamental Linkages between Spot and Derivative Markets 10

Arbitrage and the Law of One Price 10

The Storage Mechanism: Spreading Consumption across Time 11

Delivery and Settlement 12

12

Role of Derivative Markets

Risk Management 12

Making the Connection

Jet Fuel Risk Management at Southwest Airlines

Price Discovery 13

Operational Advantages

Market Efficiency 14

14

Criticisms of Derivative Markets

Misuses of Derivatives

14

15

Derivatives and Your Career

15

Sources of Information on Derivatives

16

Book Overview 16

Organization of the Book 16

Key Features of the Book 17

Specific New Features of the Eighth Edition

Use of the Book 19

Summary

Key Terms

19

19

Further Reading

20

Concept Checks

20

Questions and Problems

iv

13

20

18

Contents

PART I

v

23

Options

CHAPTER 2

Structure of Options Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

24

Development of Options Markets

Call Options

26

Put Options

26

Over-the-Counter Options Market

27

Organized Options Trading 28

Listing Requirements 29

Contract Size 29

Exercise Prices 30

Expiration Dates 30

Position and Exercise Limits 31

Options Exchanges and Trading Activity

31

Option Traders 32

Market Maker 33

Floor Broker 33

Order Book Official 34

Other Option Trading Systems 34

Off-Floor Option Traders 34

Cost and Profitability of Exchange Membership

35

Mechanics of Trading 36

Placing an Opening Order 36

Role of the Clearinghouse 36

Placing an Offsetting Order 38

Exercising an Option 39

Option Price Quotations

40

Making the Connection

Reading Option Price Quotations

Types of Options 42

Stock Options 42

Index Options 42

Currency Options 43

Other Types of Options

Real Options 44

40

43

Transaction Costs in Option Trading 45

Floor Trading and Clearing Fees 45

Commissions 45

Bid-Ask Spread 45

Other Transaction Costs 46

Regulation of Options Markets

46

Making the Connection

Suspicious Put Option Trading and Bear Stearns & Co., Inc. Implosion

Summary

Key Terms

48

48

Further Reading

49

Concept Checks

49

Questions and Problems

49

47

vi

Contents

Appendix 2.A: Margin Requirements 51

Margin Requirements on Stock Transactions 51

Margin Requirements on Option Purchases 51

Margin Requirements on the Uncovered Sale of Options

Margin Requirements on Covered Calls 52

Questions and Problems 52

Appendix 2.B: Taxation of Option Transactions

Taxation of Long Call Transactions 53

Taxation of Short Call Transactions 53

Taxation of Long Put Transactions 54

Taxation of Short Put Transactions 54

Taxation of Non-Equity Options 54

Wash and Constructive Sales 55

Questions and Problems 55

51

53

CHAPTER 3

Principles of Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Basic Notation and Terminology

58

Principles of Call Option Pricing 60

Minimum Value of a Call 60

Maximum Value of a Call 61

Value of a Call at Expiration 62

Effect of Time to Expiration 63

Effect of Exercise Price 65

Lower Bound of a European Call 68

Making the Connection

Asynchronous Closing Prices and Apparent Boundary Condition Violations

American Call Versus European Call 71

Early Exercise of American Calls on Dividend-Paying Stocks

Effect of Interest Rates 73

Effect of Stock Volatility 73

70

72

Principles of Put Option Pricing 74

Minimum Value of a Put 74

Maximum Value of a Put 76

Value of a Put at Expiration 76

Effect of Time to Expiration 77

The Effect of Exercise Price 78

Lower Bound of a European Put 80

American Put Versus European Put 82

Early Exercise of American Puts 82

Put-Call Parity 83

Effect of Interest Rates 85

Effect of Stock Volatility 86

Making the Connection

Put-Call Parity Arbitrage

Summary

Key Terms

87

88

89

Further Reading

89

Concept Checks

90

Questions and Problems

90

Appendix 3: Dynamics of Option Boundary Conditions: A Learning Exercise

93

Contents

vii

CHAPTER 4

Option Pricing Models: The Binomial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

One-Period Binomial Model

Illustrative Example 99

Hedge Portfolio 99

Overpriced Call 100

Underpriced Call 101

95

Two-Period Binomial Model

101

Making the Connection

Binomial Option Pricing, Risk Premiums, and Probabilities

Illustrative Example 105

Hedge Portfolio 106

Mispriced Call in the Two-Period World

102

107

Extensions of the Binomial Model 109

Pricing Put Options 109

American Puts and Early Exercise 111

Dividends, European Calls, American Calls, and Early Exercise 111

Extending the Binomial Model to n Periods 116

Behavior of the Binomial Model for Large n and Fixed Option Life 118

Alternative Specifications of the Binomial Model 119

Advantages of the Binomial Model 121

Making the Connection

Uses of the Binomial Option Pricing Framework in Practice

122

Software Demonstration 4.1

Calculating the Binomial Price with the Excel Spreadsheet BSMbin8e.xls

Summary

Key Terms

123

124

124

Further Reading

124

Concept Checks

125

Questions and Problems

125

CHAPTER 5

Option Pricing Models: The Black-Scholes-Merton Model . . . . . . . . . . . . . . . . . . . . . 127

Origins of the Black-Scholes-Merton Formula

127

Black-Scholes-Merton Model as the Limit of the Binomial Model

Making the Connection

Logarithms, Exponentials, and Finance

128

130

Assumptions of the Black-Scholes-Merton Model 131

Stock Prices Behave Randomly and Evolve According to a Lognormal Distribution

Risk-Free Rate and Volatility of the Log Return on the Stock

Are Constant Throughout the Option’s Life 134

No Taxes or Transaction Costs 135

Stock Pays No Dividends 135

Options Are European 135

A Nobel Formula 135

Digression on Using the Normal Distribution 136

Numerical Example 138

Characteristics of the Black-Scholes-Merton Formula

139

132

viii

Contents

Software Demonstration 5.1

Calculating the Black-Scholes-Merton Price with

the Excel Spreadsheet BSMbin8e.xls 140

Variables in the Black-Scholes-Merton Model

Stock Price 144

Exercise Price 148

Risk-Free Rate 148

Volatility or Standard Deviation 150

Time to Expiration 151

144

Black-Scholes-Merton Model When the Stock Pays Dividends

Known Discrete Dividends 154

Known Continuous Dividend Yield 155

152

Black-Scholes-Merton Model and Some Insights into American Call Options

Estimating the Volatility 157

Historical Volatility 157

Implied Volatility 160

Software Demonstration 5.2

Calculating the Historical Volatility with the Excel Spreadsheet Hisv8e.xls

Making the Connection

Smiles, Smirks, and Surfaces

Put Option Pricing Models

Key Terms

160

165

168

Managing the Risk of Options

Summary

156

170

175

176

Further Reading

176

Concept Checks

177

Questions and Problems

177

Appendix 5: A Shortcut to the Calculation of Implied Volatility

180

CHAPTER 6

Basic Option Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Terminology and Notation 184

Profit Equations 184

Different Holding Periods 186

Assumptions 186

Stock Transactions 187

Buy Stock 187

Sell Short Stock 187

Call Option Transactions

Buy a Call 189

Write a Call 193

189

Put Option Transactions

Buy a Put 195

Write a Put 198

195

Calls and Stock: The Covered Call 201

Some General Considerations with Covered Calls

Making the Connection

Alpha and Covered Calls

206

Puts and Stock: The Protective Put

207

205

Contents

ix

Making the Connection

Using the Black-Scholes-Merton Model to Analyze

the Attractiveness of a Strategy 210

Synthetic Puts and Calls

211

Software Demonstration 6.1

Analyzing Option Strategies with the Excel Spreadsheet Stratlyz8e.xls

214

217

Summary

218

Key Terms

Further Reading

218

Concept Checks

218

Questions and Problems

218

CHAPTER 7

Advanced Option Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Option Spreads: Basic Concepts 221

Why Investors Use Option Spreads 222

Notation 222

223

223

Money Spreads

Bull Spreads

Making the Connection

Spreads and Option Margin Requirements

227

Bear Spreads 227

A Note about Call Bear Spreads and Put Bull Spreads

Collars 230

Making the Connection

Designing a Collar for an Investment Portfolio

Butterfly Spreads

229

233

234

Calendar Spreads 237

Time Value Decay 239

241

Ratio Spreads

Straddles

242

246

Box Spreads

Summary

Key Terms

249

249

Further Reading

249

Concept Checks

250

Questions and Problems

250

PART II Forwards, Futures, and Swaps

253

CHAPTER 8

The Structure of Forward and Futures Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254

Development of Forward and Futures Markets 255

Chicago Futures Markets 255

Development of Financial Futures 256

Development of Options on Futures Markets 258

Parallel Development of Over-the-Counter Markets 258

Over-the-Counter Forward Market

259

x

Contents

Organized Futures Trading 259

Contract Development 260

Contract Terms and Conditions 260

Delivery Terms 261

Daily Price Limits and Trading Halts 262

Other Exchange Responsibilities 262

Futures Exchanges 262

Futures Traders 264

General Classes of Futures Traders 264

Classification by Trading Strategy 264

Classification by Trading Style 265

Off-Floor Futures Traders 266

Costs and Profitability of Exchange Membership

Forward Market Traders 267

266

Mechanics of Futures Trading 267

Placing an Order 268

Role of the Clearinghouse 268

Making the Connection

How Clearinghouses Reduce Credit Risk

Daily Settlement 270

Delivery and Cash Settlement

269

273

274

Futures Price Quotations

Types of Futures Contracts 275

Agricultural Commodities 275

Natural Resources 275

Miscellaneous Commodities 276

Foreign Currencies 276

Federal Funds and Eurodollars 276

Treasury Notes and Bonds 276

Swap Futures 277

Equities 277

Making the Connection

Reading Futures Price Quotations

278

Managed Funds 278

Hedge Funds 280

Options on Futures 280

Transaction Costs in Forward and Futures Trading

Commissions 280

Bid-Ask Spread 281

Delivery Costs 281

Regulation of Futures and Forward Markets

Summary

Key Terms

280

281

282

283

Further Reading

283

Concept Checks

284

Questions and Problems

284

Appendix 8: Taxation of Futures Transactions in the United States

Questions and Problems 286

286

Contents

xi

CHAPTER 9

Principles of Pricing Forwards, Futures, and Options on Futures . . . . . . . . . . . . . . 287

Generic Carry Arbitrage 288

Concept of Price Versus Value 288

Value of a Forward Contract 289

Price of a Forward Contract 290

Value of a Futures Contract 291

Making the Connection

When Forward and Futures Contracts Are the Same

292

Price of a Futures Contract 294

Forward Versus Futures Prices 294

Carry Arbitrage When Underlying Generates Cash Flows 295

Stock Indices and Dividends 295

Foreign Currencies and Foreign Interest Rates: Interest Rate Parity

Commodities and Storage Costs 300

Pricing Models and Risk Premiums 300

Spot Prices, Risk Premiums, and Carry Arbitrage for Generic Assets

Forward/Futures Pricing Revisited 302

Futures Prices and Risk Premia 307

Put-Call-Forward/Futures Parity 312

298

301

Pricing Options on Futures 313

Intrinsic Value of an American Option on Futures 313

Lower Bound of a European Option on Futures 314

Put-Call Parity of Options on Futures 316

Early Exercise of Call and Put Options on Futures 317

Black Futures Option Pricing Model 319

Summary

Key Terms

321

323

Further Reading

324

Concept Checks

324

Questions and Problems

324

CHAPTER 10

Futures Arbitrage Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

Short-Term Interest Rate Arbitrage 327

Carry Arbitrage and the Implied Repo Rate 327

Federal Funds Futures Carry Arbitrage and the Implied Repo Rate

Eurodollar Arbitrage 331

329

Intermediate- and Long-Term Interest Rate Arbitrage 332

Determining the Cheapest-to-Deliver Bond on the Treasury Bond Futures Contract

Delivery Options 337

Implied Repo, Carry Arbitrage, and Treasury Bond Futures 340

Software Demonstration 10.1

Identifying the Cheapest-to-Deliver Bond with the Excel Spreadsheet CTD8e.xls

Treasury Bond Futures Spreads and the Implied Repo Rate

Stock Index Arbitrage

343

342

340

334

xii

Contents

Foreign Exchange Arbitrage

347

Making the Connection

Currency-Hedged Cross-Border Index Arbitrage

Summary

Key Terms

348

350

350

Further Reading

350

Concept Checks

350

Questions and Problems

351

Appendix 10: Determining the CBOT Treasury Bond Conversion Factor

Software Demonstration 10.2

Determining the CBOT Conversion Factor with the Excel Spreadsheet CF8e.xls

353

354

CHAPTER 11

Forward and Futures Hedging, Spread, and Target Strategies . . . . . . . . . . . . . . . . . . 355

Why Hedge?

356

Hedging Concepts 357

Short Hedge and Long Hedge 357

The Basis 358

Some Risks of Hedging 362

Contract Choice 363

Margin Requirements and Marking to Market

366

Determination of the Hedge Ratio 367

Minimum Variance Hedge Ratio 368

Price Sensitivity Hedge Ratio 369

Stock Index Futures Hedging 371

Hedging Strategies 372

Foreign Currency Hedges 373

Intermediate- and Long-Term Interest Rate Hedges

Making the Connection

Hedging Contingent Foreign Currency Risk

Making the Connection

Using Derivatives in Takeovers

375

376

384

Spread Strategies 384

Intramarket Spreads 386

Intermarket Spreads 388

Target Strategies 391

Target Duration with Bond Futures 391

Alpha Capture 393

Target Beta with Stock Index Futures 396

Tactical Asset Allocation Using Stock and Bond Futures

Summary

Key Terms

401

402

Further Reading

402

Concept Checks

402

Questions and Problems

403

Appendix 11: Taxation of Hedging

406

397

Contents

xiii

CHAPTER 12

Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

Interest Rate Swaps 409

Structure of a Typical Interest Rate Swap 410

Pricing and Valuation of Interest Rate Swaps 412

Making the Connection

LIBOR and the British Bankers Association

Interest Rate Swap Strategies

417

420

Currency Swaps 423

Structure of a Typical Currency Swap 423

Pricing and Valuation of Currency Swaps 425

Currency Swap Strategies 429

Making the Connection

Valuing a Currency Swap as a Series of Currency Forward Contracts

430

Equity Swaps 433

Structure of a Typical Equity Swap 434

Pricing and Valuation of Equity Swaps 435

Equity Swap Strategies 439

Some Final Words about Swaps

Summary

Key Terms

440

441

442

Further Reading

442

Concept Checks

442

Questions and Problems

443

PART III Advanced Topics

447

CHAPTER 13

Interest Rate Forwards and Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

Forward Rate Agreements 449

Structure and Use of a Typical FRA 450

Pricing and Valuation of FRAs 452

Applications of FRAs 454

Interest Rate Options 456

Structure and Use of a Typical Interest Rate Option 457

Pricing and Valuation of Interest Rate Options 458

Interest Rate Option Strategies 460

Interest Rate Caps, Floors, and Collars 465

Interest Rate Options, FRAs, and Swaps 470

Interest Rate Swaptions and Forward Swaps

Making the Connection

Binomial Pricing of Interest Rate Options

471

472

Structure of a Typical Interest Rate Swaption 472

Equivalence of Swaptions and Options on Bonds 475

Pricing Swaptions 475

Forward Swaps 475

Applications of Swaptions and Forward Swaps 477

Summary

Key Terms

479

479

xiv

Contents

Further Reading

480

Concept Checks

480

Questions and Problems

480

CHAPTER 14

Advanced Derivatives and Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

Advanced Equity Derivatives and Strategies

Portfolio Insurance 484

Equity Forwards 489

Making the Connection

Portfolio Insurance in a Crashing Market

483

491

Equity Warrants 493

Equity-Linked Debt 493

Advanced Interest Rate Derivatives

Structured Notes 494

Mortgage-Backed Securities 496

494

Exotic Options 501

Digital and Chooser Options 502

Path-Dependent Options 505

Other Exotic Options 511

Making the Connection

Accumulator Contracts

512

Some Unusual Derivatives 512

Electricity Derivatives 513

Weather Derivatives 513

Summary

Key Terms

514

515

Further Reading

515

Concept Checks

516

Questions and Problems

516

Appendix 14: Monte Carlo Simulation

519

CHAPTER 15

Financial Risk Management Techniques and Applications . . . . . . . . . . . . . . . . . . . . . 521

Why Practice Risk Management? 521

Impetus for Risk Management 521

Benefits of Risk Management 523

Managing Market Risk 524

Delta Hedging 525

Gamma Hedging 527

Vega Hedging 529

Value at Risk (VAR) 531

A Comprehensive Calculation of VAR

Benefits and Criticisms of VAR 539

Extensions of VAR 540

Managing Credit Risk 541

Credit Risk as an Option 542

Credit Risk of Derivatives 544

537

Contents

Making the Connection

What Derivatives Tell Us About Bonds

Netting 546

Credit Derivatives

Summary

Key Terms

546

548

Making the Connection

Unfunded Synthetic CDOs

Other Types of Risks

xv

554

555

559

559

Further Reading

559

Concept Checks

560

Questions and Problems

560

CHAPTER 16

Managing Risk in an Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563

The Structure of the Risk Management Industry 563

End Users 564

Dealers 564

Other Participants in the Risk Management Industry 565

Organizing the Risk Management Function in a Company

Making the Connection

Professional Organizations in Risk Management: GARP and PRMIA

565

566

Risk Management Accounting 570

Fair Value Hedges 571

Cash Flow Hedges 572

Foreign Investment Hedges 574

Speculation 574

Some Problems in the Application of FAS 133 574

Disclosure 575

Avoiding Derivatives Losses 575

Metallgesellschaft: To Hedge or Not to Hedge? 576

Orange County, California: Playing the Odds 577

Barings PLC: How One Man Blew Up a Bank 579

Procter & Gamble: Going Up in Suds 580

Risk Management Industry Standards

Responsibilities of Senior Management

Summary

Key Terms

581

582

584

584

Further Reading

584

Concept Checks

585

Questions and Problems

585

Appendix A List of Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix B References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix C Solutions to Concept Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

588

594

608

620

643

Preface

DON CHANCE

As this book goes into its eighth edition, I continue to be amazed at how the derivatives

and risk management world have evolved. When I originally drafted a plan for the first

edition, I was told by some publishers that there was no market for a textbook on options and futures, as it was pitched at that time, and that the concept had no future. Fortunately, a predecessor of Cengage had the foresight to see that the idea was merely

ahead of its time. While much has changed in the financial world over these years, these

tools have remained an important force in our economy. Yes, I know that some say

derivatives, particularly mortgage securitization and credit default swaps, contributed to

our current economic problems. I would only counter that by noting that fire has also

contributed to death and destruction but we use it safely and productively every day.

We do so because we are informed about the costs, risks, and benefits. And that is the

purpose of this book.

Students who take a course based on this book will consist of three types: those who

will never use derivatives, those who will someday be dealers and therefore will provide

derivative products, and those who will use derivatives to solve problems and therefore

will be the end users who buy derivatives. For those who will never use derivatives, this

book will be valuable in the same sense that it is important to know such things as the

seven warning signs of cancer regardless of whether you ever have cancer. Being informed makes us better human beings and in particular, business decision makers. Students who become dealers will obviously need to know a lot more than is in this book. It

is our hope that the book will be a stepping stone toward an exciting career. For those

who become end users, the book will give the foundations that will make them smart

shoppers in the market for derivatives. It will teach them the importance of understanding the proper use of derivatives and how they are valued.

From a personal perspective, I am celebrating close to a quarter-century as an expert

in derivatives. My decision to go into this area is one I have never regretted. I know it

was probably just luck that I chose a field that would really take off. It was a bet I never

hedged and in that sense, I took a risk without properly assessing the possible consequences. We should never make decisions that way, but sometimes we get away with it.

I feel lucky in a way most people cannot imagine.

I am also lucky to have had strong support from my wife Jan, who knows this is what

I do but doesn’t really want to know any more about it than that. I don’t blame her. We

derivatives people sometimes seem off in our own little world of geekiness. Fortunately,

there are people who still love us.

ROBERT BROOKS

As we are now well into the twenty-first century and have experienced both periods of

financial calm as well as financial turmoil, the need for quality content on financial derivatives and risk management has never been greater. It is a privilege for me to collaborate with Don on such a successful book. My goal continues to be aiding students in

understanding how to make financial derivatives theory work in practice. The financial

xvi

Preface

xvii

derivatives and risk management subject area is a rapidly changing field that provides

those who learn to navigate its complexities the opportunity for a rewarding career. By

straddling the fence between the academic community and the practitioner community, I

seek to continually enhance our book’s quest to equip the next generation of financial

risk managers.

I would like to encourage college students and others reading this book to consider a

rewarding career in this field of study. From serving in a corporation, a financial services

firm, or an investment management company, the ability to provide wise financial counsel leads to a fulfilling career. Knowing that you have contributed to protecting your firm

from inappropriate financial risk or investing in an unsuitable strategy for your clients is

both financially rewarding as well as personally gratifying.

I am deeply grateful to my wife Ann and my children Joshua, Stephen, Paul, Rebekah,

Phillips, and Rachael. At the time of this writing, four children are teenagers providing

constant opportunities to refine teaching financial principles as well as apply risk management in practice. My family is a constant source of encouragement and they are all

very supportive of my activities related to this book.

DON AND BOB

We would like to thank Mike Reynolds, Executive Editor, Finance, for his continuing

support over the years; and Elizabeth Lowry, our Development Editor, for solving in a

timely manner every problem that arose during the project. We would also like to thank

Marketing Manager Nathan Anderson, to whose expertise we trust the future sales of the

book; and Abigail Greshik, our organized and detail-oriented Content Production Manager for the text.

Also, we would like to thank all those people who reviewed the 7th edition to make

the 8th edition even stronger:

Karan Bhanot, University of Texas at San Antonio

David Enke, The University of Tulsa

Merlyn Foo, Athabasca University

Christine Jiang, University of Memphis

D.K. Malhotra, Philadelphia University

Gautam Vora, University of New Mexico

A special thanks is due to John Olagues, Jim Binder, Stan Leimer, Regina Millison,

and Pratik Dhar for comments, answers, and assistance. Also, we would like to thank

all of the people over the years who have both taught from this book and learned from

it. They have, all along, generously provided constructive comments and corrections.

After twenty years, this list of names is too long to print without leaving someone out.

So to all of you unnamed heroes, we express our thanks.

We always used to feel that the errors in a book should, through attrition over the

years, disappear. We have learned otherwise. Although no one wants errors to remain,

if you ever find a book in its eighth edition without any errors, you can be assured that

the author is simply correcting old material and not keeping the book up-to-date. With a

field as dynamic as derivatives, extensive changes are inevitable. Despite Herculean efforts to cleanse this work, there are surely some errors remaining. We feel fairly confident, however, that they are not errors of fact, but merely accidental oversights and

perhaps typos that just did not get caught as we read and re-read the material. Unlike

most authors, who we think would rather hide known errors, we maintain a list of such

xviii

Preface

errors on this book’s Web site. (That’s http://www.cengage.com/finance/chance for the

general site that links you to the error page.) If you see something that does not make

sense, check the Web address mentioned above and see if it’s there. If not, then send us

an email by using the Contact Us form on the book’s Web site.

Or just send us an email anyway, whether or not you are students or faculty. Tell us

what you like or don’t like about the book. We would love to hear from you.

Don M. Chance, dchance@lsu.edu

William H. Wright, Jr. Endowed Chair for Financial Services

Department of Finance

2163 Patrick F. Taylor Hall

E. J. Ourso College of Business

Louisiana State University

Baton Rouge, LA 70803

Robert Brooks, rbrooks@cba.ua.edu

Wallace D. Malone, Jr. Endowed Chair of Financial Management

Department of Finance

The University of Alabama

200 Alston Hall, Box 870224

Tuscaloosa, AL 35487

March 2009

We view risk as an asset.

Noel Donohoe, Goldman Sachs

Risk, July 2004, p. 42

This page intentionally left blank

CHAPTER

1

Introduction

It is only by risking our persons from one hour to another that we live at all.

William James

The Will to Believe, 1897

CHAPTER

OBJECTIVES

• Provide brief

introductions to the

different types of

derivatives: options,

forward contracts,

futures contracts, and

swaps

• Reacquaint you with

the concepts of risk

preference, short

selling, repurchase

agreements, the riskreturn relationship,

and market efficiency

• Define the important

concept of theoretical

fair value, which will

be used throughout

the book

• Explain the

relationship between

spot and derivative

markets through the

mechanisms of

arbitrage, storage, and

delivery

• Identify the role that

derivative markets

play through their

four main advantages

• Address some

criticisms of

derivatives

In the course of running a business, decisions are made in the presence of risk. A decision

maker can confront one of two types of risk. Some risks are related to the underlying nature of the business and deal with such matters as the uncertainty of future sales or the

cost of inputs. These risks are called business risks. Most businesses are accustomed to

accepting business risks. Indeed, the acceptance of business risks and its potential rewards

are the foundations of capitalism. Another class of risks deals with uncertainties such

as interest rates, exchange rates, stock prices, and commodity prices. These are called

financial risks.

Financial risks are a different matter. The paralyzing uncertainty of volatile interest

rates can cripple the ability of a firm to acquire financing at a reasonable cost, which enable it to provide its products and services. Firms that operate in foreign markets can have

excellent sales performance offset if their own currency is strong. Companies that use raw

materials can find it difficult to obtain their basic inputs at a price that will permit profitability. Managers of stock portfolios deal on a day-to-day basis with wildly unpredictable

and sometimes seemingly irrational financial markets.

Although our financial system is replete with risk, it also provides a means of dealing

with risk in the form of derivatives. Derivatives are financial instruments whose returns

are derived from those of other financial instruments. That is, their performance depends

on how other financial instruments perform. Derivatives serve a valuable purpose in providing a means of managing financial risk. By using derivatives, companies and individuals can transfer, for a price, any undesired risk to other parties who either have risks

that offset or want to assume that risk.

Although derivatives have been around in some form for centuries, their growth has

accelerated rapidly during the last several decades. They are now widely used by corporations, financial institutions, professional investors, and individuals. Certain types of derivatives are traded actively in public markets, similar to the stock exchanges with which

you are probably already somewhat familiar. The vast majority of derivatives, however, are

created in private transactions in over-the-counter markets. Just as a corporation may buy

a tract of land for the purpose of ultimately putting up a factory, so may it also engage in a

derivatives transaction. In neither case is the existence or amount of the transaction easy

for outsiders to determine. Nonetheless, we have fairly accurate data on the amount of derivatives activity in public markets and reasonably accurate data, based on surveys, on the

amount of derivatives activity in private markets. We shall explore the public market data

in later chapters. If you need to be convinced that derivatives are worth studying, consider

this: The Bank for International Settlements of Basel, Switzerland, estimated that at the end

of 2007, over-the-counter derivatives contracts outstanding worldwide covered underlying

assets of over $596 trillion. In comparison, gross domestic product in the United States at

1

2

Chapter 1

Introduction

the end of 2007 was about $15 trillion. As we shall see later, measuring the derivatives

market this way can give a false impression of the size of the market. Nonetheless, the

market value of these contracts totals about $9.1 trillion, making the derivatives market a

sizable force in the global economy.

This book is an introductory treatment of derivatives. Derivatives can be based on

real assets, which are physical assets and include agricultural commodities, metals, and

sources of energy. Although a few of these will come up from time to time in this book,

our focus will be directed toward derivatives on financial assets, which are stocks,

bonds/loans, and currencies. In this book you will learn about the characteristics of the

institutions and markets where these instruments trade, the manner in which derivative

prices are determined, and the strategies in which they are used. Toward the end of

the book, we will cover the way in which derivatives are used to manage the risk of a

company.

This chapter welcomes you to the world of derivatives and provides an introduction to

or a review of some financial concepts that you will need in order to understand derivatives. Let us begin by exploring the derivatives markets more closely and defining what we

mean by these types of instruments.

DERIVATIVE MARKETS AND INSTRUMENTS

An asset is an item of ownership having positive monetary value. A liability is an item of

ownership having negative monetary value. The term “instrument” is used to describe either assets or liabilities. Instrument is the more general term, vague enough to encompass

the underlying asset or liability of derivative contracts. A contract is an enforceable legal

agreement. A security is a tradeable instrument representing a claim on a group of assets.

In the markets for assets, purchases and sales require that the underlying asset be delivered either immediately or shortly thereafter. Payment usually is made immediately,

although credit arrangements are sometimes used. Because of these characteristics, we

refer to these markets as cash markets or spot markets. The sale is made, the payment

is remitted, and the good or security is delivered. In other situations, the good or security

is to be delivered at a later date. Still other types of arrangements allow the buyer or

seller to choose whether or not to go through with the sale. These types of arrangements

are conducted in derivative markets.

In contrast to the market for assets, derivative markets are markets for contractual

instruments whose performance is determined by the way in which another instrument

or asset performs. Notice that we referred to derivatives as contracts. Like all contracts,

they are agreements between two parties—a buyer and a seller—in which each party does

something for the other. These contracts have a price, and buyers try to buy as cheaply

as possible while sellers try to sell as dearly as possible. This section briefly introduces

the various types of derivative contracts: options, forward contracts, futures contracts,

and swaps and related derivatives.

Options

An option is a contract between two parties—a buyer and a seller—that gives the buyer

the right, but not the obligation, to purchase or sell something at a later date at a price

agreed upon today.

The option buyer pays the seller a sum of money called the price or premium. The

option seller stands ready to sell or buy according to the contract terms if and when

the buyer so desires. An option to buy something is referred to as a call; an option to

sell something is called a put. Although options trade in organized markets, a large

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