Sách Introduction to derivatives and risk management 8e by chance

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 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,
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,
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


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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