Derivatives

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Foreword xvii

Preface xix

Acknowledgments xxi

About the CFA Institute Investment Series xxiii

Chapter 1 Derivative Markets and Instruments 1

Learning Outcomes 1

1. Derivatives: Introduction, Definitions, and Uses 1

2. The Structure of Derivative Markets 5

2.1. Exchange-Traded Derivatives Markets 6

2.2. Over-the-Counter Derivatives Markets 8

3. Types of Derivatives: Introduction, Forward Contracts 10

3.1. Forward Commitments 10

4. Types of Derivatives: Futures 14

5. Types of Derivatives: Swaps 18

6. Contingent Claims: Options 22

6.1. Options 22

7. Contingent Claims: Credit Derivatives 30

8. Types of Derivatives: Asset-Backed Securities and Hybrids 33

8.1. Hybrids 35

9. Derivatives Underlyings 36

9.1. Equities 36

9.2. Fixed-Income Instruments and Interest Rates 36

9.3. Currencies 37

9.4. Commodities 37

9.5. Credit 37

9.6. Other 37

10. The Purposes and Benefits of Derivatives 39

10.1. Risk Allocation, Transfer, and Management 40

10.2. Information Discovery 41

10.3. Operational Advantages 41

10.4. Market Efficiency 42

11. Criticisms and Misuses of Derivatives 42

11.1. Speculation and Gambling 43

11.2. Destabilization and Systemic Risk 43

12. Elementary Principles of Derivative Pricing 45

12.1. Storage 46

12.2. Arbitrage 47

Summary 52

Problems 54

Chapter 2 Basics of Derivative Pricing and Valuation 61

Learning Outcomes 61

1. Introduction 62

2. Basic Derivative Concepts, Pricing the Underlying 62

2.1. Basic Derivative Concepts 62

2.2. Pricing the Underlying 64

3. The Principle of Arbitrage 68

3.1. The (In)Frequency of Arbitrage Opportunities 69

3.2. Arbitrage and Derivatives 69

3.3. Arbitrage and Replication 70

3.4. Risk Aversion, Risk Neutrality, and Arbitrage-Free Pricing 71

3.5. Limits to Arbitrage 72

4. Pricing and Valuation of Forward Contracts: Pricing vs. Valuation; Expiration; Initiation 74

4.1. Pricing and Valuation of Forward Commitments 75

5. Pricing and Valuation of Forward Contracts: Between Initiation and Expiration; Forward Rate Agreements 79

5.1. A Word about Forward Contracts on Interest Rates 80

6. Pricing and Valuation of Futures Contracts 82

7. Pricing and Valuation of Swap Contracts 84

8. Pricing and Valuation of Options 87

8.1. European Option Pricing 88

9. Lower Limits for Prices of European Options 94

10. Put–Call Parity, Put–Call–Forward Parity 97

10.1. Put–Call–Forward Parity 101

11. Binomial Valuation of Options 103

12. American Option Pricing 107

Summary 110

Problems 111

Chapter 3 Pricing and Valuation of Forward Commitments 117

Learning Outcomes 117

1. Introduction to Pricing and Valuation of Forward Commitments 117

1.1. Principles of Arbitrage-Free Pricing and Valuation of Forward Commitments 118

1.2. Pricing and Valuing Generic Forward and Futures Contracts 119

2. Carry Arbitrage 124

2.1. Carry Arbitrage Model When There Are No Underlying Cash Flows 124

2.2. Carry Arbitrage Model When Underlying Has Cash Flows 131

3. Pricing Equity Forwards and Futures 135

3.1. Equity Forward and Futures Contracts 135

3.2. Interest Rate Forward and Futures Contracts 138

4. Pricing Fixed-Income Forward and Futures Contracts 147

4.1. Comparing Forward and Futures Contracts 153

5. Pricing and Valuing Swap Contracts 154

5.1. Interest Rate Swap Contracts 156

6. Pricing and Valuing Currency Swap Contracts 163

7. Pricing and Valuing Equity Swap Contracts 171

Summary 176

Problems 179

Chapter 4 Valuation of Contingent Claims 187

Learning Outcomes 187

1. Introduction and Principles of a No- Arbitrage Approach to Valuation 188

1.1. Principles of a No- Arbitrage Approach to Valuation 188

2. Binomial Option Valuation Model 190

3. One- Period Binomial Model 192

4. Binomial Model: Two- Period (Call Options) 199

5. Binomial Model: Two- Period (Put Options) 203

6. Binomial Model: Two- Period (Role of Dividends & Comprehensive Example) 207

7. Interest Rate Options & Multiperiod Model 213

7.1. Multiperiod Model 215

8. Black–Scholes–Merton (BSM) Option Valuation Model, Introduction and Assumptions of the BSM Model 216

8.1. Introductory Material 216

8.2. Assumptions of the BSM Model 216

9. BSM Model: Components 218

10. BSM Model: Carry Benefits and Applications 222

11. Black Option Valuation Model and European Options on Futures 226

11.1. European Options on Futures 226

12. Interest Rate Options 228

13. Swaptions 232

14. Option Greeks and Implied Volatility: Delta 234

14.1. Delta 235

15. Gamma 238

16. Theta 241

17. Vega 242

18. Rho 243

19. Implied Volatility 244

Summary 247

Problems 249

Chapter 5 Credit Default Swaps 255

Learning Outcomes 255

1. Introduction 255

2. Basic Definitions and Concepts 255

2.1. Types of CDS 257

3. Important Features of CDS Markets and Instruments, Credit and Succession Events, and Settlement Proposals 258

3.1. Credit and Succession Events 260

3.2. Settlement Protocols 261

3.3. CDS Index Products 262

3.4. Market Characteristics 264

4. Basics of Valuation and Pricing 265

4.1. Basic Pricing Concepts 265

4.2. The Credit Curve and CDS Pricing Conventions 268

4.3. CDS Pricing Conventions 269

4.4. Valuation Changes in CDS during Their Lives 270

4.5. Monetizing Gains and Losses 271

5. Applications of CDS 272

5.1. Managing Credit Exposures 273

6. Valuation Differences and Basis Trading 277

Summary 279

Problems 280

Chapter 6 Introduction to Commodities and Commodity Derivatives 285

Learning Outcomes 285

1. Introduction 285

2. Commodity Sectors 286

2.1. Commodity Sectors 288

3. Life Cycle of Commodities 290

3.1. Energy 291

3.2. Industrial/Precious Metals 292

3.3. Livestock 294

3.4. Grains 295

3.5. Softs 295

4. Valuation of Commodities 296

5. Commodities Futures Markets: Participants 298

5.1. Futures Market Participants 298

6. Commodity Spot and Futures Pricing 302

7. Theories of Futures Returns 306

7.1. Theories of Futures Returns 306

8. Components of Futures Returns 313

9. Contango, Backwardation, and the Roll Return 317

10. Commodity Swaps 320

10.1. Total Return Swap 322

10.2. Basis Swap 323

10.3. Variance Swaps and Volatility Swaps 323

11. Commodity Indexes 324

11.1. S&p Gsci 327

11.2. Bloomberg Commodity Index 327

11.3. Deutsche Bank Liquid Commodity Index 327

11.4. Thomson Reuters/CoreCommodity CRB Index 327

11.5. Rogers International Commodity Index 328

11.6. Rebalancing Frequency 328

11.7. Commodity Index Summary 328

Summary 329

References 331

Problems 331

Chapter 7 Currency Management: An Introduction 339

Learning Outcomes 339

1. Introduction 340

2. Review of Foreign Exchange Concepts 340

2.1. Spot Markets 341

2.2. Forward Markets 343

2.3. FX Swap Markets 346

2.4. Currency Options 347

3. Currency Risk and Portfolio Risk and Return 347

3.1. Return Decomposition 347

3.2. Volatility Decomposition 350

4. Strategic Decisions in Currency Management: Overview 353

4.1. The Investment Policy Statement 354

4.2. The Portfolio Optimization Problem 354

4.3. Choice of Currency Exposures 356

5. Strategic Decisions in Currency Management: Spectrum of Currency Risk Management Strategies 359

5.1. Passive Hedging 359

5.2. Discretionary Hedging 359

5.3. Active Currency Management 360

5.4. Currency Overlay 360

6. Strategic Decisions in Currency Management: Formulating a Currency Management Program 363

7. Active Currency Management: Based on Economic Fundamentals, Technical Analysis, and the Carry Trade 365

7.1. Active Currency Management Based on Economic Fundamentals 365

7.2. Active Currency Management Based on Technical Analysis 367

7.3. Active Currency Management Based on the Carry Trade 368

8. Active Currency Management: Based on Volatility Trading 370

9. Currency Management Tools: Forward Contracts, FX Swaps, and Currency Options 375

9.1. Forward Contracts 376

9.2. Currency Options 383

10. Currency Management Strategies 385

10.1. Over- /Under- Hedging Using Forward Contracts 386

10.2. Protective Put Using OTM Options 387

10.3. Risk Reversal (or Collar) 387

10.4. Put Spread 388

10.5. Seagull Spread 388

10.6. Exotic Options 389

10.7. Section Summary 390

11. Hedging Multiple Foreign Currencies 393

11.1. Cross Hedges and Macro Hedges 393

11.2. Minimum- Variance Hedge Ratio 397

11.3. Basis Risk 397

12. Currency Management Tools and Strategies: A Summary 400

13. Currency Management for Emerging Market Currencies 404

13.1. Special Considerations in Managing Emerging Market Currency Exposures 404

13.2. Non- Deliverable Forwards 406

Summary 407

References 409

Problems 410

Chapter 8 Options Strategies 421

Learning Outcomes 421

1. Introduction 422

2. Position Equivalencies 422

2.1. Synthetic Forward Position 423

2.2. Synthetic Put and Call 426

3. Covered Calls and Protective Puts 428

3.1. Investment Objectives of Covered Calls 428

4. Investment Objectives of Protective Puts 436

4.1. Loss Protection/Upside Preservation 437

4.2. Profit and Loss at Expiration 439

5. Equivalence to Long Asset/Short Forward Position 441

5.1. Writing Puts 442

6. Risk Reduction Using Covered Calls and Protective Puts 444

6.1. Covered Calls 445

6.2. Protective Puts 445

6.3. Buying Calls and Writing Puts on a Short Position 445

7. Spreads and Combinations 448

7.1. Bull Spreads and Bear Spreads 448

8. Straddle 457

8.1. Collars 460

8.2. Calendar Spread 463

9. Implied Volatility and Volatility Skew 465

10. Investment Objectives and Strategy Selection 469

10.1. The Necessity of Setting an Objective 469

10.2. Criteria for Identifying Appropriate Option Strategies 470

11. Uses of Options in Portfolio Management 472

11.1. Covered Call Writing 472

11.2. Put Writing 474

11.3. Long Straddle 475

11.4. Collar 478

11.5. Calendar Spread 478

12. Hedging an Expected Increase in Equity Market Volatility 480

12.1. Establishing or Modifying Equity Risk Exposure 482

Summary 485

Problems 487

Chapter 9 Swaps, Forwards, and Futures Strategies 493

Learning Outcomes 493

1. Managing Interest Rate Risk with Swaps 493

1.1. Changing Risk Exposures with Swaps, Futures, and Forwards 494

2. Managing Interest Rate Risk with Forwards, Futures, and Fixed- Income Futures 498

2.1. Fixed- Income Futures 500

3. Managing Currency Exposure 506

3.1. Currency Swaps 506

3.2. Currency Forwards and Futures 510

4. Managing Equity Risk 511

4.1. Equity Swaps 511

4.2. Equity Forwards and Futures 513

4.3. Cash Equitization 516

5. Volatility Derivatives: Futures and Options 517

5.1. Volatility Futures and Options 518

6. Volatility Derivatives: Variance Swaps 520

7. Using Derivatives to Manage Equity Exposure and Tracking Error 523

7.1. Cash Equitization 524

8. Using Derivatives in Asset Allocation 525

8.1. Changing Allocations between Asset Classes Using Futures 525

8.2. Rebalancing an Asset Allocation Using Futures 528

8.3. Changing Allocations between Asset Classes Using Swaps 529

9. Using Derivatives to Infer Market Expectations 531

9.1. Using Fed Funds Futures to Infer the Expected Average Federal Funds Rate 531

9.2. Inferring Market Expectations 533

Summary 534

Problems 535

Chapter 10 Introduction to Risk Management 543

Learning Outcomes 543

1. Introduction 543

2. The Risk Management Process 545

3. The Risk Management Framework 547

4. Risk Governance − An Enterprise View 554

4.1. An Enterprise View of Risk Governance 554

5. Risk Tolerance 556

6. Risk Budgeting 558

7. Identification of Risk − Financial and Non- Financial Risk 561

7.1. Financial Risks 561

7.2. Non- Financial Risks 563

8. Identification of Risk − Interactions Between Risks 567

9. Measuring and Modifying Risk − Drivers and Metrics 571

9.1. Drivers 571

9.2. Metrics 572

10. Methods of Risk Modification − Prevention, Avoidance, and Acceptance 576

10.1. Risk Prevention and Avoidance 577

10.2. Risk Acceptance: Self- Insurance and Diversification 578

11. Methods of Risk Modification − Transfer, Shifting, Choosing a Method for Modifying 579

11.1. Risk Shifting 581

11.2. How to Choose Which Method for Modifying Risk 583

Summary 585

Problems 587

Chapter 11 Measuring and Managing Market Risk 591

Learning Outcomes 591

1. Introduction 592

1.1. Understanding Value at Risk 592

2. Estimating VaR 596

3. The Parametric Method of VaR Estimation 598

4. The Historical Simulation Method of VaR Estimation 602

5. The Monte Carlo Simulation Method of VaR Estimation 605

6. Advantages and Limitations of VaR and Extensions of VaR 608

6.1. Advantages of VaR 608

6.2. Limitations of VaR 609

6.3. Extensions of VaR 611

7. Other Key Risk Measures − Sensitivity Risk Measures; Sensitivity Risk Measures 613

7.1. Sensitivity Risk Measures 614

8. Scenario Risk Measures 618

8.1. Historical Scenarios 618

8.2. Hypothetical Scenarios 620

9. Sensitivity and Scenario Risk Measures and VaR 623

9.1. Advantages and Limitations of Sensitivity Risk Measures and Scenario Risk Measures 624

10. Using Constraints in Market Risk Management 627

10.1. Risk Budgeting 628

10.2. Position Limits 629

10.3. Scenario Limits 629

10.4. Stop- Loss Limits 630

10.5. Risk Measures and Capital Allocation 630

11. Applications of Risk Measures 632

11.1. Market Participants and the Different Risk Measures They Use 632

12. Pension Funds and Insurers 637

12.1. Insurers 639

Summary 641

Reference 643

Problems 643

Chapter 12 Risk Management for Individuals 651

Learning Outcomes 651

1. Introduction 652

2. Human Capital, Financial Capital, and Economic Net Worth 652

2.1. Human Capital 653

2.2. Financial Capital 656

2.3. Economic Net Worth 661

3. A Framework for Individual Risk Management 661

3.1. The Risk Management Strategy for Individuals 661

3.2. Financial Stages of Life 662

4. The Individual Balance Sheet 665

4.1. Traditional Balance Sheet 665

4.2. Economic (Holistic) Balance Sheet 666

4.3. Changes in Economic Net Worth 668

5. Individual Risk Exposures 671

5.1. Earnings Risk 671

5.2. Premature Death Risk 672

5.3. Longevity Risk 673

5.4. Property Risk 674

5.5. Liability Risk 674

5.6. Health Risk 675

6. Life Insurance: Uses, Types, and Elements 676

6.1. Life Insurance 677

7. Life Insurance: Pricing, Policy Cost Comparison, and Determining Amount Needed 680

7.1. Mortality Expectations 680

7.2. Calculation of the Net Premium and Gross Premium 682

7.3. Cash Values and Policy Reserves 684

7.4. Consumer Comparisons of Life Insurance Costs 685

7.5. How Much Life Insurance Does One Need? 687

8. Other Types of Insurance 688

8.1. Property Insurance 690

8.2. Health/Medical Insurance 692

8.3. Liability Insurance 693

8.4. Other Types of Insurance 693

9. Annuities: Types, Structure, and Classification 694

9.1. Parties to an Annuity Contract 694

9.2. Classification of Annuities 695

10. Annuities: Advantages and Disadvantages of Fixed and Variable Annuities 698

10.1. Volatility of Benefit Amount 698

10.2. Flexibility 699

10.3. Future Market Expectations 699

10.4. Fees 700

10.5. Inflation Concerns 700

10.6. Payout Methods 700

10.7. Annuity Benefit Taxation 701

10.8. Appropriateness of Annuities 701

11. Risk Management Implementation: Determining the Optimal Strategy and Case Analysis 703

11.1. Determining the Optimal Risk Management Strategy 703

11.2. Analyzing an Insurance Program 705

12. The Effect of Human Capital on Asset Allocation and Risk Reduction 712

12.1. Asset Allocation and Risk Reduction 716

Summary 718

References 720

Problems 720

Chapter 13 Case Study in Risk Management: Private Wealth 727

Learning Outcomes 727

1. Introduction and Case Background 727

1.1. Background of Eurolandia 728

1.2. The Schmitt Family in Their Early Career Stage 730

Summary 772

Problems 773

Chapter 14 Integrated Cases in Risk Management: Institutional 777

Learning Outcomes 777

1. Introduction 777

2. Financial Risks Faced by Institutional Investors 778

References 831

Glossary 833

About the Editors and Authors 845

Index 849