Contents
About the Authors xix
Preface xxi
Acknowledgments xxv
Notation xxvii
PART I
INVESTMENT ENVIRONMENT
1 Bonds and Money-Market Instruments 3
1.1 Bonds 3
1.1.1 General Characteristics of Bonds 3
1.1.2 Bonds by Issuers 17
1.2 Money-Market Instruments 25
1.2.1 Definition 25
1.2.2 The Role of the Central Bank 25
1.2.3 T-Bills 26
1.2.4 Certificates of Deposit 28
1.2.5 Bankers’ Acceptances 29
1.2.6 Commercial Papers 29
1.2.7 Interbank Deposits 30
1.2.8 Repo and Reverse Repo Market Instruments 30
1.3 End of Chapter Summary 32
1.4 References and Further Reading 33
1.4.1 Books and Papers 33
1.4.2 Websites and Others 33
1.5 Problems 34
1.5.1 Problems on Bonds 34
1.5.2 Problems on Money-Market Instruments 36
1.6 Appendix: Sector Breakdown of the Euro, the UK and the Japan
Corporate Bond Markets 37
2 Bond Prices and Yields 41
2.1 Introduction to Bond Pricing 41
2.2 Present Value Formula 43
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2.2.1 Time-Value of Money 43
2.2.2 The Mathematics of Discounting 43
2.2.3 Nominal versus Real Interest Rates 45
2.2.4 Time Basis and Compounding
Frequency Conventions 46
2.2.5 Continuous Compounding 47
2.3 Taxonomy of Rates 49
2.3.1 Coupon Rate and Current Yield 49
2.3.2 Yield to Maturity 49
2.3.3 Spot Zero-Coupon (or Discount) Rate 51
2.3.4 Forward Rates 52
2.3.5 Bond Par Yield 54
2.4 End of Chapter Summary 54
2.5 References and Further Reading 54
2.6 Problems 55
PART II
TERM STRUCTURE OF INTEREST RATES
3 Empirical Properties and Classical Theories of the Term Structure 63
3.1 Definition and Properties of the Term Structure 63
3.1.1 What Kind of Shape Can It Take? 65
3.1.2 How Does It Evolve over Time? 68
3.2 Classical Theories of the Term Structure 81
3.2.1 The Pure Expectations Theory 82
3.2.2 The Pure Risk Premium Theory 83
3.2.3 The Market Segmentation Theory 85
3.2.4 The Biased Expectations Theory:
An Integrated Approach 86
3.2.5 Illustration and Empirical Validation 86
3.2.6 Summary and Extensions 87
3.3 End of Chapter Summary 88
3.4 References and Further Reading 89
3.4.1 On the Empirical Behavior of the Yield Curve 89
3.4.2 On the Principal Component Analysis
of the Yield Curve 90
3.4.3 On the Classical Theories of the Term Structure
of Interest Rates 90
3.5 Problems 91
4 Deriving the Zero-Coupon Yield Curve 96
4.1 Deriving the Nondefault Treasury Zero-Coupon Yield Curve 96
4.1.1 How to Select a Basket of Bonds? 96
4.1.2 Direct Methods 97
4.1.3 Indirect Methods 103
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4.2 Deriving the Interbank Zero-Coupon Rate Curve 130
4.2.1 How to Select the Basket of Instruments? 130
4.2.2 Interpolation Methods 132
4.2.3 Least Squares Methods Based on Rates 132
4.2.4 Least Squares Methods Based on Prices 133
4.3 Deriving Credit Spread Term Structures 136
4.3.1 Disjoint Methods 136
4.3.2 Joint Methods 137
4.4 End of Chapter Summary 142
4.5 References and Further Reading 144
4.6 Problems 146
4.7 Appendix: A Useful Modified Newton’s Algorithm 155
PART III
HEDGING INTEREST-RATE RISK
5 Hedging Interest-Rate Risk with Duration 163
5.1 Basics of Interest-Rate Risk: Qualitative Insights 163
5.1.1 The Five Theorems of Bond Pricing 163
5.1.2 Reinvestment Risk 164
5.1.3 Capital Gain Risk 165
5.1.4 Qualifying Interest-Rate Risk 166
5.2 Hedging with Duration 167
5.2.1 Using a One-Order Taylor Expansion 167
5.2.2 Duration, $Duration and Modified Duration 170
5.2.3 How to Hedge in Practice? 173
5.3 End of Chapter Summary 175
5.4 References and Further Reading 176
5.4.1 Books 176
5.4.2 Papers 176
5.5 Problems 177
6 Beyond Duration 182
6.1 Relaxing the Assumption of a Small Shift 182
6.1.1 Using a Second-Order Taylor Expansion 182
6.1.2 Properties of Convexity 185
6.1.3 Hedging Method 187
6.2 Relaxing the Assumption of a Parallel Shift 188
6.2.1 A Common Principle 188
6.2.2 Regrouping Risk Factors through
a Principal Component Analysis 192
6.2.3 Hedging Using a Three-Factor Model
of the Yield Curve 195
6.3 End of Chapter Summary 199
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6.4 References and Further Reading 200
6.5 Problems 201
PART IV
INVESTMENT STRATEGIES
7 Passive Fixed-Income Portfolio Management 213
7.1 Straightforward Replication 213
7.2 Replication by Stratified Sampling 214
7.3 Tracking-Error Minimization 216
7.3.1 Optimization Procedure 216
7.3.2 Bond Return Covariance Matrix Estimation 217
7.4 Factor-Based Replication 226
7.5 Derivatives-Based Replication 229
7.6 Pros and Cons of Stratified Sampling versus
Tracking-Error Minimization 230
7.7 End of Chapter Summary 230
7.8 References and Further Reading 231
7.8.1 Books and Papers 231
7.8.2 Websites 231
7.9 Problems 231
8 Active Fixed-Income Portfolio Management 233
8.1 Market Timing: Trading on Interest-Rate Predictions 233
8.1.1 Timing Bets on No Change in the Yield Curve
or “Riding the Yield Curve” 234
8.1.2 Timing Bets on Interest-Rate Level 236
8.1.3 Timing Bets on Specific Changes in the
Yield Curve 238
8.1.4 Scenario Analysis 251
8.1.5 Active Fixed-Income Style Allocation Decisions 255
8.2 Trading on Market Inefficiencies 268
8.2.1 Trading within a Given Market: The Bond
Relative Value Analysis 269
8.2.2 Trading across Markets: Spread
and Convergence Trades 276
8.3 End of Chapter Summary 282
8.4 References and Further Reading 283
8.4.1 On Active Fixed-Income Strategies 283
8.4.2 On Active Asset Allocation Decisions 284
8.4.3 Others 286
8.5 Problems 286
9 Performance Measurement on Fixed-Income Portfolios 293
9.1 Return Measures 293
9.1.1 Arithmetic Rate of Return 293
9.1.2 Geometric Rate of Return 294
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9.2 Risk-Adjusted Performance Evaluation 295
9.2.1 Absolute Risk-Adjusted Performance Evaluation 296
9.2.2 Relative Risk-Adjusted Performance Evaluation 299
9.3 Application of Style Analysis to Performance Evaluation
of Bond Portfolio Managers: An Example 309
9.3.1 Alpha Analysis 310
9.3.2 Passive Versus Active Managers 313
9.4 End of Chapter Summary 314
9.5 References and Further Reading 315
9.5.1 Books and Papers 315
9.5.2 Websites 316
9.6 Problems 316
PART V
SWAPS AND FUTURES
10 Swaps 325
10.1 Description of Swaps 325
10.1.1 Definition 325
10.1.2 Terminology and Conventions 325
10.2 Pricing and Market Quotes 326
10.2.1 Pricing of Swaps 326
10.2.2 Market Quotes 333
10.3 Uses of Swaps 334
10.3.1 Optimizing the Financial Conditions of a Debt 335
10.3.2 Converting the Financial Conditions of a Debt 336
10.3.3 Creating New Assets Using Swaps 337
10.3.4 Hedging Interest-Rate Risk Using Swaps 339
10.4 Nonplain Vanilla Swaps 342
10.4.1 Accrediting, Amortizing and Roller Coaster Swaps 342
10.4.2 Basis Swap 343
10.4.3 Constant Maturity Swap and Constant
Maturity Treasury Swap 343
10.4.4 Forward-Starting Swap 344
10.4.5 Inflation-Linked Swap 344
10.4.6 Libor in Arrears Swap 344
10.4.7 Yield-Curve Swap 345
10.4.8 Zero-Coupon Swap 345
10.5 End of Chapter Summary 346
10.6 References and Further Reading 346
10.6.1 Books and Papers 346
10.6.2 Websites 347
10.7 Problems 347
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11 Forwards and Futures 353
11.1 Definition 353
11.2 Terminology, Conventions and Market Quotes 354
11.2.1 Terminology and Conventions 354
11.2.2 Quotes 356
11.3 Margin Requirements and the Role of the Clearing House 358
11.4 Conversion Factor and the Cheapest-to-Deliver Bond 359
11.4.1 The Cheapest to Deliver on the Repartition Date 360
11.4.2 The Cheapest to Deliver before
the Repartition Date 361
11.5 Pricing of Forwards and Futures 362
11.5.1 Forward-Spot Parity or How to Price
a Forward Contract? 362
11.5.2 The Forward Contract Payoff 364
11.5.3 Relation between Forward and Futures Prices 365
11.6 Uses of Forwards and Futures 365
11.6.1 Pure Speculation with Leverage Effect 365
11.6.2 Fixing Today the Financial Conditions of a Loan
or Investment in the Future 366
11.6.3 Detecting Riskless Arbitrage Opportunities
Using Futures 367
11.6.4 Hedging Interest-Rate Risk Using Futures 368
11.7 End of Chapter Summary 370
11.8 References and Further Reading 371
11.8.1 Books and Papers 371
11.8.2 Websites of Futures Markets and of the Futures
Industry Association 371
11.9 Problems 372
11.10 Appendix: Forward and Futures Prices Are Identical
When Interest Rates Are Constant 375
PART VI
MODELING THE TERM STRUCTURE OF INTEREST RATES AND CREDIT SPREADS
12 Modeling the Yield Curve Dynamics 381
12.1 The Binomial Interest-Rate Tree Methodology 382
12.1.1 Building an Interest-Rate Tree 382
12.1.2 Calibrating an Interest-Rate Tree 384
12.2 Continuous-Time Models 387
12.2.1 Single-Factor Models 388
12.2.2 Multifactor Models 392
12.3 Arbitrage Models 396
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12.3.1 A Discrete-Time Example: Ho and Lee’s
Binomial Lattice 396
12.3.2 Arbitrage Models in Continuous Time 401
12.4 End of Chapter Summary 406
12.5 References and Further Reading 407
12.6 Problems 411
12.7 Appendix 1: The Hull and White Trinomial Lattice 413
12.7.1 Discretizing the Short Rate 413
12.7.2 Calibrating the Lattice to the Current
Spot Yield Curve 416
12.7.3 Option Pricing 419
12.8 Appendix 2: An Introduction to Stochastic
Processes in Continuous Time 420
12.8.1 Brownian Motion 420
12.8.2 Stochastic Integral 423
12.8.3 Stochastic Differential Equations (SDE) 425
12.8.4 Asset Price Process 426
12.8.5 Representation of Brownian Martingales 426
12.8.6 Continuous-Time Asset Pricing 427
12.8.7 Feynman–Kac Formula 431
12.8.8 Application to Equilibrium Models
of the Term Structure 432
13 Modeling the Credit Spreads Dynamics 437
13.1 Analyzing Credit Spreads 438
13.1.1 Ratings 438
13.1.2 Default Probability 440
13.1.3 The Severity of Default 441
13.2 Modeling Credit Spreads 441
13.2.1 Structural Models 442
13.2.2 Subsequent Models 446
13.2.3 Reduced-Form Models 448
13.2.4 Historical versus Risk-Adjusted
Probability of Default 450
13.3 End of Chapter Summary 452
13.4 References and Further Reading 453
13.4.1 Books and Papers 453
13.4.2 Websites 454
13.5 Problems 455
PART VII
PLAIN VANILLA OPTIONS AND MORE EXOTIC DERIVATIVES
14 Bonds with Embedded Options and Options on Bonds 459
14.1 Callable and Putable Bonds 459
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14.1.1 Institutional Aspects 459
14.1.2 Pricing 460
14.1.3 OAS Analysis 467
14.1.4 Effective Duration and Convexity 468
14.2 Convertible Bonds 470
14.2.1 Institutional Aspects 470
14.2.2 Valuation of Convertible Bonds 473
14.2.3 Convertible Arbitrage 479
14.3 Options on Bonds 482
14.3.1 Definition 482
14.3.2 Uses 483
14.3.3 Pricing 487
14.4 End of Chapter Summary 491
14.5 References and Further Reading 492
14.5.1 On Callable and Putable Bonds 492
14.5.2 On Convertible Bonds 492
14.5.3 On Options on Bonds 493
14.6 Problems 494
14.7 Appendix: Bond Option Prices in the Hull
and White (1990) Model 498
14.7.1 Call on Zero-Coupon Bond 499
14.7.2 Call on Coupon Bond 499
15 Options on Futures, Caps, Floors and Swaptions 500
15.1 Options on Futures 500
15.1.1 Definition and Terminology 500
15.1.2 Pricing and Hedging Options on Futures 502
15.1.3 Market Quotes 505
15.1.4 Uses of Futures Options 508
15.2 Caps, Floors and Collars 508
15.2.1 Definition and Terminology 508
15.2.2 Pricing and Hedging Caps, Floors and Collars 510
15.2.3 Market Quotes 514
15.2.4 Uses of Caps, Floors and Collars 516
15.3 Swaptions 520
15.3.1 Definition and Terminology 520
15.3.2 Pricing and Hedging Swaptions 521
15.3.3 Market Quotes 526
15.3.4 Uses of Swaptions 526
15.4 End of Chapter Summary 527
15.5 References and Further Reading 528
15.5.1 Books and Papers 528
15.5.2 Websites 529
15.6 Problems 529
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15.7 Appendix 1: Proof of the Cap and Floor
Formulas in the Black (1976) Model 534
15.8 Appendix 2: Proof of the Swaption Formula
in the Black (1976) Model 535
15.9 Appendix 3: Forward and Futures Option Prices Written on T-Bond
and Libor in the Hull and White (1990) Model 536
15.9.1 Options on Forward Contracts 536
15.9.2 Options on Futures Contracts 537
15.10 Appendix 4: Cap, Floor and Swaption Prices in the Hull
and White (1990) Model 539
15.10.1 Cap and Floor 539
15.10.2 Swaption 540
15.11 Appendix 5: Market Models (BGM/Jamshidian Approach) 541
15.11.1 Why Define New Variables? 541
15.11.2 Building New Variables 542
15.11.3 The Dynamics of L(t, θ) and K(t, t + θ) 543
15.11.4 Pricing of Caps 545
15.11.5 Calibration of the Model 546
16 Exotic Options and Credit Derivatives 548
16.1 Interest-Rate Exotic Options 548
16.1.1 Barrier Caps and Floors 548
16.1.2 Bounded Caps, Floors, Barrier Caps and Floors 550
16.1.3 Cancelable Swaps 551
16.1.4 Captions and Floortions 551
16.1.5 Choosercaps and Flexicaps-and-Floors 551
16.1.6 Contingent Premium Caps and Floors 553
16.1.7 Extendible Swaps 554
16.1.8 Incremental Fixed Swaps 554
16.1.9 Index Amortizing Bonds and Swaps 555
16.1.10 Marked-to-Market Caps 557
16.1.11 Moving Average Caps and Floors 557
16.1.12 N-Caps and Floors 558
16.1.13 Q-Caps and Floors 558
16.1.14 Range Accrual Swaps 559
16.1.15 Ratchet Caps and Floors 560
16.1.16 Reflex Caps and Floors 561
16.1.17 Rental Caps and Floors 562
16.1.18 Rolling Caps and Floors 562
16.1.19 Spread Options 563
16.1.20 Subsidized Swaps 563
16.1.21 Pricing and Hedging Interest-Rate Exotic Options 565
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16.2 Credit Derivatives 565
16.2.1 The Significance of Credit Derivatives 565
16.2.2 Types of Credit Derivatives 567
16.3 End of Chapter Summary 575
16.4 References and Further Reading 575
16.4.1 On Interest-Rate Exotic Options 575
16.4.2 On Credit Derivatives 576
16.4.3 On Numerical Methods (See the Appendix 2) 576
16.4.4 Websites and Others 577
16.5 Problems 577
16.6 Appendix 1: Pricing and Hedging Barrier Caps and Floors
in the Black Model 580
16.6.1 Barrier Cap Formulas 580
16.6.2 Barrier Floor Formulas 581
16.6.3 Barrier Cap and Floor Greeks 581
16.7 Appendix 2: Numerical Methods 583
16.7.1 Monte Carlo Simulations 583
16.7.2 Finite-Difference Methods 585
PART VIII
SECURITIZATION
17 Mortgage-Backed Securities 593
17.1 Description of MBSs 593
17.1.1 Definition 593
17.1.2 The Amortization Mechanism 593
17.1.3 The Prepayment Feature 596
17.1.4 Typology of MBS 596
17.2 Market Quotes and Pricing 598
17.2.1 Market Quotes 599
17.2.2 Pricing of MBS 600
17.3 End of Chapter Summary 603
17.4 References and Further Reading 604
17.4.1 Books and Papers 604
17.4.2 Websites 605
17.5 Problems 605
18 Asset-Backed Securities 607
18.1 Description of ABSs 607
18.1.1 Definition 607
18.1.2 Credit Enhancement 607
18.1.3 Cash-Flow Structure 608
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18.2 Market Quotes and Pricing 610
18.3 CAT Bonds and CAT Derivatives 612
18.4 End of Chapter Summary 615
18.5 References and Further Reading 615
18.6 Problems 616
Subject Index 617
Author Index 629