Fixed-Income Securities: Valuation, Risk Management and Portfolio Strategies (The Wiley Finance Series)

Fixed-Income Securities......Page 4
Contents......Page 10
About the Authors......Page 22
Preface......Page 24
Acknowledgments......Page 28
Notation......Page 30
PART I INVESTMENT ENVIRONMENT......Page 34
1.1.1 General Characteristics of Bonds......Page 36
1.1.2 Bonds by Issuers......Page 50
1.2.2 The Role of the Central Bank......Page 58
1.2.3 T-Bills......Page 59
1.2.4 Certificates of Deposit......Page 61
1.2.6 Commercial Papers......Page 62
1.2.8 Repo and Reverse Repo Market Instruments......Page 63
1.3 End of Chapter Summary......Page 65
1.4.2 Websites and Others......Page 66
1.5.1 Problems on Bonds......Page 67
1.5.2 Problems on Money-Market Instruments......Page 69
1.6 Appendix: Sector Breakdown of the Euro, the UK and the Japan Corporate Bond Markets......Page 70
2.1 Introduction to Bond Pricing......Page 74
2.2.2 The Mathematics of Discounting......Page 76
2.2.3 Nominal versus Real Interest Rates......Page 78
2.2.4 Time Basis and Compounding Frequency Conventions......Page 79
2.2.5 Continuous Compounding......Page 80
2.3.2 Yield to Maturity......Page 82
2.3.3 Spot Zero-Coupon (or Discount) Rate......Page 84
2.3.4 Forward Rates......Page 85
2.5 References and Further Reading......Page 87
2.6 Problems......Page 88
PART II TERM STRUCTURE OF INTEREST RATES......Page 94
3.1 Definition and Properties of the Term Structure......Page 96
3.1.1 What Kind of Shape Can It Take?......Page 98
3.1.2 How Does It Evolve over Time?......Page 101
3.2 Classical Theories of the Term Structure......Page 114
3.2.1 The Pure Expectations Theory......Page 115
3.2.2 The Pure Risk Premium Theory......Page 116
3.2.3 The Market Segmentation Theory......Page 118
3.2.5 Illustration and Empirical Validation......Page 119
3.2.6 Summary and Extensions......Page 120
3.3 End of Chapter Summary......Page 121
3.4.1 On the Empirical Behavior of the Yield Curve......Page 122
3.4.3 On the Classical Theories of the Term Structure of Interest Rates......Page 123
3.5 Problems......Page 124
4.1.1 How to Select a Basket of Bonds?......Page 129
4.1.2 Direct Methods......Page 130
4.1.3 Indirect Methods......Page 136
4.2.1 How to Select the Basket of Instruments?......Page 163
4.2.3 Least Squares Methods Based on Rates......Page 165
4.2.4 Least Squares Methods Based on Prices......Page 166
4.3.1 Disjoint Methods......Page 169
4.3.2 Joint Methods......Page 170
4.4 End of Chapter Summary......Page 175
4.5 References and Further Reading......Page 177
4.6 Problems......Page 179
4.7 Appendix: A Useful Modified Newton’s Algorithm......Page 188
PART III HEDGING INTEREST-RATE RISK......Page 192
5.1.1 The Five Theorems of Bond Pricing......Page 196
5.1.2 Reinvestment Risk......Page 197
5.1.3 Capital Gain Risk......Page 198
5.1.4 Qualifying Interest-Rate Risk......Page 199
5.2.1 Using a One-Order Taylor Expansion......Page 200
5.2.2 Duration, $Duration and Modified Duration......Page 203
5.2.3 How to Hedge in Practice?......Page 206
5.3 End of Chapter Summary......Page 208
5.4.2 Papers......Page 209
5.5 Problems......Page 210
6.1.1 Using a Second-Order Taylor Expansion......Page 215
6.1.2 Properties of Convexity......Page 218
6.1.3 Hedging Method......Page 220
6.2.1 A Common Principle......Page 221
6.2.2 Regrouping Risk Factors through a Principal Component Analysis......Page 225
6.2.3 Hedging Using a Three-Factor Model of the Yield Curve......Page 228
6.3 End of Chapter Summary......Page 232
6.4 References and Further Reading......Page 233
6.5 Problems......Page 234
PART IV INVESTMENT STRATEGIES......Page 242
7.1 Straightforward Replication......Page 246
7.2 Replication by Stratified Sampling......Page 247
7.3.1 Optimization Procedure......Page 249
7.3.2 Bond Return Covariance Matrix Estimation......Page 250
7.4 Factor-Based Replication......Page 259
7.5 Derivatives-Based Replication......Page 262
7.7 End of Chapter Summary......Page 263
7.9 Problems......Page 264
8.1 Market Timing: Trading on Interest-Rate Predictions......Page 266
8.1.1 Timing Bets on No Change in the Yield Curve or “Riding the Yield Curve\"......Page 267
8.1.2 Timing Bets on Interest-Rate Level......Page 269
8.1.3 Timing Bets on Specific Changes in the Yield Curve......Page 271
8.1.4 Scenario Analysis......Page 284
8.1.5 Active Fixed-Income Style Allocation Decisions......Page 288
8.2 Trading on Market Inefficiencies......Page 301
8.2.1 Trading within a Given Market: The Bond Relative Value Analysis......Page 302
8.2.2 Trading across Markets: Spread and Convergence Trades......Page 309
8.3 End of Chapter Summary......Page 315
8.4.1 On Active Fixed-Income Strategies......Page 316
8.4.2 On Active Asset Allocation Decisions......Page 317
8.5 Problems......Page 319
9.1.1 Arithmetic Rate of Return......Page 326
9.1.2 Geometric Rate of Return......Page 327
9.2 Risk-Adjusted Performance Evaluation......Page 328
9.2.1 Absolute Risk-Adjusted Performance Evaluation......Page 329
9.2.2 Relative Risk-Adjusted Performance Evaluation......Page 332
9.3 Application of Style Analysis to Performance Evaluation of Bond Portfolio Managers: An Example......Page 342
9.3.1 Alpha Analysis......Page 343
9.3.2 Passive Versus Active Managers......Page 346
9.4 End of Chapter Summary......Page 347
9.5.1 Books and Papers......Page 348
9.6 Problems......Page 349
PART V SWAPS AND FUTURES......Page 354
10.1.2 Terminology and Conventions......Page 358
10.2.1 Pricing of Swaps......Page 359
10.2.2 Market Quotes......Page 366
10.3 Uses of Swaps......Page 367
10.3.1 Optimizing the Financial Conditions of a Debt......Page 368
10.3.2 Converting the Financial Conditions of a Debt......Page 369
10.3.3 Creating New Assets Using Swaps......Page 370
10.3.4 Hedging Interest-Rate Risk Using Swaps......Page 372
10.4.1 Accrediting, Amortizing and Roller Coaster Swaps......Page 375
10.4.3 Constant Maturity Swap and Constant Maturity Treasury Swap......Page 376
10.4.6 Libor in Arrears Swap......Page 377
10.4.8 Zero-Coupon Swap......Page 378
10.6.1 Books and Papers......Page 379
10.7 Problems......Page 380
11.1 Definition......Page 386
11.2.1 Terminology and Conventions......Page 387
11.2.2 Quotes......Page 389
11.3 Margin Requirements and the Role of the Clearing House......Page 391
11.4 Conversion Factor and the Cheapest-to-Deliver Bond......Page 392
11.4.1 The Cheapest to Deliver on the Repartition Date......Page 393
11.4.2 The Cheapest to Deliver before the Repartition Date......Page 394
11.5.1 Forward-Spot Parity or How to Price a Forward Contract?......Page 395
11.5.2 The Forward Contract Payoff......Page 397
11.6.1 Pure Speculation with Leverage Effect......Page 398
11.6.2 Fixing Today the Financial Conditions of a Loan or Investment in the Future......Page 399
11.6.3 Detecting Riskless Arbitrage Opportunities Using Futures......Page 400
11.6.4 Hedging Interest-Rate Risk Using Futures......Page 401
11.7 End of Chapter Summary......Page 403
11.8.2 Websites of Futures Markets and of the Futures Industry Association......Page 404
11.9 Problems......Page 405
11.10 Appendix: Forward and Futures Prices Are Identical When Interest Rates Are Constant......Page 408
PART VI MODELING THE TERM STRUCTURE OF INTEREST RATES AND CREDIT SPREADS......Page 410
12 Modeling the Yield Curve Dynamics......Page 414
12.1.1 Building an Interest-Rate Tree......Page 415
12.1.2 Calibrating an Interest-Rate Tree......Page 417
12.2 Continuous-Time Models......Page 420
12.2.1 Single-Factor Models......Page 421
12.2.2 Multifactor Models......Page 425
12.3.1 A Discrete-Time Example: Ho and Lee’s Binomial Lattice......Page 429
12.3.2 Arbitrage Models in Continuous Time......Page 434
12.4 End of Chapter Summary......Page 439
12.5 References and Further Reading......Page 440
12.6 Problems......Page 444
12.7.1 Discretizing the Short Rate......Page 446
12.7.2 Calibrating the Lattice to the Current Spot Yield Curve......Page 449
12.7.3 Option Pricing......Page 452
12.8.1 Brownian Motion......Page 453
12.8.2 Stochastic Integral......Page 456
12.8.3 Stochastic Differential Equations (SDE)......Page 458
12.8.5 Representation of Brownian Martingales......Page 459
12.8.6 Continuous-Time Asset Pricing......Page 460
12.8.7 Feynman–Kac Formula......Page 464
12.8.8 Application to Equilibrium Models of the Term Structure......Page 465
13 Modeling the Credit Spreads Dynamics......Page 470
13.1.1 Ratings......Page 471
13.1.2 Default Probability......Page 473
13.2 Modeling Credit Spreads......Page 474
13.2.1 Structural Models......Page 475
13.2.2 Subsequent Models......Page 479
13.2.3 Reduced-Form Models......Page 481
13.2.4 Historical versus Risk-Adjusted Probability of Default......Page 483
13.3 End of Chapter Summary......Page 485
13.4.1 Books and Papers......Page 486
13.4.2 Websites......Page 487
13.5 Problems......Page 488
PART VII PLAIN VANILLA OPTIONS AND MORE EXOTIC DERIVATIVES......Page 490
14.1.1 Institutional Aspects......Page 492
14.1.2 Pricing......Page 493
14.1.3 OAS Analysis......Page 500
14.1.4 Effective Duration and Convexity......Page 501
14.2.1 Institutional Aspects......Page 503
14.2.2 Valuation of Convertible Bonds......Page 506
14.2.3 Convertible Arbitrage......Page 512
14.3.1 Definition......Page 515
14.3.2 Uses......Page 516
14.3.3 Pricing......Page 520
14.4 End of Chapter Summary......Page 524
14.5.2 On Convertible Bonds......Page 525
14.5.3 On Options on Bonds......Page 526
14.6 Problems......Page 527
14.7 Appendix: Bond Option Prices in the Hull and White (1990) Model......Page 531
14.7.2 Call on Coupon Bond......Page 532
15.1.1 Definition and Terminology......Page 533
15.1.2 Pricing and Hedging Options on Futures......Page 535
15.1.3 Market Quotes......Page 538
15.2.1 Definition and Terminology......Page 541
15.2.2 Pricing and Hedging Caps, Floors and Collars......Page 543
15.2.3 Market Quotes......Page 547
15.2.4 Uses of Caps, Floors and Collars......Page 549
15.3.1 Definition and Terminology......Page 553
15.3.2 Pricing and Hedging Swaptions......Page 554
15.3.4 Uses of Swaptions......Page 559
15.4 End of Chapter Summary......Page 560
15.5.1 Books and Papers......Page 561
15.6 Problems......Page 562
15.7 Appendix 1: Proof of the Cap and Floor Formulas in the Black (1976) Model......Page 567
15.8 Appendix 2: Proof of the Swaption Formula in the Black (1976) Model......Page 568
15.9.1 Options on Forward Contracts......Page 569
15.9.2 Options on Futures Contracts......Page 570
15.10.1 Cap and Floor......Page 572
15.10.2 Swaption......Page 573
15.11.1 Why Define New Variables?......Page 574
15.11.2 Building New Variables......Page 575
15.11.3 The Dynamics of L(t, q) and K(t, t + q)......Page 576
15.11.4 Pricing of Caps......Page 578
15.11.5 Calibration of the Model......Page 579
16.1.1 Barrier Caps and Floors......Page 581
16.1.2 Bounded Caps, Floors, Barrier Caps and Floors......Page 583
16.1.5 Choosercaps and Flexicaps-and-Floors......Page 584
16.1.6 Contingent Premium Caps and Floors......Page 586
16.1.8 Incremental Fixed Swaps......Page 587
16.1.9 Index Amortizing Bonds and Swaps......Page 588
16.1.11 Moving Average Caps and Floors......Page 590
16.1.13 Q-Caps and Floors......Page 591
16.1.14 Range Accrual Swaps......Page 592
16.1.15 Ratchet Caps and Floors......Page 593
16.1.16 Reflex Caps and Floors......Page 594
16.1.18 Rolling Caps and Floors......Page 595
16.1.20 Subsidized Swaps......Page 596
16.2.1 The Significance of Credit Derivatives......Page 598
16.2.2 Types of Credit Derivatives......Page 600
16.4.1 On Interest-Rate Exotic Options......Page 608
16.4.3 On Numerical Methods (See the Appendix 2)......Page 609
16.5 Problems......Page 610
16.6.1 Barrier Cap Formulas......Page 613
16.6.3 Barrier Cap and Floor Greeks......Page 614
16.7.1 Monte Carlo Simulations......Page 616
16.7.2 Finite-Difference Methods......Page 618
PART VIII SECURITIZATION......Page 622
17.1.2 The Amortization Mechanism......Page 626
17.1.4 Typology of MBS......Page 629
17.2 Market Quotes and Pricing......Page 631
17.2.1 Market Quotes......Page 632
17.2.2 Pricing of MBS......Page 633
17.3 End of Chapter Summary......Page 636
17.4.1 Books and Papers......Page 637
17.5 Problems......Page 638
18.1.2 Credit Enhancement......Page 640
18.1.3 Cash-Flow Structure......Page 641
18.2 Market Quotes and Pricing......Page 643
18.3 CAT Bonds and CAT Derivatives......Page 645
18.5 References and Further Reading......Page 648
18.6 Problems......Page 649
Subject Index......Page 650
Author Index......Page 662