Bond pricing and yield-curve modelling: a structural approach
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| adam_text | Contents
Acknowledgements page xxiii
Symbols and Abbreviations xxv
Part I The Foundations
1 What This Book Is About 3
1.1 My Goal in Writing This Book 3
1.2 What My Account Leaves Out 5
1.3 Affine Models 6
1.4 A Simple Taxonomy 8
1.5 The Choice of Variables 10
1.5.1 Latent versus Observable Variables 10
1.5.2 The Spanning Problem 15
1.5.3 The Constraint Problem 16
1.6 Why Do We Need No-Arbitrage Models After All? 19
1.7 Stamp Collecting and Shallow versus Deep Explanations 20
1.8 The Ideal Reader and Plan of the Book 21
2 Definitions, Notation and a Few Mathematical Results 24
2.1 The Purpose of This Chapter 24
2.2 The Building Blocks 24
2.2.1 Arbitrage 24
2.2.2 Pseudo-Arbitrage 25
2.2.3 Sharpe Ratios 27
2.2.4 Bond Prices and Yields 28
2.2.5 Duration and Convexity 31
2.2.6 Forward Rates 32
2.3 Log Prices and Log Returns 33
2.4 Dimensional Analysis 34
Contents
viii
2.5 Appendix 2A: Vectors and Matrices 36
2.5.1 Definition 36
2.5.2 Transformations of Vectors 37
2.5.3 Orthogonal Matrices 38
2.5.4 Row Vectors 39
2.5.5 Exponential of a Matrix 40
2.6 Appendix 2B: Mean-Reverting and AR(1) Processes 41
2.6.1 The Omstein—Uhlenbeck Process 41
2.6.2 The AR(1) Process 42
2.6.3 Parallels between AR(1) Processes and the
Omstein—Uhlenbeck Process 43
2.7 Appendix 2C: Some Results from Stochastic Calculus 44
2.7.1 Ito’s Lemma 44
2.7.2 Stochastic-Calculus Rules for dptdxt 45
2.7.3 Expectations of Ito Integrals 46
2.7.4 The Ito Isometry 47
2.7.5 Risk-less Portfolios 48
3 Links among Models, Monetary Policy and the Macroeconomy 49
3.1 The Purpose of This Chapter 49
3.2 The Monetary Channels 50
3.3 A Modelling Framework 52
3.4 The Monetary Actions: A Simple Model 56
3.5 Calibrating Reduced-Form Models 5 8
3.5.1 General Considerations 58
3.5.2 Assessing the Quality of the Calibration Process 60
3.5.3 State Variables versus Model Parameters 61
4 Bonds: Their Risks and Their Compensations 63
4.1 The Purpose of This Chapter 63
4.2 Nominal Rates, Inflation and Real Rates: A Qualitative
Discussion 64
4.2.1 Inflation Risk 64
4.2.2 Real-Rate Risk 65
4.2.3 Putting the Pieces Together 66
4.3 Real-World and Risk-Neutral Probabilities: The Market
Price of Risk 68
4.3.1 Introducing the F and Q Measures 69
4.3.2 Introducing the Market Price of Risk 72
4.4 An Important First Result: Bond Prices as Q-Expectations 76
4.5 The Price Process and Its Expectations 77
4.5.1 The General Case 77
Contents ix
4.5.2 The Affine Case 78
4.6 Nominal Rates, Inflation and Real Rates: Definitions 79
5 The Risk Factors in Action 81
5.1 The Purpose of This Chapter 81
5.2 Expectations and Risk Premia during an Important Market
Period 81
5.2.1 An Account of What Happened 81
5.2.2 Possible Explanations of What Happened 85
5.3 How Can We Estimate Risk Premia? 87
5.4 Different Types of Risk Premia 88
5.5 What Are Investors Compensated For? 91
5.5.1 Decomposition of the Risk Premium 91
5.5.2 ‘Which’ Liquidity Are TIPS-Investors
Compensated For? 93
5.6 What Is and What Is Not a True Risk Premium 94
5.7 Does It Matter if a Risk Premium Is ‘Really’ a Risk
Premium? 96
6 Principal Components: Theory 98
6.1 The Purpose of This Chapter 98
6.2 What Are Principal Components? 98
6.2.1 The Axis Rotation 98
6.2.2 The Signal and the Noise 103
6.3 How Many Principal Components Do We Need for Yields? 103
6.4 First Conclusions 104
6.5 Some Mathematical Results 105
7 Principal Components: Empirical Results 108
7.1 The Purpose of This Chapter 108
7.2 Nominal Rates 108
7.2.1 Descriptive Features 108
7.2.2 Mean-Reverting Properties — Each PC in Isolation 112
7.2.3 The Joint Mean-Reverting Behaviour of Principal
Components 116
7.3 Real Rates and Break-Even Inflation 122
7.4 Correlation between Nominal, Inflation and Real Principal
Components 128
Part II The Building Blocks: A First Look
8 Expectations 137
8.1 The Purpose of This Chapter 137
X
Contents
8.2 Linking Expectations with No-Arbitrage 137
8.2.1 A One-Factor World 138
8.2.2 Moving to Many Factors 141
8.3 An Example: A Mean-Reverting Process for the Short Rate 143
8.4 Expectations and Survey Data 145
9 Convexity: A First Look 147
9.1 The Purpose of This Chapter 147
9.2 Where Does Convexity Come from? 147
9.3 The Links between Convexity and Jensen’s Inequality 149
9.3.1 A Special but Important Case: Gaussian Random
Variables 150
9.4 What Does Convexity Depend On? 152
9.5 Why Convexity Is Different 154
9.6 Why Isn’t Convexity‘Always Good’? 156
9.7 Who Sets the Price of Convexity? A Bit of Story-Telling 157
10 A Preview: A First Look at the Vasicek Model 160
10.1 The Purpose of This Chapter 160
10.2 The Vasicek Model 161
10.3 Properties of the Vasicek Model 161
10.3.1 Distributional Properties of the Vasicek Model 161
10.3.2 Bond Prices in the Vasicek Model 165
10.3.3 The Duration in the Vasicek Model 165
10.3.4 Yield Volatilities in the Vasicek Model 168
10.4 Rate Expectations and the Shape of the Vasicek Yield Curve 168
10.5 Convexity in the Vasicek Model 170
10.5.1 An Expression for Convexity 170
10.5.2 Convexity and the Volatility of Yields 171
10.5.3 How Big Should One Expect the Convexity Effect
to Be? 172
10.5.4 What Is the ‘Right’ Reversion Speed? 173
10.6 The Risk Premium in the Vasicek Model 175
10.7 The Functional Form of the Market Price of Risk 176
10.8 The Link between the Market Price of Risk and the Sharpe
Ratio 178
10.9 Appendix 10A: Proof that
r, = {e-«( -«b)}ro + {l - e~K(f-“»] + f0 e-K(,-s)ardzs 181
Part III The Conditions of No-Arbitrage
11 No-Arbitrage in Discrete Time 185
11.1 The Purpose of This Chapter 185
Contents
xx
11.2 Type-I Arbitrage 186
11.3 Bounds to the Price-Correction Term: Type-I
Arbitrage 188
11.4 Bounds to the Price-Correction Term: Type-II
Arbitrage 189
11.5 A Useful Rewriting 192
11.6 Extension to Many Factors 193
11.7 The Task of the Long-Term Bond Investor 195
12 No-Arbitrage in Continuous Time 196
12.1 The Purpose of This Chapter *■ 196
12.2 Constructing a Risk-Less Portfolio: The Market Price of
Risk Again 196
12.3 Interpretations of the Market Price of Risk 199
12.4 Excess Returns 200
12.5 What the Market Price of Risk Can Depend On 201
12.6 Appendix 12A: The Market Price of Risk and Excess
Return with Many Factors 202
13 No-Arbitrage with State Price Deflators 206
13.1 The Purpose of This Chapter 206
13.2 A Bird’s Eye View of the ‘Traditional’ and ‘Modem’
Approaches 207
13.3 Pricing Assets: The Building-Blocks Approach 208
13.4 A Beautiful Result: The Change of Measure 211
13.4.1 Prices as Expectations in the Risk-Neutral
Measure — Again 211
13.4.2 The Equivalence of the State-Price Deflator and the
Stochastic Discount Factor 213
13.5 The Process for the State-Price Deflator 214
13.6 Special Assets: Discount Bonds 216
13.7 Deriving the Drift of the State-Price Deflator 216
13.8 The Short Rate Again 218
13.9 Deriving the Volatility of the State-Price Deflator 219
13.9.1 Evaluation of the Three Terms 220
13.9.2 The Link between the Volatility of the State-Price
Deflator and the Market Price of Risk 221
13.9.3 Where Does the Volatility of Bonds Come from? 222
13.9.4 Summary of Results 223
14 No-Arbitrage Conditions for Real Bonds 224
14.1 The Purpose of This Chapter 224
14.2 The Expression for the Real State-Price Deflator 224
Contents
xii
14.3 The Process for the Real State-Price Deflator 226
14.4 The Link between Break-Even Inflation and Inflation
Expectations 229
14.4.1 Inflation Expectation Under F 230
14.4.2 Inflation Expectation under Q 232
14.4.3 Inflation Expectation under T 233
14.4.4 Inflation Expectations under Different Measures 234
14.5 The Risk Premium as a Covariance 235
14.6 Moving to an Affine World 238
14.7 The Market Price of Inflation Risk - Affine Models 239
15 Links with an Economics-Based Description of Rates 241
15.1 The Purpose of This Chapter 241
15.2 First Derivation of the SDF 242
15.3 From the SDF to Risk Premia 245
15.4 Real versus Nominal Prices 248
15.5 Idiosyncratic Risk 249
15.6 The Links between the SDF and the Risk-Less Rate 250
15.6.1 The No-Uncertainty Case 251
15.6.2 Reintroducing Uncertainty 252
15.6.3 But Does It Work? 253
15.7 SDFs in Continuous and Discrete Time 256
15.8 A More General Result for the Sharpe Ratio 257
Part IV Solving the Models
16 Solving Affine Models: The Vasicek Case 263
16.1 Purpose of This Chapter 263
16.2 The Replication Approach to Solving for Bond Prices: The
Vasicek Model 264
16.2.1 The PDE Satisfied by Bond Prices 264
16.3 A Special Case: Affine Term Structures 266
16.4 The Vasicek Case 269
16.5 Affinity of the Vasicek Model under F and under Q 271
16.6 Observations about the Solution 272
16.6.1 Yields 272
16.6.2 The Volatility Structure 273
16.6.3 Forward Rates 273
16.6.4 Calibrating to the Volatility Structure: Factorization 276
16.6.5 Fitting to the Yield Curve 277
16.7 Why Do We Care about a Humped Volatility Curve? 281
16.8 How to Lengthen the Short Blanket 282
Contents xiii
17 First Extensions 285
17.1 The Purpose of This Chapter 285
17.2 Affine Models with Many State Variables 285
17.2.1 The N = 2 Case 287
17.2.2 An Expression for the Variance for Generic N 288
17.2.3 Stability 290
17.2.4 Changing Variables 291
17.3 Multivariable Exponentially Affine Models 292
17.4 General Properties of the Solutions 293
17.4.1 Yields and Forward Rates 293
17.4.2 Distributional Properties , 294
17.5 Appendix 17A: Derivation of the Variance of a
One-Dimensional Mean-Reverting Process 295
17.6 Appendix 17B: Derivation of the Variance of a
Multidimensional Mean-Reverting Process 296
17.7 Appendix 17C: Stability of the Mean-Reverting System 297
18 A General Pricing Framework 299
18.1 The Purpose of This Chapter 299
18.2 What Is an Affine Model? 300
18.3 The General Strategy 301
18.4 Summary of the Equations Derived in Appendix 18A 303
18.5 Various Additional Results 304
18.5.1 Expression for the Yield 304
18.5.2 Expression for the Yield Covariance Matrix and
the Yield Volatilities 305
18.5.3 Expression for the Volatility of the Instantaneous
Forward Rates 306
18.6 Derivation of the Mean and Variance of the State Variables 307
18.7 Now We Have Solved (Almost) Any Affine Model 309
18.7.1 Simple Vasicek 309
18.7.2 The Doubly-Mean-Reverting Vasicek Model 310
18.7.3 The Trebly-Mean-Reverting Vasicek Model 311
18.7.4 The Stochastic-Market-Price-of-Risk Model 312
18.8 Appendix 18A: Solving for B (r) and A(r) 313
18.8.1 Solving the ODE for ~Z?(r) 314
18.8.2 Solving the ODE for A(r) 316
18.9 Appendix 18B 323
18.9.1 The Meaning of 323
18.10 Explicit Calculation of the Formal Solution 3?t = o 324
18.10.1 The Up-and-Down Theorem 325
18.10.2 Commutation Relationships for A and f (A) 326
XIV
Contents
18.10.3 Time Derivative of eAt 327
18.10.4 Integral of e** 327
18.10.5 Evaluation of the Integral [ /Qr e~c TMe~Cx Jr] 328
19 The Shadow Rate: Dealing with a Near-Zero Lower Bound 329
19.1 The Purpose of This Chapter 329
19.2 Motivation: Why the Shadow Rate Matters 330
19.3 How the Shadow Rate Affects the Whole Yield Curve 332
19.4 The Modelling Approach 333
19.4.1 The Setting 333
19.4.2 An Approximate Solution 334
19.5 Does It Matter? 339
19.5.1 The Shadow and Short Rates Compared 339
19.5.2 The Effect of the Shadow Rate on Long Yields 339
19.5.3 Sensitivity of the Results to the Floor Level 343
19.6 A Broader View of the Topic 343
Part V The Value of Convexity
20 The Value of Convexity 351
20.1 The Purpose of This Chapter 351
20.2 Break-Even Volatility --- The Vasicek Setting 351
20.3 Problems with the Vasicek Version of the Break-Even
Volatility 355
20.4 Generalizing to Many Factors 357
20.4.1 Calculating the Terms ~c , ~~c 2, and ~c 4 360
20.4.2 Expressing the Convexity in Terms of Yield
Volatilities 362
20.5 What to Do with This Expression for the Convexity 363
20.5.1 An Important Aside 364
20.6 An Intuitive Aside: Simplifying the Analysis 365
20.7 A Graphical Interpretation 368
20.8 Appendix 20A 369
21 A Model-Independent Approach to Valuing Convexity 371
21.1 The Purpose of This Chapter 371
21.2 Equivalent Affine Models 373
21.3 The Expression for Convexity in an Affine Setting 374
21.4 An Expression for the Theoretical Convexity of the
Portfolio 377
21.5 Theoretical Convexity as a Function of Market Observables 380
21.5,1 Theoretical Portfolio Convexity as a Function of
Forward Rates
380
Contents
xv
21.5.2 The Portfolio Time Decay as a Function of ‘Carry’
and ‘Roll-Down’ 381
21.6 What These Results Imply 383
21.7 Linking the Term ^TrfS^DS] with Yield Volatilities 384
21.8 Making the Weights (Almost) Model Independent 386
21.9 How General Are the Results? 388
21.10 Model-Based or Empirical? 389
22 Convexity: Empirical Results 391
22.1 The Purpose of This Chapter 391
22.2 The Strategy: A Reminder ; 393
22.3 Setting Up the Strategy 395
22.3.1 Determining the Optimal Weights 395
22.3.2 Estimating the Yield Volatilities 396
22.4 Results 398
22.4.1 Is the Yield Curve Fairly Curved? 398
22.4.2 Why Are the Strategies Not Always Profitable? 402
22.4.3 Is the Strength of the Signal Correlated with the
Money Made? 405
22.4.4 Explaining the Residuals — Residual Exposure? 406
22.4.5 Explaining the Residuals — Wrong
Volatility Estimate? 409
22.5 Conclusions 411
Part VI Excess Returns
23 Excess Returns: Setting the Scene 415
23.1 The Purpose of This Chapter 415
23.2 The (Local) Expectation Hypothesis 415
23.3 What One Really Tests for When One Tests the (L)EH 417
23.4 Defining Excess Returns 419
23.4.1 General Exact Results 419
23.4.2 Special Cases 420
23.4.3 Approximate Results for the r = n = 1 Case 421
23.5 Expressing Excess Returns as a Function of Forward Rates 422
23.6 Excess Returns with Real Rates 422
23.7 Excess Returns: Links with Carry, Roll-Down and Related
Market Lore 425
23.8 Why ‘Carry’ and ‘Roll-Down’ Matter 429
24 Risk Premia, the Market Price of Risk and Expected Excess
Returns 431
24.1 The Purpose of This Chapter 431
XVI
Contents
24.2 Decomposing and Interpreting the Approximate Excess
Returns 432
24.2.1 The Carry’ Description . 432
24.2.2 The ‘Forwards-Come-True’ Condition 432
24.3 From Excess Returns to the Market Price of Risk 433
24.3.1 Market Yields versus Expected Yields 433
24.4 The Link between Excess Returns and Term Premia 436
24.5 The Link between Term Premia and Expected Excess
Returns 438
24.6 Reconciling Results 440
24.7 Expected versus Realized Excess Returns 441
24.8 Forwards-Come-True versus Yields-Don’t-Move:
Roll-Down Again 446
24.9 When to Invest 448
25 Excess Returns: Empirical Results 449
25.1 The Purpose of This Chapter 449
25.2 Understanding the Empirical Setting 450
25.2.1 The Empirical Questions 450
25.2.2 A Very Important Caveat on Spanning 452
25.2.3 The Methodological Dilemma 454
25.3 Unconditional Results: Nominal Bonds 455
25.4 Regression Results: Nominal Bonds 457
25.4.1 1- to 10-Year Returns 457
25.4.2 Effectiveness of Various Regressors 459
25.4.3 5-Year Returns: Comparison with
Cochrane-Piazzesi (2005) 461
25.5 Where Has the Volatility Gone? 462
25.6 Regression Results: Real Bonds 463
25.7 The Data 464
25.8 The Real Excess Returns 464
25.9 Extracting the Real-Rate Risk Premium 468
25.10 Estimating the Inflation Premium in Nominal Bonds 470
25.10.1 Isolating the Liquidity Component 471
26 Excess Returns: The Recent Literature — I 473
26.1 The Purpose of This Chapter 473
26.2 The Early Work 474
26.3 Cochrane and Piazzesi (2005) 475
26.4 Critical Assessment of the Cochrane-Piazzesi
Results 478
26.5 Robustness of the Tent Shape: Tents versus Bats 478
Contents xvii
26.6 The Link Between the Tent and the Bat Factors:
Constrained Regressions 482
26.6.1 Constrained Regression: The
Investigation Methodology 483
26.6.2 Constrained Regression: Results 485
26.6.3 Constrained Regression: First Conclusions 487
26.7 The Link between the Tent and the Slope Factors 488
26.7.1 Tent versus Slope Shape Similarity: The
Investigation Methodology 488
26.7.2 Tent versus Slope Shape Similarity: Results f 490
26.8 Exploring the Economic Robustness of Tent versus Slope
Predictions 491
26.8.1 Tent versus Slope Robustness: Methodology 491
26.8.2 Tent versus Slope Robustness: Results 493
26.8.3 Tent versus Slope Robustness: Conclusions 495
27 Excess Returns: The Recent Literature — II 497
27.1 The Purpose of This Chapter 497
27.2 The Work of Radwanski (2010) 498
27.2.1 Features and Highlights of the Radwanski Results 498
27.2.2 The Methodology and Results 499
27.2.3 Comments and Conclusions 503
27.3 The Work of Ludvigson and Ng (2009) 504
27.3.1 Main Results 504
27.3.2 The Spanning of Yield Curve Factors Revisited:
Implication for Affine Models 507
27.4 Yield-Curve Spanning: Why One May Need Five Factors
After All 508
27.4.1 The Essentially Affine Description 509
27.4.2 Switching to Yields as State Variables 511
27.4.3 Augmenting the State Vector 511
27.4.4 Switching Back to an ‘Augmented’ Set of Yields as
State Variables 512
27.4.5 The Subtle Role of ‘Measurement Error’ 513
27.4.6 Spanning in Principle versus Spanning in Practice 513
27.5 The Work of Cieslak and Povala 514
27.5.1 The Set-Up and Main Features 514
27.5.2 The Investigation Methodology and Results 515
27.5.3 The Link with Forward-Rate-Based RPFs 519
27.5.4 Intrinsic Limitations of Forward-Rate-Based
Factors 520
27.5.5 Implications for Term-Structure Models 522
Contents
xviii
27.5.6 Re-Interpretation of the Cieslak-Povala RPF:
Conditional Slope and Level 522
27.6 Related Work . 525
28 Why Is the Slope a Good Predictor? 527
28.1 The Purpose of This Chapter 527
28.2 What Does Not Qualify as an Explanation 528
28.3 Excess Returns, the Slope and the Real Economy 529
28.4 The Data-Generating, Subjective and Risk-Neutral
Measures 531
28.5 Does It Matter? 533
28.6 Why Is the Slope Significant? A
Heterogeneous-Expectations Model 534
28.7 Why Is the Slope Significant? An Over-reaction Model 538
28.8 The Model in Detail 539
28.8.1 The Actions of the Central Bank 539
28.8.2 The Investors’ Expectations 541
28.8.3 The Bond Price Formation 541
28.8.4 The Excess Returns 542
28.8.5 The Simulations 542
28.8.6 Summary of Results 546
29 The Spanning Problem Revisited 547
29.1 The Purpose of This Chapter 547
29.2 What Is the Spanning Problem? 547
29.3 The Empirical Spanning Problem 548
29.4 The Theoretical Spanning Problem 551
29.5 The Modelling Choices to Handle the Spanning Problem 552
Part VII What the Models Tell Us
30 The Doubly Mean-Reverting Vasicek Model 559
30.1 The Purpose of This Chapter 559
30.2 The Doubly Mean-Reverting Vasicek Model 560
30.3 Bond Prices and Properties of the Solution 561
30.4 The Volatility of the Instantaneous Forward Rate 562
30.5 The Building Blocks 564
30.6 Initial Conclusions 568
30.7 Quality of the Fit 569
30.7.1 Calibrating the Model to the Volatility Structure 569
30.7.2 Calibrating the Model to the Yield Curve 571
30.8 The Value of Convexity 573
30.9 What Happened to the Measure? 574
Contents xix
31 Real Yields, Nominal Yields and Inflation: The
D’Amico-Kim-Wei Model 575
31.1 The Purpose of This Chapter 575
31.2 Empirical Findings about Inflation 576
31.3 The No-Arbitrage Relationships 577
31.3.1 What the No-Arbitrage Relationships Really Imply 579
31.4 The Assumptions About the Process for the State Variables 581
31.5 Inflation Expectations and Risk Premia 582
31.6 Adding Liquidity 583
31.7 The Parameter Estimation Procedure and Results 584
31.7.1 The Difficulty of Parameter Estimation 586
31.8 Nominal and Real Rate Expectations and Risk Premia 588
31.8.1 Full-Sample Analysis 588
31.8.2 Prediction of Nominal and Real Excess Returns 589
31.8.3 Analysis of the May-September 2013 Events 594
31.9 Conclusions 596
31.10 Related Work 599
32 From Snapshots to Structural Models: The Diebold—Rudebusch
Approach 602
32.1 The Purpose of This Chapter 602
32.2 Turning a Snapshot Model into a Dynamic Model 603
32.3 Turning a Dynamic Model into a No-Arbitrage Affine
Model 606
32.4 Are the Variables Really Principal Components? 610
32.5 Dealing with Liquidity 612
32.5.1 On-the-Run, Off-the-Run Bonds 612
32.5.2 The Modelling Approach 613
32.5.3 The Results 615
32.5.4 Conclusions 616
33 Principal Components as State Variables of Affine Models: The
PC A Affine Approach 618
33.1 The Purpose of This Chapter 618
33.2 Why PC-Based Models Are Special (Again) 620
33.3 Specified-Variable Models Revisited 622
33.3.1 Parameter Constraints for PC A Prespecified Models 624
33.4 Our Strategy to Link the P- and Q-Measures 625
33.5 The Set-Up 626
33.5.1 Notation 626
33.5.2 The Geometry (Kinematics) of the Problem 626
33.5.3 The Dynamics of the Problem 627
XX
Contents
33.5.4 Solution 628
33.5.5 Necessary Conditions for Identifiability 629
33.6 Theoretical Results 631
33.6.1 Impossibility of Identification When /C Is
Diagonal 631
33.6.2 What Does It Mean to Require that the Factors ~x t
Should Be Principal Components? 632
33.6.3 Constraints on /C for Identifiability 633
33.6.4 What the Q-measure Reversion-Speed Matrix
Affects 635
33.7 Moving from the Q- to the P-Measure 639
33.8 Estimating the Parameters of if o and 7Z 641
33.9 Calibration of the Model 643
33.9.1 Cross-Sectional Fit to Yields 643
33.9.2 Estimating the Values of the Eigenvalues ~T 644
33.9.3 Estimating the ‘Level’ Constant, ur 644
33.10 Calibration Results 644
33.11 Generalizable Results on Term Premia from a PC-Based
Affine Model 649
33.12 The Existential Dilemma 654
33.13 Appendix 33A: Proof of the Constraints on the
Reversion-Speed Matrix JC® 657
33.13.1 Preliminaries 657
33.13.2 Some Ancillary Results 658
33.13.3 The Derivation of the Main Result 659
33.13.4 The Conditions on the Vector ~e 660
33.14 Appendix 33B: Switching Regressors 661
34 Generalizations: The Adrian-Crump-Moench Model 663
34.1 The Purpose of This Chapter 663
34.2 The Strategy Behind the Adrian-Crump-Moench Model 664
34.3 A High-Level Description of the Model 665
34.4 State-Price Deflators: Generalizing the Results 667
34.5 Establishing an Expression for the Excess Returns 671
34.6 The Estimation Procedure 676
34.7 Establishing a Link with the Affine Model: The Discount
Factor 677
34.8 Some Observations 679
34.9 Results 680
34.9.1 Full-Sample Analysis 680
34.9.2 Analysis of the May-September 2013 Events 683
34.10 Conclusions 687
Contents xxi
35 An Affine, Stochastic-Market-Price-of-Risk Model 688
35.1 The Purpose of This Chapter 688
35.2 Why Do We Need Another Affine Model? 689
35.3 Another Justification for a Stochastic-Market-Price-of-Risk
Model 691
35.4 The Model 693
35.5 In Which Measure(s) Are We Working? 694
35.6 The Qualitative Behaviour of the Model 696
35.7 Calibration of the Model 698
35.8 Calibration Results 700
35.9 Comments on the Solution 705
35.10 Term Premia in the Stochastic-Market-Price-of-Risk Model 708
36 Conclusions 714
36.1 What Have We Learnt? 714
36.1.1 The Road Followed 714
36.1.2 The Case for the Prosecution: Models
As Regurgitators 715
36.1.3 The Case for the Defence: Models as Enforcers of
Parsimony 716
36.1.4 The Case for the Defence: Models as Enforcers of
Cross-Sectional Restrictions 718
36.1.5 The Case for the Defence: Models as Revealers of
Forward-Looking Informations 719
36.1.6 The Case for the Defence: Models as Integrators 720
36.1.7 The Case for the Defence: Models as Enhancers of
Understanding 721
References 725
Index 737
|
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| author | Rebonato, Riccardo |
| author_GND | (DE-588)142802816 |
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| building | Verbundindex |
| bvnumber | BV045003503 |
| classification_rvk | QK 620 |
| ctrlnum | (OCoLC)1030532678 (DE-599)BVBBV045003503 |
| discipline | Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV045003503 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:06:42Z |
| institution | BVB |
| isbn | 9781107165854 1107165857 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030395603 |
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| spelling | Rebonato, Riccardo Verfasser (DE-588)142802816 aut Bond pricing and yield-curve modelling a structural approach Riccardo Rebonato Cambridge Cambridge University Press 2018 xxvii, 752 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Rentenmarkt (DE-588)4177794-3 gnd rswk-swf Zinsstruktur (DE-588)4067855-6 gnd rswk-swf Rentenmarkt (DE-588)4177794-3 s Zinsstruktur (DE-588)4067855-6 s DE-604 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030395603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rebonato, Riccardo Bond pricing and yield-curve modelling a structural approach Rentenmarkt (DE-588)4177794-3 gnd Zinsstruktur (DE-588)4067855-6 gnd |
| subject_GND | (DE-588)4177794-3 (DE-588)4067855-6 |
| title | Bond pricing and yield-curve modelling a structural approach |
| title_auth | Bond pricing and yield-curve modelling a structural approach |
| title_exact_search | Bond pricing and yield-curve modelling a structural approach |
| title_full | Bond pricing and yield-curve modelling a structural approach Riccardo Rebonato |
| title_fullStr | Bond pricing and yield-curve modelling a structural approach Riccardo Rebonato |
| title_full_unstemmed | Bond pricing and yield-curve modelling a structural approach Riccardo Rebonato |
| title_short | Bond pricing and yield-curve modelling |
| title_sort | bond pricing and yield curve modelling a structural approach |
| title_sub | a structural approach |
| topic | Rentenmarkt (DE-588)4177794-3 gnd Zinsstruktur (DE-588)4067855-6 gnd |
| topic_facet | Rentenmarkt Zinsstruktur |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030395603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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