Krippner Zero Lower Bound Term Structure Modeling

A Practitioner's Guide
2015
ISBN: 978-1-137-40182-3
Verlag: Palgrave Macmillan US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 436 Seiten

Reihe: Applied Quantitative Finance

Nominal yields on government debt in several countries have fallen very near their zero lower bound (ZLB), causing a liquidity trap and limiting the capacity to stimulate economic growth. This book provides a comprehensive reference to ZLB structure modeling in an applied setting.

Leo Krippner is Senior Advisor to the Research Section of the Economics Department at the Reserve Bank of New Zealand.

Autoren/Hrsg.

Krippner, L.

Inhaltsverzeichnis

1;Cover;1
2;Title;4
3;Copyright;5
4;Dedication;6
5;Contents;8
6;List of Figures;14
7;List of Tables;18
8;Preface;20
9;Acknowledgments;22
10;Selected List of Notation;24
11;Classification and Abbreviations for Term Structure Models;28
12;1 Introduction;30
12.1;1.1 Chapteroverview;31
12.2;1.2 Suggested reading;32
12.2.1;1.2.1 Group 1:Generalmonetary policy readers;33
12.2.2;1.2.2 Group 2:General financialmarket readers;33
12.2.3;1.2.3 Group 3:Termstructuremodelers;33
12.3;1.3 Data;34
12.4;1.4 Availability of results and code;35
12.5;1.5 References to the literature;35
12.6;1.6 Other preliminaries;36
13;2 ANew Framework for a New Environment;37
13.1;2.1 Monetary policy;37
13.1.1;2.1.1 Pre-GFC;37
13.1.2;2.1.2 Post-GFC;42
13.2;2.2 Termstructuremodeling;46
13.2.1;2.2.1 Pre-GFC;47
13.2.2;2.2.2 Post-GFC;51
13.3;2.3 Shadow/ZLBtermstructuremodels;57
13.3.1;2.3.1 ZLBmechanism;57
13.3.2;2.3.2 Options to hold physical currency;64
13.4;2.4 Monetary policy revisited;66
13.5;2.5 AlternativeZLBmodels;68
13.5.1;2.5.1 Square-root termstructuremodels;70
13.5.2;2.5.2 Log-normal termstructuremodels;71
13.5.3;2.5.3 QuadraticGaussian termstructuremodels;71
13.6;2.6 Summary;72
14;3 Gaussian Affine Term StructureModels;73
14.1;3.1 GATSMs;74
14.1.1;3.1.1 GATSMspecification;74
14.1.2;3.1.2 GATSMdynamics and related calculations;76
14.1.3;3.1.3 GATSMtermstructure;79
14.2;3.2 GATSMestimation;79
14.2.1;3.2.1 Kalman filter equations and related parameters;81
14.2.2;3.2.2 Partial estimation;83
14.2.3;3.2.3 Full estimation;85
14.3;3.3 Worked example:ANSM(2);88
14.3.1;3.3.1 ANSM(2) Specification;89
14.3.2;3.3.2 ANSM(2)Termstructure;89
14.3.3;3.3.3 Partial ANSM(2) estimation with the Kalman filter;94
14.3.4;3.3.4 FullANSM(2) estimationwith theKalman filter;98
14.4;3.4 OtherGATSMs;103
14.4.1;3.4.1 ANSM(3);104
14.4.2;3.4.2 Higher-orderANSMs;109
14.4.3;3.4.3 Non-arbitrage-freeANSMs;112
14.4.4;3.4.4 StationaryGATSMs;114
14.4.5;3.4.5 StationaryGATSMswith repeated eigenvalues;118
14.5;3.5 Empirical applications;119
14.5.1;3.5.1 Yield curve data set;119
14.5.2;3.5.2 ANSM(2) results;121
14.5.3;3.5.3 ANSM(3) results;125
14.6;3.6 Alternative estimationmethods;128
14.6.1;3.6.1 Estimation using forward rates;128
14.6.2;3.6.2 Estimation using bond prices;131
14.7;3.7 Summary;131
15;4 Krippner Framework for ZLB Term StructureModeling;133
15.1;4.1 K-AGMexposition;133
15.1.1;4.1.1 K-AGMIntuition;134
15.1.2;4.1.2 K-AGMoption effect;135
15.1.3;4.1.3 K-AGMforward rates;139
15.1.4;4.1.4 Observations on theK-AGMframework;140
15.1.5;4.1.5 Comparison with related results in the literature;142
15.1.6;4.1.6 K-AGMinterest rates and bond prices;143
15.2;4.2 K-AGMestimation;145
15.2.1;4.2.1 K-AGMs and nonlinearKalman filters;145
15.2.2;4.2.2 Partial estimation;146
15.2.3;4.2.3 Full estimation;153
15.3;4.3 Worked example:K-ANSM(2);154
15.3.1;4.3.1 K-ANSM(2) specification;154
15.3.2;4.3.2 K-ANSM(2) shadowtermstructure;156
15.3.3;4.3.3 K-ANSM(2)ZLB termstructure;157
15.3.4;4.3.4 K-ANSM(2)Estimation;158
15.4;4.4 OtherK-AGMs;162
15.4.1;4.4.1 K-ANSM(3);163
15.4.2;4.4.2 Higher-orderK-ANSMs;164
15.4.3;4.4.3 Non-arbitrage-freeK-ANSMs;164
15.4.4;4.4.4 StationaryK-AGMs;167
15.5;4.5 Empirical applications;169
15.5.1;4.5.1 K-ANSM(2) results;169
15.5.2;4.5.2 K-ANSM(3) results;173
15.6;4.6 Alternative estimationmethods;175
15.6.1;4.6.1 Estimation using forward rates;175
15.6.2;4.6.2 Estimation using bond prices;180
15.6.3;4.6.3 Iterative estimation usingGATSMs;183
15.7;4.7 Summary;185
16;5 Black Framework for ZLB Term StructureModeling;187
16.1;5.1 TheB-AGMframework principles;188
16.1.1;5.1.1 Initial comparison of the B-AGM and K-AGM frameworks;192
16.2;5.2 B-AGMimplementation;196
16.2.1;5.2.1 Customized calculationmethods;196
16.2.2;5.2.2 Finite differencemethods;197
16.2.3;5.2.3 Latticemethods;198
16.2.4;5.2.4 MonteCarlomethods;199
16.3;5.3 B-AGMMonteCarlo implementations;200
16.3.1;5.3.1 B-AGMMonteCarlo specification;201
16.3.2;5.3.2 Computing time for B-AGM Monte Carlo simulations;206
16.3.3;5.3.3 Antithetic sampling;208
16.3.4;5.3.4 Other potentially useful standard speed-up methods;209
16.3.5;5.3.5 Worked example:B-ANSM(2);209
16.3.6;5.3.6 OtherB-AGMs;212
16.4;5.4 K-AGM as a control variate for B-AGM Monte Carlo simulations;213
16.4.1;5.4.1 Defining the control variate;214
16.4.2;5.4.2 B-AGM(1) illustration;216
16.4.3;5.4.3 Extensions tomore than one state variable;220
16.5;5.5 B-AGMestimation;226
16.5.1;5.5.1 Partial estimation;227
16.5.2;5.5.2 Full estimation;232
16.5.3;5.5.3 Alternative estimationmethods;234
16.6;5.6 Approximations toB-AGMs;234
16.6.1;5.6.1 K-AGMs as approximations toB-AGMs;234
16.6.2;5.6.2 B-AGMcumulant approximations;239
16.6.3;5.6.3 Non-arbitrage-free B-ANSMs;243
16.6.4;5.6.4 ApplyingB-AGMapproximations;244
16.7;5.7 Summary;245
17;6 K-ANSMFoundations and EffectiveMonetary Stimulus;247
17.1;6.1 Overviewof the economicmodel and its development;248
17.1.1;6.1.1 Establishing theGCE;249
17.1.2;6.1.2 The nominal termstructure in theGCE;250
17.1.3;6.1.3 Amacroeconomic interpretation of theGCE;252
17.1.4;6.1.4 GCE generalizations;253
17.2;6.2 ANSMs as the reduced-formGCE termstructure;254
17.2.1;6.2.1 ANSMspecifications;255
17.2.2;6.2.2 GCE short rate andANSMshort rate;257
17.2.3;6.2.3 GCE and ANSM long-horizon short rate expectations;258
17.2.4;6.2.4 GCE andANSMshort rate expectations;259
17.2.5;6.2.5 Long-run GCE volatility effect and the ANSMLevel volatility effect;263
17.2.6;6.2.6 Other volatility effects;263
17.2.7;6.2.7 Parsimonious ANSMstate equations;268
17.2.8;6.2.8 ANSMmacroeconomic interpretation;273
17.3;6.3 UsingANSMs to represent the shadowtermstructure;275
17.4;6.4 Theoretical case for theK-AGMframework;276
17.4.1;6.4.1 Pricing in the B-AGM and K-AGM frameworks;277
17.4.2;6.4.2 The GCE market portfolio and discount rates without physical currency;280
17.4.3;6.4.3 The market portfolio and discount rates with physical currency;281
17.5;6.5 The EMSmeasure ofmonetary policy;282
17.5.1;6.5.1 EMS Principles;283
17.5.2;6.5.2 K-ANSMEMSmeasure;286
17.5.3;6.5.3 Worked example:K-ANSM(2)EMS;287
17.5.4;6.5.4 K-ANSM(3)EMS;291
17.6;6.6 Summary;298
18;7 Monetary Policy Applications;300
18.1;7.1 OverviewofK-ANSMs, estimation, and empirical results;301
18.2;7.2 Measures of the stance ofmonetary policy;305
18.2.1;7.2.1 Overviewof threemonetary policymeasures;306
18.2.2;7.2.2 Monetary policymeasures in theZLBenvironment;307
18.3;7.3 The ShadowShortRate (SSR);313
18.3.1;7.3.1 Theoretical overview;313
18.3.2;7.3.2 Empirical overview;315
18.3.3;7.3.3 Empirical evidence;316
18.3.4;7.3.4 SSRsummary;321
18.4;7.4 The ExpectedTime toZero (ETZ);322
18.4.1;7.4.1 Theoretical overview;323
18.4.2;7.4.2 Empirical overviewand evidence;324
18.5;7.5 The EffectiveMonetary Stimulus (EMS);324
18.5.1;7.5.1 Theoretical overview;325
18.5.2;7.5.2 Empirical overviewand evidence;327
18.5.3;7.5.3 Linking the SSRand the EMS;332
18.5.4;7.5.4 EMS summary;332
18.6;7.6 K-ANSMmacrofinance relationships;333
18.6.1;7.6.1 K-ANSM Level and long-horizon macroeconomic surveys;334
18.6.2;7.6.2 K-ANSMEMS andmacroeconomic data;336
18.6.3;7.6.3 K-ANSM(3)EMS and currencies;338
18.7;7.7 Summary;343
19;8 FinancialMarket Applications;344
19.1;8.1 Fixed interest portfolio risk;345
19.1.1;8.1.1 Security and portfolio risk;345
19.1.2;8.1.2 Fixed interest security and portfolio risk in non-ZLB environments;346
19.1.3;8.1.3 Fixed interest security and portfolio risk in ZLB environments;349
19.2;8.2 Arisk framework based onANSMs;353
19.2.1;8.2.1 ANSMtermstructure shifts;354
19.2.2;8.2.2 ANSMfactor durations;354
19.2.3;8.2.3 ANSMfixed interest portfolio risk;356
19.3;8.3 Worked example:ANSM(2);358
19.3.1;8.3.1 ANSM(2) yield curve shifts;358
19.3.2;8.3.2 ANSM(2)duration vector;361
19.3.3;8.3.3 Level duration approximation to Level shifts;362
19.3.4;8.3.4 Slope duration approximation to Slope shifts;363
19.3.5;8.3.5 ANSM(2)fixed interest portfolio risk;365
19.3.6;8.3.6 Extension toANSM(3);367
19.4;8.4 Arisk framework based onK-ANSMs;367
19.4.1;8.4.1 K-ANSMyield curve shifts;368
19.4.2;8.4.2 K-ANSMfactor durations;369
19.4.3;8.4.3 K-ANSMfixed interest portfolio risk;371
19.5;8.5 Worked example:K-ANSM(2);372
19.5.1;8.5.1 K-ANSM(2) termstructure specification;372
19.5.2;8.5.2 K-ANSM(2)duration vector;373
19.5.3;8.5.3 Non-ZLBenvironment;373
19.5.4;8.5.4 ZLB environment;379
19.5.5;8.5.5 A perspective on the K-ANSM versus ANSM factor duration results;386
19.6;8.6 Bond option pricing;387
19.6.1;8.6.1 ANSMoption pricing;388
19.6.2;8.6.2 K-AGMoption pricing;391
19.6.3;8.6.3 B-AGMoption pricing;393
19.7;8.7 Summary;395
20;9 Conclusion and Future Research Directions;396
20.1;9.1 Summary;396
20.2;9.2 The case forK-ANSMs;398
20.3;9.3 Future research directions;401
21;Appendix A: Matrix Notation;404
21.1;A.1 Scalars, vectors, andmatrices;404
21.2;A.2 Matrix transpose;405
21.3;A.3 Some special and usefulmatrices;405
21.4;A.4 Matrix addition and subtraction;407
21.5;A.5 Matrixmultiplication;407
21.5.1;A.5.1 Multiplying two vectors;407
21.5.2;A.5.2 Multiplying twomatrices;408
21.5.3;A.5.3 Need for matrix notation in term structure modeling;409
21.5.4;A.5.4 The identitymatrix revisited;409
21.5.5;A.5.5 Powers ofmatrices;410
21.5.6;A.5.6 Multiplying partitionedmatrices;410
21.5.7;A.5.7 Multiplying amatrix by a scalar;410
21.6;A.6 Matrix inverse;411
21.7;A.7 Matrix decompositions;412
21.7.1;A.7.1 Cholesky decomposition;412
21.7.2;A.7.2 Eigensystemdecomposition;412
21.7.3;A.7.3 Jordan decomposition;413
21.7.4;A.7.4 Using eigensystemand Jordan decompositions;415
21.8;A.8 Thematrix exponential;416
21.9;A.9 Matrix calculus;418
22;Notes;420
23;Bibliography;424
24;Index;430