Bond pricing and yield-curve modelling : a structural approach

781 Pages·2018·16.34 MB·English

by  Rebonato

BondPricingandYield-CurveModelling
AStructuralApproach
This book provides the theoretical foundations (no-arbitrage, convexity, expecta-
tions,affinemodelling)foratreatmentofgovernmentbondmarkets;presentsand
criticallydiscussesthewealthofempiricalfindingsthathaveappearedintheliter-
atureinthelastdecade;andintroducesthe‘structural’modelsthatareusedbycen-
tralbanks,institutionalinvestors,sovereignwealthfunds,academicsandadvanced
practitionerstomodeltheyieldcurve,toanswerpolicyquestions,toestimatethe
magnitudeoftheriskpremium,togaugemarketexpectationsandtoassessinvest-
mentopportunities.Thebookweavesprecisetheorywithup-to-dateempiricalevi-
dencetobuild,withtheminimummathematicalsophisticationrequiredforthetask,
acriticalunderstandingofwhatdrivesthegovernmentbondmarket.
RiccardoRebonatoisProfessorofFinanceattheEDHECBusinessSchoolandthe
EDHECRiskInstituteandholdstheEDHECPIMCOResearchChair.Hehasbeen
GlobalHeadofFixedIncomeandFXAnalyticsatPIMCOandHeadofResearch,
RiskManagementandDerivativesTradingatseveralmajorinternationalbanks.He
haspreviouslyheldacademicpositionsatImperialCollegeandOxfordUniversity,
andhasbeenaboarddirectorfortheInternationalSwapsandDerivativesAssocia-
tion(ISDA)andtheGlobalAssociationofRiskProfessionals(GARP).Hecurrently
sitsontheboardofTheNineDotsPrize.Heistheauthorofseveralbooksandarti-
clesinfinanceandriskmanagement,includingPortfolioManagementunderStress
(2004).

Bond Pricing and
Yield-Curve Modelling
A Structural Approach
Riccardo Rebonato
EDHECBusinessSchool
EDHECRiskInstitute
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107165854
DOI:10.1017/9781316694169
©RiccardoRebonato2018
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2018
PrintedintheUnitedKingdombyClays,StIvesplc
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ISBN978-1-107-16585-4Hardback
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Tothememoryofmyfather,tomywifeandtomyson,withthanks.

Contents
Acknowledgements pagexxiii
SymbolsandAbbreviations xxv
PartI TheFoundations
1 WhatThisBookIsAbout 3
1.1 MyGoalinWritingThisBook 3
1.2 WhatMyAccountLeavesOut 5
1.3 AffineModels 6
1.4 ASimpleTaxonomy 8
1.5 TheChoiceofVariables 10
1.5.1 LatentversusObservableVariables 10
1.5.2 TheSpanningProblem 15
1.5.3 TheConstraintProblem 16
1.6 WhyDoWeNeedNo-ArbitrageModelsAfterAll? 19
1.7 StampCollectingandShallowversusDeepExplanations 20
1.8 TheIdealReaderandPlanoftheBook 21
2 Definitions,NotationandaFewMathematicalResults 24
2.1 ThePurposeofThisChapter 24
2.2 TheBuildingBlocks 24
2.2.1 Arbitrage 24
2.2.2 Pseudo-Arbitrage 25
2.2.3 SharpeRatios 27
2.2.4 BondPricesandYields 28
2.2.5 DurationandConvexity 31
2.2.6 ForwardRates 32
2.3 LogPricesandLogReturns 33
2.4 DimensionalAnalysis 34
viii Contents
2.5 Appendix2A:VectorsandMatrices 36
2.5.1 Definition 36
2.5.2 TransformationsofVectors 37
2.5.3 OrthogonalMatrices 38
2.5.4 RowVectors 39
2.5.5 ExponentialofaMatrix 40
2.6 Appendix2B:Mean-RevertingandAR(1)Processes 41
2.6.1 TheOrnstein–UhlenbeckProcess 41
2.6.2 TheAR(1)Process 42
2.6.3 ParallelsbetweenAR(1)Processesandthe
Ornstein–UhlenbeckProcess 43
2.7 Appendix2C:SomeResultsfromStochasticCalculus 44
2.7.1 Ito’sLemma 44
2.7.2 Stochastic-CalculusRulesfordpdx 45
t t
2.7.3 ExpectationsofItoIntegrals 46
2.7.4 TheItoIsometry 47
2.7.5 Risk-lessPortfolios 48
3 LinksamongModels,MonetaryPolicyandtheMacroeconomy 49
3.1 ThePurposeofThisChapter 49
3.2 TheMonetaryChannels 50
3.3 AModellingFramework 52
3.4 TheMonetaryActions:ASimpleModel 56
3.5 CalibratingReduced-FormModels 58
3.5.1 GeneralConsiderations 58
3.5.2 AssessingtheQualityoftheCalibrationProcess 60
3.5.3 StateVariablesversusModelParameters 61
4 Bonds:TheirRisksandTheirCompensations 63
4.1 ThePurposeofThisChapter 63
4.2 NominalRates,InflationandRealRates:AQualitative
Discussion 64
4.2.1 InflationRisk 64
4.2.2 Real-RateRisk 65
4.2.3 PuttingthePiecesTogether 66
4.3 Real-WorldandRisk-NeutralProbabilities:TheMarket
PriceofRisk 68
4.3.1 IntroducingthePandQMeasures 69
4.3.2 IntroducingtheMarketPriceofRisk 72
4.4 AnImportantFirstResult:BondPricesasQ-Expectations 76
4.5 ThePriceProcessandItsExpectations 77
4.5.1 TheGeneralCase 77
Contents ix
4.5.2 TheAffineCase 78
4.6 NominalRates,InflationandRealRates:Definitions 79
5 TheRiskFactorsinAction 81
5.1 ThePurposeofThisChapter 81
5.2 ExpectationsandRiskPremiaduringanImportantMarket
Period 81
5.2.1 AnAccountofWhatHappened 81
5.2.2 PossibleExplanationsofWhatHappened 85
5.3 HowCanWeEstimateRiskPremia? 87
5.4 DifferentTypesofRiskPremia 88
5.5 WhatAreInvestorsCompensatedFor? 91
5.5.1 DecompositionoftheRiskPremium 91
5.5.2 ‘Which’LiquidityAreTIPS-Investors
CompensatedFor? 93
5.6 WhatIsandWhatIsNotaTrueRiskPremium 94
5.7 DoesItMatterifaRiskPremiumIs‘Really’aRisk
Premium? 96
6 PrincipalComponents:Theory 98
6.1 ThePurposeofThisChapter 98
6.2 WhatArePrincipalComponents? 98
6.2.1 TheAxisRotation 98
6.2.2 TheSignalandtheNoise 103
6.3 HowManyPrincipalComponentsDoWeNeedforYields? 103
6.4 FirstConclusions 104
6.5 SomeMathematicalResults 105
7 PrincipalComponents:EmpiricalResults 108
7.1 ThePurposeofThisChapter 108
7.2 NominalRates 108
7.2.1 DescriptiveFeatures 108
7.2.2 Mean-RevertingProperties–EachPCinIsolation 112
7.2.3 TheJointMean-RevertingBehaviourofPrincipal
Components 116
7.3 RealRatesandBreak-EvenInflation 122
7.4 CorrelationbetweenNominal,InflationandRealPrincipal
Components 128
PartII TheBuildingBlocks:AFirstLook
8 Expectations 137
8.1 ThePurposeofThisChapter 137