Handbook of Financial Econometrics, Volume 1: Tools and Techniques (Handbooks in Finance)

809 Pages·2009·4.49 MB·English

by  Yacine Ait-Sahalia

Handbook of
FINANCIAL ECONOMETRICS
1
VOLUME
HANDBOOKS
IN
FINANCE
SeriesEditor
WILLIAM T. ZIEMBA
AdvisoryEditors
KENNETH J. ARROW
GEORGE C. CONSTANTINIDES
B. ESPEN ECKBO
HARRY M. MARKOWITZ
ROBERT C. MERTON
STEWART C. MYERS
PAUL A. SAMUELSON
WILLIAM F. SHARPE
Handbook of
FINANCIAL ECONOMETRICS
Tools and Techniques
1
VOLUME
Editedby
YACINEAÏT-SAHALIA
BendheimCenterforFinance
PrincetonUniversity
Princeton,NJ
LARSPETERHANSEN
DepartmentofEconomics
TheUniversityofChicago
Chicago,IL
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09 10 10 9 8 7 6 5 4 3 2 1
INTRODUCTION TO THE SERIES
Advisory Editors
KennethJ.Arrow,StanfordUniversity;GeorgeC.Constantinides,UniversityofChicago;
B. Espen Eckbo, Dartmouth College; Harry M. Markowitz, University of California,
San Diego; Robert C. Merton, Harvard University; Stewart C. Myers, Massachusetts
Instituteof Technology;PaulA.Samuelson,MassachusettsInstituteof Technology;and
William F. Sharpe,Stanford University.
The Handbooks in Finance are intended to be a definitive source for comprehensive and
accessible information. Each volume in the series presents an accurate,self-contained
survey of a subfield of finance,suitable for use by finance and economics professors and
lecturers,professional researchers,and graduate students and as a teaching supplement.
The goal is to have a broad group of outstanding volumes in various areas of finance.
WilliamT. Ziemba
University of British Columbia
v
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CONTENTS
ListofContributors xxv
Volume 1: Tools and Techniques
1 OperatorMethodsforContinuous-TimeMarkovProcesses 1
YacineAït-Sahalia,LarsPeterHansen,andJoséA.Scheinkman
1. Introduction 2
2. AlternativeWaystoModelaContinuous-TimeMarkovProcess 3
2.1. TransitionFunctions 3
2.2. SemigroupofConditionalExpectations 4
2.3. InfinitesimalGenerators 5
2.4. QuadraticForms 7
2.5. StochasticDifferentialEquations 8
2.6. Extensions 8
2.6.1. TimeDeformation 8
2.6.2. SemigroupPricing 10
3. ParametrizationsoftheStationaryDistribution:CalibratingtheLongRun 11
3.1. Wong’sPolynomialModels 12
3.2. StationaryDistributions 14
3.3. FittingtheStationaryDistribution 15
3.4. NonparametricMethodsforInferringDriftorDiffusionCoefficients 18
4. TransitionDynamicsandSpectralDecomposition 20
4.1. QuadraticFormsandImpliedGenerators 21
4.1.1. ImpliedGenerator 21
4.1.2. Symmetrization 23
4.2. PrincipalComponents 24
4.2.1. Existence 25
4.2.2. SpectralDecomposition 27
4.2.3. Dependence 28
4.3. Applications 30
4.3.1. Zipf’sLaw 30
4.3.2. StationarityandVolatility 30
4.3.3. ApproximatingVarianceProcesses 32
4.3.4. ImitatingLongMemoryProcesses 33
vii
viii Contents
5. HermiteandRelatedExpansionsofaTransitionDensity 36
5.1. ExponentialExpansion 36
5.2. HermiteExpansionoftheTransitionFunction 37
5.2.1. ChangeofVariableandRescaling 38
5.2.2. CoefficientsoftheExpansion 39
5.3. LocalExpansionsoftheLog-TransitionFunction 40
5.3.1. Expansionin(cid:2) 41
5.3.2. LeadingTerm 42
5.3.3. NextTwoTerms 43
5.3.4. RemainingTerms 44
5.3.5. ExpansionsinPowersofx−x 44
0
6. ObservableImplicationsandTests 45
6.1. LocalCharacterization 45
6.2. TotalPositivityandTestingforJumps 47
6.3. PrincipalComponentApproach 48
6.4. TestingtheSpecificationofTransitions 49
6.5. TestingMarkovianity 52
6.6. TestingSymmetry 53
6.7. RandomTimeChanges 54
7. ThePropertiesofParameterEstimators 55
7.1. MaximumLikelihoodEstimation 55
7.2. EstimatingtheDiffusionCoefficientinthePresenceofJumps 57
7.3. MaximumLikelihoodEstimationwithRandomSamplingTimes 58
8. Conclusions 61
Acknowledgments 62
References 62
2 ParametricandNonparametricVolatilityMeasurement 67
TorbenG.Andersen,TimBollerslev,andFrancisX.Diebold
1. Introduction 68
2. VolatilityDefinitions 69
2.1. Continuous-TimeNo-ArbitragePriceProcesses 69
2.2. Notional,Expected,andInstantaneousVolatility 74
2.3. VolatilityModelingandMeasurement 82
3. ParametricMethods 84
3.1. Continuous-TimeModels 85
3.1.1. ContinuousSamplePathDiffusions 85
3.1.2. JumpDiffusionsandLévy-DrivenProcesses 90
3.2. Discrete-TimeModels 92
3.2.1. ARCHModels 96
3.2.2. StochasticVolatilityModels 99
Contents ix
4. NonparametricMethods 103
4.1. ARCHFiltersandSmoothers 103
4.2. RealizedVolatility 109
5. DirectionsforFutureResearch 124
Acknowledgments 124
References 124
3 NonstationaryContinuous-TimeProcesses 139
FedericoM.BandiandPeterC.B.Phillips
1. Introduction 140
2. IntuitionandConditions 143
3. ScalarDiffusionProcesses 147
3.1. GeneralizedDensityEstimationforSDPs 151
3.2. NWKernelEstimationoftheInfinitesimalMomentsofanSDP 156
3.2.1. TheChoiceofBandwidth 162
3.3. ExtensionsinKernelEstimationforSDPs 164
3.3.1. Double-Smoothing 164
3.3.2. LocalLinearandPolynomialEstimation 166
3.3.3. FiniteSampleRefinements 168
3.4. UsingNonparametricInformationtoEstimateandTestParametricModels
forSDPs 170
3.5. Time-InhomogeneousSDPs 171
3.6. AnEmpiricalApplication:StochasticVolatility 173
4. ScalarJump-DiffusionProcesses 174
4.1. GeneralizedDensityEstimationforSJDPs 177
4.2. NWKernelEstimationoftheInfinitesimalMomentsofanSJDP 179
4.3. AnEmpiricalApplication:StochasticVolatility 182
5. MultivariateDiffusionProcesses 184
5.1. GeneralizedDensityEstimationforMDPs 188
5.2. NWKernelEstimationoftheInfinitesimalMomentsofanMDP 190
6. ConcludingRemarks 194
Acknowledgments 196
References 196
4 EstimatingFunctionsforDiscretelySampledDiffusion-TypeModels 203
BoMartinBibby,MartinJacobsen,andMichaelSørensen
1. Introduction 204
2. EstimatingFunctions 206
2.1. MartingaleEstimatingFunctions 208
3. EstimatingFunctionsforDiffusion-TypeProcesses 212
3.1. LimitResultsforDiffusionProcesses 213
3.2. MaximumLikelihoodEstimation 215