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

809 Pages·2009·4.49 MB·English
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Preview Handbook of Financial Econometrics, Volume 1: Tools and Techniques (Handbooks in Finance)

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 Amsterdam•Boston•Heidelberg•London NewYork•Oxford•Paris•SanDiego SanFrancisco•Singapore•Sydney•Tokyo North-HollandisanimprintofElsevier North-HollandisanimprintofElsevier TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK Radarweg29,POBox211,1000AEAmsterdam,TheNetherlands Copyright©2010,ElsevierB.V.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical, includingphotocopying,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfrom thepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthePublisher’spermissionspoliciesandour arrangementswithorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensingAgency,canbe foundatourwebsite:www.elsevier.com/permissions.Thisbookandtheindividualcontributionscontainedinitareprotected undercopyrightbythePublisher(otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenourunderstanding, changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusinganyinformation, methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethodstheyshouldbemindfuloftheir ownsafetyandthesafetyofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliabilityforanyinjury and/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,orfromanyuseoroperationof anymethods,products,instructions,orideascontainedinthematerialherein. BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary LibraryofCongressCataloging-in-PublicationData Applicationsubmitted ISBN:978-0-444-50897-3 ForinformationonallNorth-Hollandpublications visitourwebsiteatwww.elsevierdirect.com Typesetby:diacriTech,India PrintedandboundintheUnitedStatesofAmerica 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 This page intentionally left blank 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

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