Table Of ContentADVANCED TEXTS IN ECONOMETRICS
General Editors
Manuel Arellano Guido Imbens Grayham E. Mizon
Adrian Pagan Mark Watson
Advisory Editor
C. W. J. Granger
Other Advanced Texts in Econometrics
ARCH:SelectedReadings
EditedbyRobertF.Engle
AsymptoticTheoryforIntegratedProcesses
ByH.PeterBoswijk
BayesianInferenceinDynamicEconometricModels
ByLucBauwens,MichelLubrano,andJean-Fran¸coisRichard
Co-integration,ErrorCorrection,andtheEconometricAnalysisofNon-StationaryData
ByAnindyaBanerjee,JuanJ.Dolado,JohnW.Galbraith,andDavidHendry
DynamicEconometrics
ByDavidF.Hendry
FiniteSampleEconometrics
ByAmanUllah
GeneralizedMethodofMoments
ByAlastairHall
Likelihood-BasedInferenceinCointegratedVectorAutoregressiveModels
BySørenJohansen
Long-RunEconometricRelationships:ReadingsinCointegration
EditedbyR.F.EngleandC.W.J.Granger
Micro-EconometricsforPolicy,Program,andTreatmentEffect
ByMyoung-jaeLee
ModellingEconometricSeries:ReadingsinEconometricMethodology
EditedbyC.W.J.Granger
ModellingNon-LinearEconomicRelationships
ByCliveW.J.GrangerandTimoTer¨asvirta
ModellingSeasonality
EditedbyS.Hylleberg
Non-StationaryTimesSeriesAnalysisandCointegration
EditedbyColinP.Hargeaves
OutlierRobustAnalysisofEconomicTimeSeries
ByAndr´eLucas,PhilipHansFranses,andDickvanDijk
PanelDataEconometrics
ByManuelArellano
PeriodicityandStochasticTrendsinEconomicTimeSeries
ByPhilipHansFranses
ProgressiveModelling:Non-nestedTestingandEncompassing
EditedbyMassimilianoMarcellinoandGrayhamE.Mizon
ReadinginUnobservedComponents
EditedbyAndrewHarveyandTommasoProietti
StochasticLimitTheory:AnIntroductionforEconometricians
ByJamesDavidson
StochasticVolatility
EditedbyNeilShephard
TestingExogeneity
EditedbyNeilR.EricssonandJohnS.Irons
TheEconometricsofMacroeconomicModelling
ByGunnarB˚ardsen,ØyvindEitrheim,EilevS.Jansen,andRagnarNymoen
TimeSerieswithLongMemory
EditedbyPeterM.Robinson
Time-Series-BasedEconometrics:UnitRootsandCo-integrations
ByMichioHatanaka
WorkbookonCointegration
ByPeterReinhardHansenandSørenJohansen
STOCHASTIC VOLATILITY
Selected Readings
Edited by
NEIL SHEPHARD
1
3
GreatClarendonStreet,Oxfordox26dp
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(cid:1)NeilShephard,2005
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Contents
ListofContributors vii
GeneralIntroduction 1
PartI. Modelbuilding 35
1. ASubordinatedStochasticProcessModelwithFiniteVariance
forSpeculativePrices 37
PeterK.Clark
2. FinancialReturnsModelledbytheProductofTwoStochastic
Processes—AStudyofDailySugarPrices,1961–79 60
StephenJ.Taylor
3. TheBehaviorofRandomVariableswithNonstationary
VarianceandtheDistributionofSecurityPrices 83
BarrRosenberg
4. ThePricingofOptionsonAssetswithStochasticVolatilities 109
JohnHullandAlanWhite
5. TheDynamicsofExchangeRateVolatility:
AMultivariateLatentFactorArchModel 130
FrancisX.DieboldandMarcNerlove
6. MultivariateStochasticVarianceModels 156
AndrewHarvey,EstherRuizandNeilShephard
7. StochasticAutoregressiveVolatility:AFrameworkfor
VolatilityModeling 177
TorbenG.Andersen
8. LongMemoryinContinuous-timeStochasticVolatilityModels 209
FabienneComteandEricRenault
PartII. Inference 245
9. BayesianAnalysisofStochasticVolatilityModels 247
EricJacquier,NicholasG.PolsonandPeterE.Rossi
10. StochasticVolatility:LikelihoodInferenceand
ComparisonwithARCHModels 283
SangjoonKim,NeilShephardandSiddharthaChib
vi Contents
11. EstimationofStochasticVolatilityModelswithDiagnostics 323
A.RonaldGallant,DavidHsiehandGeorgeTauchen
PartIII. Optionpricing 355
12. PricingForeignCurrencyOptionswithStochasticVolatility 357
AngeloMelinoandStuartM.Turnbull
13. AClosed-FormSolutionforOptionswithStochastic
VolatilitywithApplicationstoBondandCurrencyOptions 382
StevenL.Heston
14. AStudyTowardsaUnifiedApproachtotheJointEstimationof
ObjectiveandRiskNeutralMeasuresforthePurposeof
OptionsValuation 398
MikhailChernovandEricGhysels
PartIV. Realisedvariation 449
15. TheDistributionofRealizedExchangeRateVolatility 451
TorbenG.Andersen,TimBollerslev,FrancisX.Diebold
andPaulLabys
16. EconometricAnalysisofRealizedVolatilityanditsuse
inEstimatingStochasticVolatilityModels 480
OleE.Barndorff-NielsenandNeilShephard
AuthorIndex 515
SubjectIndex 523
List of Contributors
Andersen, Torben, Finance Department, Kellogg School of Management,
NorthwesternUniversity,2001SheridanRd,Evanston,IL60208,U.S.A.
Barndorff-Nielsen,OleE.,DepartmentofMathematicalSciences,Universityof
Aarhus,NyMunkegade,DK-8000AarhusC,Denmark.
Bollerslev, Tim, Department of Economics, Duke University, Box 90097,
Durham,NC27708-0097,U.S.A.
Chernov, Mikhail, Columbia Business School, Columbia University, 3022
Broadway,UrisHall413,NewYork,NY10027,U.S.A.
Clark,Peter,GraduateSchoolofManagement,UniversityofCalifornia,Davis,
CA95616-8609,U.S.A.
Comte,Fabienne,UFRBiome´dicale,Universite´ Rene´ Descartes-Paris5,45rue
desSaints-Pe`res,75270Pariscedex06,France.
Diebold, Frank, Department of Economics, University of Pennsylvania, 3718
LocustWalk,Philadelphia,PA19104-6297,U.S.A.
Gallant, A. Ronald, Fuqua School of Business, Duke University, DUMC Box
90120,W425,Durham,NC27708-0120,U.S.A.
Ghysels,Eric,DepartmentofEconomics,UniversityofNorthCarolina–Chapel
Hill,GardnerHall,CB3305ChapelHill,NC27599-3305,U.S.A.
Harvey,Andrew,DepartmentofEconomics,UniversityofCambridge,Sidgwick
Avenue,CambridgeCB39DD,U.K.
Heston, Steven, Department of Finance, Robert H Smith School of Business,
University of Maryland, Van Munching Hall, College Park, MD 20742,
U.S.A.
Hsieh, David, Fuqua School of Business, Duke University, Box 90120, 134
TowerviewDrive,DurhamNC27708-0120,U.S.A.
Hull,John,FinanceGroup,JosephL.RotmanSchoolofManagement,Univer-
sityofToronto,105St.GeorgeStreet,Toronto,OntarioM5S3E6,Canada.
Jacquier,Eric,3000CoteSainte-Catherine,FinanceDepartment,H.E.C.Mon-
treal,MontrealPQH3T2A7,Canada.
Kim,Sangjoon,RBSSecuritiesJapanLimited,RiversideYomiuriBuilding,36-2
Nihonbashi-Hakozakicho,Chuo-ku,Tokyo103-0015,Japan.
Labys,Paul,CharlesRiverAssociates,Inc.,SaltLakeCity,U.S.A.
Melino, Angelo, Department of Economics, University of Toronto, 150 St.
GeorgeStreet,Toronto,OntarioM5S3G7,Canada.
Nerlove,Marc,DepartmentofAgriculturalandResourceEconomics,University
ofMaryland,CollegePark,MD20742,U.S.A.
Polson, Nicholas, Chicago Business School, University of Chicago, 1101 East
58thStreet,Chicago,IL60637,U.S.A.
Renault,Eric,DepartmentofEconomics,UniversityofNorthCarolina,Chapel
Hill,GardnerHall,CB3305ChapelHill,NC27599–3305,U.S.A.
Rosenberg,Barr.
viii ListofContributors
Rossi, Peter, Chicago Business School, University of Chicago, 1101 East 58th
Street,Chicago,IL60637,U.S.A.
Ruiz, Esther, Department of Statistics, Universidad Carlos III de Madrid, C/
Madrid,126–28903,Getafe,Madrid,Spain.
Shephard,Neil,NuffeldCollege,UniversityofOxford,OxfordOX11NF,U.K.
Siddhartha, Chib, John M. Olin School of Business, Washington University in
St.Louis,CampusBox1133,1BrookingsDrive,St.Louis,MO63130,U.S.A.
Taylor,Stephen,DepartmentofAccountingandFinance,ManagementSchool,
LancasterUniversity,LancasterLA14YX,U.K.
Tauchen, George, Department of Economics, Duke University, Box 90097,
Durham,NC27708-0097,U.S.A.
Turnbull,Stuart,DepartmentofFinance,BauerCollegeofBusiness,University
ofHouston,334MelHall,Houston,TX77204-6021,U.S.A.
White, Alan, Finance Group, Joseph L. Rotman School of Management, Uni-
versityofToronto,105St.GeorgeStreet,Toronto,OntarioM5S3E6,Canada.
General Introduction
neil shephard
Overview
Stochastic volatility (SV) is the main concept used in the fields of financial
economics and mathematical finance to deal with time-varying volatility in
financialmarkets.InthisbookIbringtogethersomeofthemainpaperswhich
haveinfluencedthefieldoftheeconometricsofstochasticvolatilitywiththehope
that this will allow students and scholars to place this literature in a wider
context.Wewillseethatthedevelopmentofthissubjecthasbeenhighlymulti-
disciplinary,withresultsdrawnfromfinancialeconomics,probabilitytheoryand
econometrics, blending to produce methods and models which have aided our
understanding of the realistic pricing of options, efficient asset allocation and
accurateriskassessment.
Time-varying volatility and codependence is endemic in financial markets.
Only for very low frequency data, such as monthly or yearly asset returns, do
theseeffectstendtotakeabackseatandtheassumptionofhomogeneityseems
not to be entirely unreasonable. This has been known for a long time, early
comments include Mandelbrot (1963), Fama (1965) and Officer (1973). It was
also clear to the founding fathers of modern continuous time finance that
homogeneity was an unrealistic if convenient simplification, e.g. Black and
Scholes (1972, p. 416) wrote ‘‘...there is evidence of non-stationarity in the
variance. More work must be done to predict variances using the information
available.’’ Heterogeneity has deep implications for the theory and practice of
financial economics and econometrics. In particular, asset pricing theory is
dominatedbytheideathathigherrewardsmaybeexpectedwhenwefacehigher
risks, but these risks change through time in complicated ways. Some of the
changes in the level of risk can be modelled stochastically, where the level of
volatility anddegreeofcodependencebetweenassetsisallowedtochangeover
time.Suchmodelsallowustoexplain,forexample,empiricallyobserveddepart-
ures from Black–Scholes–Merton prices for options and understand why we
should expect to see occasional dramatic moves in financial markets. More
generally, as with all good modern econometrics, they bring the application of
economicsclosertotheempiricalrealityoftheworldwelivein,allowingusto
makebetterdecisions,inspirenewtheoryandimprovemodelbuilding.
