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1、TheAnnalsofAppliedStatistics2009,Vol.3,No.1,422–457DOI:10.1214/08-AOAS200cInstituteofMathematicalStatistics,2009HIGHFREQUENCYMARKETMICROSTRUCTURENOISEESTIMATESANDLIQUIDITYMEASURESByYacineA¨ıt-Sahalia1,2andJialinYu2PrincetonUniversityandColumbiaUniversityUsingrecentadvancesinthee
2、conometricsliterature,wedisen-tanglefromhighfrequencyobservationsonthetransactionpricesofalargesampleofNYSEstocksafundamentalcomponentandamicrostructurenoisecomponent.Wethenrelatethesestatisticalmeasurementsofmarketmicrostructurenoisetoobservablecharac-teristicsoftheunderlyingst
3、ocksand,inparticular,todifferentfi-nancialmeasuresoftheirliquidity.Wefindthatmoreliquidstocksbasedonfinancialcharacteristicshavelowernoiseandnoise-to-signalratiomeasuredfromtheirhighfrequencyreturns.Wethenexaminewhetherthereexistsacommon,market-wide,factorinhighfrequencystock-levelm
4、easurementsofnoise,andwhetherthatfactorispricedinassetreturns.1.Introduction.Understandingvolatilityanditsdynamicsliesattheheartofassetpricing.Astheprimarymeasureofriskinmodernfinance,volatilitydrivestheconstructionofoptimalportfolios,thehedgingandpric-ingofoptionsandotherderivat
5、ivesecuritiesorthedeterminationofafirm’sexposuretoavarietyofriskfactorsandthecompensationitcanexpecttoearnfromthoseriskexposures.Italsoplaysacriticalroleindiscoveringtradingandinvestmentopportunitieswhichprovideanattractiverisk-returntrade-off.Itisthereforenotsurprisingthatvolatil
6、ityestimationandinferencehasattractedmuchattentioninthefinancialeconometricandstatisticalliter-ature,includingtheseminalARCHmodelofEngle(1982).Indeed,manyarXiv:0906.1444v1[stat.AP]8Jun2009estimatorsareavailabletomeasureanasset’svolatilityfromadiscretepricesample.Butatleastinthefr
7、ameworkofparametricmodels,onewilloftenstartwiththesumofsquaredlog-returns,asnotonlythesimplestandmostReceivedAugust2007;revisedFebruary2008.1SupportedinpartbyNSFGrantsSES-03-50772andDMS-05-32370.2SupportedbytheMorganStanleyequitymarketmicrostructureresearchgrant.Keywordsandphras
8、es.Marketmicrostructurenoise,robustvolatilityes