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1、ReviewofDerivativesResearch,3,263–282(1999)°c2000KluwerAcademicPublishers,Boston.ManufacturedinTheNetherlands.TheDynamicsoftheS&P500ImpliedVolatilitySurfaceGEORGESKIADOPOULOS*gskiadopoulos@hotmail.comAthensDerivativesExchangeResearchandDevelopmentGro
2、up.andAssociateResearchFellowattheFinancialOptionsResearchCentre,Chrisanthemon76,N.Iraklio14121,Athens,GreeceSTEWARTHODGESs.d.hodges@warwick.ac.ukDirectoroftheFinancialOptionsResearchCentre,WarwickBusinessSchool,UniversityofWarwick,CoventryCV47AL,UKL
3、ESCLEWLOWlesclewlow@compuserve.comAssociateResearchFellowattheFinancialOptionsResearchCentreAbstract.Thisempiricalstudyismotivatedbytheliteratureon“smile-consistent”arbitragepricingwithstochasticvolatility.Weinvestigatethenumberandshapeofshocksthatmo
4、veimpliedvolatilitysmilesandsurfacesbyapplyingPrincipalComponentsAnalysis.Twocomponentsareidentifiedunderavarietyofcriteria.Subsequently,wedevelopa“Procrustes”typerotationinordertointerprettheretainedcomponents.Theresultshaveimplicationsforbothoptionp
5、ricingandhedgingandfortheeconomicsofoptionpricing.Keywords:volatilitysmile,volatilitysurface,impliedvolatility,principalcomponentsanalysis.JELclassification:G13.Thedevelopingliteratureon“smileconsistent”no-arbitragestochasticvolatilitymodels(Dupire,19
6、92,1993;DermanandKani,1998;LedoitandSanta-Clara,1998)hasbeenmotivatedbytheneedtopriceandhedgeexoticoptionsconsistentlywiththepricesofstandardEuropeanoptions.Theobjectiveofthispaperistoinvestigatethedynamicsofimpliedvolatilities,sincethisisanecessaryp
7、rerequisitefortheimplementationofthesemodels.Inrecentyearsconsiderableinteresthasfocusedonthebehavioroftheimpliedvolatilitiesofoptionscontracts,derivedfrominvertingBlack–Scholes(1973)model.Theempiricalevidenceshows(seeRubinstein,1985,1994;DermanandKa
8、ni,1998)thatimpliedvolatil-*Wewouldliketothankparticipantsatthe1998meetingsoftheEuropeanandFrenchFinanceAssociations,whereanearlierversionofthispaperwiththetitle“TheDynamicsofSmiles,”waspresented,andespeciallythediscussantsMichaelRockingerandNormanSt
