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1、10AppliedVolatilityandCorrelationModellingUsingExcel∗FRED´ERICKBOURGOIN´ABSTRACTThischapterimplementsarangeofunivariateandmultivariatemodelswithinMicrosoftExcel.Thisisextremelyusefulasalargeproportionoffinanceprofessionals,studentsandresearchersthatarefamiliarwiththispackage.Weshowhowtoge
2、nerateone-stepaheadforecastsofvolatilityusingtheJPMorganRiskMetricsmodel,JPMorganRiskMetricsmodelwithanoptimaldecay,aGARCHmodelwithandwithoutavariancereductiontechniqueandfinallyusingtheGJRmodeltoaccountforasymmetricreactiontonews.Acomparisonofforecastsismadeandsomeusefulinsightstotheeffic
3、iencyofthemodelsishighlighted.Inthesecondpartofthischapter,wemodelthetime-varyingcorrelationusingdifferentmodels.AswiththeunivariateapproachthisincludestheJPMorganRiskMetricsmodelwithandwithoutoptimaldecay,aGARCHmodelwithandwithoutvariancereductionandfinallytheso-called“FastGARCH”modelofw
4、hichtheauthorhaspreviouslymadesignificantcontributionstotheliterature.10.1INTRODUCTIONThepracticabilityofmultivariateGARCHmodelshasbeenthesubjectofseveralarticlesinthepastfewyears,particularlyregardingthefeasibilityoflargesizeproblems(Athayde,2001;Bourgoin,2000,2002;EngleandMezrich,1995,1
5、996;DingandEngle,1994;Ledoit,2001;Ledoitetal.,2001).Somemodelsworkwellonlyonspecificdata,liketheorthogonalGARCH(AlexanderandChibumba,1997)withyieldcurveortermstructureofimpliedvolatilities(seeBourgoin(2000)forthereasons).Becauseallthesemodelsrequirecomplexoptimisationroutinesandtricks,GAR
6、CHmodelshavealwaysrequiredspecialsoftwarelikeRats(RegressionAnalysisofTimeSeries),Eviews,Matlab,S-Plus,Gauss,OxorevenspecialC++code.Inthischapter,wewilltrytoprovideanunderstandablewaytoconstructGARCHmodels,bothunivariateandmultivariatemodels,usingExcel,themostwidelyusedfinancialapplicatio
7、ninthemarketplace.TwoExcelspreadsheetsareprovidedontheCD-Rom,onefortheunivariatemodelsandanotheroneforthemultivariatemodels(Bourgoin001.xls,andBourgoin002.xls,respectively).∗TheviewsexpressedhereinarethoseoftheauthoranddonotnecessarilyreflecttheviewsofBarclaysGlobalInvesto
