金融计量 Chris Brooks

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1、MotivationsofUsingARCHARCHModelsGARCHModelsMultivariateGARCHmodelsFinancialEconometricsLecture5:ModellingVolatilityandCorrelationDayongZhangResearchInstituteofEconomicsandManagementAutumn,2012SouthwesternUniversityofFinanceandEconomicsFinancialEconometricsL

2、ectureNotes5:VolatilityMotivationsofUsingARCHARCHModelsGARCHModelsMultivariateGARCHmodelsLearningOutcomes◮Discussthespecialfeaturesoffinancialdata,motivatetheuseofARCHmodels◮TestforARCHeffectintimeseriesdata◮ContrastvariousmodelsfromtheGARCHfamily◮Maximumlike

3、lihoodestimation◮ConstructmultivariateconditionalvolatilitymodelsSouthwesternUniversityofFinanceandEconomicsFinancialEconometricsLectureNotes5:VolatilityMotivationsofUsingARCHARCHModelsGARCHModelsMultivariateGARCHmodelsFinancialRegularitiesThelinearstructur

4、al(andtimeseries)modelscannotexplainanumberofimportantfeaturescommontomuchfinancialdata.Volatilityclustering:“Largechangestendtofollowbylargechanges,...,andsmallchangestendtofollowbysmallchanges...”.Forexample:.12.08.04.00-.04-.08-.12-.1625507510012515017520

5、0S&P500ReturnsSouthwesternUniversityofFinanceandEconomicsFinancialEconometricsLectureNotes5:VolatilityMotivationsofUsingARCHARCHModelsGARCHModelsMultivariateGARCHmodelsFinancialRegularitiesCont’dLeptokurtosis:fattailsorthicktails.Kurtosismeasuresthepeakedne

6、ssorflatnessofthedistributionoftheseries.KurtosisiscomputedasXN41yi−y¯K=(1)Nσˆi=1Itequals3foranormaldistributionandabove3forleptokurtosis,wherethedistributionispeakedrelativetothenormaldistribution.SouthwesternUniversityofFinanceandEconomicsFinancialEconom

7、etricsLectureNotes5:VolatilityMotivationsofUsingARCHARCHModelsGARCHModelsMultivariateGARCHmodelsLeptokurtosis:exampleSouthwesternUniversityofFinanceandEconomicsFinancialEconometricsLectureNotes5:VolatilityMotivationsofUsingARCHARCHModelsGARCHModelsMultivari

8、ateGARCHmodelsFinancialRegularitiesCont’dLeverageeffects:thatischangesinstockpricestendtobenegativelycorrelatedwithchangesinvolatility,firstnotedbyBlack(1976).Afirmwithdebtandequityoutstandingtypicallybec