GARCH-(1-1)英文介绍(附R语言).pptx

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1、GARCH101Introductionoftheuseofgarch/archmodels1CissyEngle,R.(2001)."GARCH101:TheUseofARCH/GARCHModelsinAppliedEconometrics."JournalofEconomicPerspectives15(4):157-168.OUTLINECOMPARISONWITHOLSWHENTOUSEGARCH/ARCHDEVELOPMENTOFGARCH/ARCHFUNCTIONOFASSETRETURNGARCHSPECIFICATIONASI

2、MPLEEXAMPLEOFGARCH(1,1)AVALUE-AT-RISKEXAMPLEGARCHIMPLEMENTINR2COMPARISONWITHOLSOLSGARCHDeterminationHowmuchonevariablechangesinresponsetoanothervariablechangeSizeoferror,i.e.volatilityAssumptionhomoskedasticityheteroskedasticityStandarderrorsTobecorrectedTobemodeled3WHENTOUSE

3、GARCH/ARCHDependentvariableisreturnonanassetorportfolio;varianceisrisklevel;Magnitudeoferrortermsvariesovertime;Goalistomeasurevolatility(financialdecision)----riskanalysis,portfolioselection,andderivativepricing.(Generalized)AutoRegressiveConditionalHeteroskedasticity(GARCH/

4、ARCH)isdesignedtosolvetheseissues.4Weightsnevergozerocompletely.DEVELOPMENTOFGARCH/ARCHRollingstandarddeviationARCHGARCHWeightsaretobeestimatedVarianceoftomorrow’sreturnisequallyweightedaverageoffixednumberofmostrecentobservations5FUNCTIONOFASSETRETURN:returnonanassetorportfo

5、lio;:meanvalueof,whichisexpectedvaluebasedonpastinformation;:standarddeviationof:errortermforthepresentperiod6GARCHSPECIFICATIONF(varianceofnextperiod)=weightedaverageoflongrunaveragevariance+variancepredictedforthisperiod(ARCHterm)+newinformationinthisperiod(GARCHterm)GARCH(

6、1,1):，，，areweightsrespectively.And<1Aftercollation,theGARCHmodellookslike:7ASIMPLEEXAMPLEOFGARCH(1,1)8GARCH(1,1):Example:atraderknowsthatlong-runaveragedailystandarddeviationoftheS&P500is1%,theforecasthemadeyesterdaywas2%,andtheunexpectedreturnobservedtodayis3%,weightsforthea

7、bovereturnare0.02,0.9,0.08.Whatistheexpectedreturnfortomorrow?Answer:COMPUTATIONOFGARCHF(varianceofperiod1)=weightedaverageoflongrunaveragevariance+variancepredictedforperiod0+newinformationinperiod0F(varianceofperiod2)=weightedaverageoflongrunaveragevariance+variancepredicte

8、dforperiod1+newinformationinperiod1………F(varianceofperiodn)=weighteda