VaR值计算-参数、半参、非参

CalculateVaRusingthreemethods:Parametric,NonparametricandSemiparametricAbstractValueatrisk(VAR)isastatisticalmeasurementoftotalportfoliorisk,takenastheworstlossataspecificconfidenceleveloverthehorizon.VaRisthedollarorpercentagelossinportfolio(asset)valuethatwillbeequaledorexceededonlyXpercentofthetime.Inotherwords,thereisanXpercentprobabilitythatthelossinportfoliovaluewillbeequaltoorgreaterthantheVaRmeasure.TocalculatetheVaR,therearethreemethods:parametric,nonparametricandsemiparametric.CalculatingparametricVaRisasimplematterbutrequiresassumingthatassetreturnsconformtoastandardnormaldistribution.WeusuallyusehistoricalsimulationmethodasnonparametricmethodtoestimateVaR.Thismethodjustusehistoricaldata,andwedon’tneedtoknowthedistributionoftheassetreturn.Thedistributionisinthedata.Semiparametricmethodisahybridmethod.ItusebothparametricandnonparametricmethodstoestimateVaR.AfterusingnonparametricestimatingVaR,weassumethattheassetreturndensityhasapolynomialefttail,andthetailindexisa.thesemiparametricmodelcombingparametricandnonparametriccomponents.Threemethodshavetheiradvantagesanddisadvantages,wecalculateVaRusingthesemethodsandcontrasttheresultswithoutbacktesting.Butweuset-testtofindifthereexistasignificantdifferencebetweenthethree.Andwefoundthatthesethreeshavenosignificantdifference.Keywords:VaR,parametric,nonparametric,semiparametric1.IntroductionInthisdecadeValueatRisk(VaR)hasbecameaverypopularmeasureofmarketrisk.VaRisthelossontheportfoliothatwillnotbeexceededwithaspecifiedprobabilityoveraspecifiedtimehorizon.VaRisanextremelypowerfulriskmeasure,becauseitcanbecalculatedassuminganykindofdistributionsofportfolioreturns.VaRwasdevelopedasanefficient,inexpensivemethodtodetermineeconomicriskexposureofbankswithcomplexdiversifiedassetsholding.ThemethodtoestimateVaRareoftenasfollowing:parametric,nonprarmetric,semiparametric.ParametricsimulationforestimatingVaRrequirestheassumptionofanormaldistribution.Thisisbecausethemethodutilizestheexpectedreturnandstandarddeviationreturns.Nonparametricsimulationrevaluesaportfoliousingactualvaluesforriskfactorstakenfromhistoricaldata.Butthereisonlyonepathofportfoliovalueandwecouldsufferhighvarianceofriskfactors.Semiparametricsimulationapproachrevaluesaportfoliocombiningparametricandnonparametriccomponents.Inthispaper,weassumetheassetreturnhasapolynomiallefttail.Butitcantakemodelriskiftherealdistributionisdifferentfromassumption.Inthispaper,wecontrastthesethreemethodstocalculateVaRtofindwhichthebettermeasurementis.Weuse20company10yearsstockpriceasourobjections.AndusingRasouranalysistool.2.Valueatriskmethods2.1ParametricmethodTheparametricapproachassumingthatassetreturnsconformtoastandardnormaldistribution.Recallthatastandardnormaldistributionisdefinedbytwoparameters,itsmean(u=0)andstandarddeviation(=1),andisperfectlysymmetricwith50%ofthedistributionlyingtotherightofthemeanand50%lyingtotheleftofthemean.Figure1.VaRestimatingbyparametricmethodFigure1illustratesthestandardnormaldistributionandthecumulativeprobabilitiesunderthecurve.Wehavecriticalz-valuesof-1.28,-1.65,and-2.33for10%,5%,and1%lowertailprobabilities,respectively.WecannowdefinepercentVaRmathematicallyas:zVaRwhere:aRV=theprobabilityvalueatriskz=thecriticalz-valueonthenormaldistributionandtheselectedprobability=thestandarddeviationofdailyreturnsonapercentagebasisThismethodiseasytoimplement,andcalculationscanbeperformedquickly.Buttheassumptionofnormalityistroublesomebecausemanyassetexhibitskewedreturndistribution.Whenadistributionhas“fattail”,VaRwilltendtounderestimatethelossanditsassociatedprobability.Theresultsusingthismethodsasfollowing:Table1.CalculateVaRusingparametricmethodVaR2016.4~2015.42015.4~2014.42014.4~2013.42013.4~2012.42012.4~2011.042011.4~2010.42010.4~2009.42009.4~2008.42008.4~2007.42007.4~2006.4appl0.0320.2030.0240.0330.0270.0400.0250.0580.0470.033ba0.0330.0180.0220.0200.0290.0310.0300.0490.0260.022c0.0350.0190.0230.0310.2420.0340.0720.1680.0450.014cat0.0290.0210.0180.0260.0380.0320.0390.0600.0280.028cvx0.0290.0200.0130.0160.0280.0230.0200.0510.0250.021dis0.0260.0180.0190.0180.0300.0270.0270.0500.0220.017ge0.0380.0140.0160.0180.0280.0340.0390.0670.0210.011gs0.0280.0180.0190.0230.0370.0310.0290.1010.0410.023ibm0.0230.0170.0180.0160.0210.0190.0170.0380.0240.015jpm0.0400.0190.0190.0260.0380.0270.0360.0940.0350.018mcd0.0210.0130.0120.0150.0160.0170.0170.0390.0230.017mmm0.0190.0140.0150.0140.0250.0350.0200.0390.0200.019msft0.0280.0200.0260.0180.0220.0220.0240.0470.0240.020nke0.0270.0190.0180.0190.0270.0310.0450.0800.0350.016pfe0.0280.0160.0170.0140.0230.0200.0210.0390.0190.024pg0.0190.0120.0160.0130.0150.0650.0190.0390.0150.015utx0.0220.0160.0150.0180.0290.0240.0210.0430.0210.019vz0.0280.0150.0180.0140.0160.0200.0180.0470.0270.018wmt0.0220.0140.0140.0150.0150.0130.0140.0310.0250.018xom0.0240.0170.0130.0150.0230.0220.0190.0470.0240.0182.2NonparametricMethodWeusuallyusehistoricalsimulationmethodasnonparametricmethodtoestimateVaR.ThehistoricalmethodsforestimatingVaRisoftenreferredtoasthehistoricalsimulationmethods