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AssessingthecontributionofsubindexestosystemicriskontheWarsawStockExchange...
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riskintheChinesebankingsectorbyusingDCC-MIDASapproachwiththeStudent’st
distribution.
Someresearcherstakeintoaccounttherestrictiveassumptionofellipticalcon-
ditionaldistributions.Themultivariatedistributionscalledcopulas(Sklar1959)are
foundtobeveryflexibletoolindependencemodelingandriskestimation(Fabozzi
etal.2013,Gongetal.2014,GuloksuzandKumar2020).
OhandPatton(2018)proposednewclassofcopula-baseddynamicmodels.The
factorcopulas(Manneretal.2020)wereusedformodelinghighdimensionalcondi-
tionaldistributions,facilitatingtheestimationofawidevarietyofmeasuresofsystemic
risk.Thenewmodelwasusedtostudyacollectionofdailycreditdefaultswap(CDS)
spreadson100U.S.firms.
Therestofthearticleisorganizedasfollows.Thenextsectionoutlinesthemeth-
odologyapplied.Inthefourthchapterthedatasetandempiricalresultsaredescribed.
Thelastsectionconcludesthepaper.
3.Methodology
Inthissectionwebrieflypresentdynamicmodelandmeasureofsystemicriskthat
areusedinempiricalpartofpaper.
3.1.Dynamicconditionalcorrelationmodel
TheconditionalcorrelationmodelofBollerslev(1990)allowsthetimevarying
covariancematrixtobedecomposedintostandarddeviationsandconstantcorrela-
tions.Tse(2000)andEngleandSheppard(2001)introducedatestforconstantcor-
relationandprovedtheusefulnessofthistest.WetakethemodelsintroducedbyTse
andTsui(2002)andEngle(2002)intoconsiderationwithcorrelationmatrixthatvar-
iesintime.Inbothcasesitisassumedthatobservationsareconditionallymultivariate
normalwithanexpectedvalueofzeroandatime-varyingcovariancematrix.Thenor-
malityassumptionisthereforeveryrestrictive,andthismodelhasundergonemany
modifications.OneofthemistheapplicationofcopulasintroducedbySklar(1959),the
replacementofthemultivariateellipticaldistributionswithcopulas,andthemultivar-
iatecumulativedistributionswithuniform(oninterval[0,1])marginaldistributions.
Let
r
t
=
(
r
mt
ł
r
st
)
′
bethevectorofreturnsofthemainindexandsubindex,respectively.
Sklar’stheoremstatesthatjointdistributionFcanbewrittenas:
F
(|ł
r
t
μ
t
h
t
)
=
CFr
(
m
(
mt
|
μ
mt
ł
h
mt
)
ł
Fr
s
(
st
|
μ
st
ł
h
st
)
)
,
(1)
whereCisacopulafunctionthatdescribesthedependencestructurewhileF
mandF
sare
marginaldistributionfunctions.Thetermsμ
mtandμ
stareconditionalmeanswhileh
mt
andh
stareconditionalvariances,respectively.WefilterthereturnsusingtheVector
AutoregressionModel,whereasconditionalvariancesaremodeledwithGARCH(1,1)
