Table Of ContentLecture Notes in Statistics 213
Proceedings
Piotr Jaworski
Fabrizio Durante
Wolfgang Karl Härdle Editors
Copulae in
Mathematical
and Quantitative
Finance
Proceedings of the Workshop Held in
Cracow, 10 11 July 2012
–
Lecture Notes in Statistics 213
EditedbyP.Bickel,P.J.Diggle,S.E.Fienberg,U.Gather,
I.Olkin,S.Zeger
Forfurthervolumes:
http://www.springer.com/series/694
Piotr Jaworski Fabrizio Durante
(cid:2) (cid:2)
Wolfgang Karl Ha¨rdle
Editors
Copulae in Mathematical
and Quantitative Finance
Proceedings of the Workshop Held in Cracow,
10-11 July 2012
123
Editors
PiotrJaworski FabrizioDurante
FacultyofMathematics,Informatics, SchoolofEconomicsandManagement
andMechanics FreeUniversityofBozen-Bolzano
UniversityofWarsaw Bozen
Warszawa Italy
Poland
WolfgangKarlHa¨rdle
L.v.BortkiewiczChairofStatistics,C.A.S.E.
CentreforAppliedStatisticsand
Economics
Humboldt-Universita¨tzuBerlin
Berlin
Germany
ISSN0930-0325
ISBN978-3-642-35406-9 ISBN978-3-642-35407-6(eBook)
DOI10.1007/978-3-642-35407-6
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013940256
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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Foreword
The workshop“Copulae in Mathematicaland QuantitativeFinance”took place in
Cracow (Poland)on10th and 11thJuly 2012.Thismeeting was honouredto be a
satelliteeventofthe6thEuropeanCongressofMathematics,whichwasheldinthe
samecitytheweekbefore(2.07.2012–7.07.2012).
The event gathered65 participantsfrom 18 countries, across Europeand other
continents, in the old and prestigious city of Cracow, a pearl of Polish art and
culturalheritageandalsoagreatscientificcentre.Inspiredbytheniceatmosphere
ofthevenuealltheparticipantswereactivelyinvolvedininterestingandstimulating
discussionsaboutcopulatheoryanditsapplications.
The workshopwas precededby a shortcourse “Copulae Calibrationin Theory
and Practise” consisting of two sections organized by Claudia Czado and Eike
Brechmann (Technische Universita¨t Mu¨nchen, Germany) and by Wolfgang K.
Ha¨rdle and Ostap Okhrin (C.A.S.E. Humboldt-Universita¨t zu Berlin, Germany).
The course was particularly devoted both to PhD students and youngresearchers,
who have found challenging ideas about multivariate copula models, and to
practitioners, who have particularly benefited of practical implementation of the
proposedmethodologies.
Asmembersoftheorganizingcommitteeoftheworkshop,wehavetheprivilege
and the great pleasure to present this volume collecting results and achievements
discussedbytheparticipants.Itisanotherconfirmationthattheeventwasfruitfulfor
furtherscientificdevelopments.Therefore,wewouldliketoexpressourgratitudeto
alltheparticipantsfortheirdelightfulcombinationofscholarlyinquiryandcheerful
convivialitywhichconfirmcopulatheorybeingsuchanactiveareaofresearch.
We also would like to acknowledge the support of the institutional organizers
of the workshop: Polish Mathematical Society, C.A.S.E.—Center for Applied
Statistics and Economics (Humboldt-Universita¨t zu Berlin, Germany) and Stefan
Banach International Mathematical Center (Institute of Mathematics of Polish
v
vi Foreword
AcademyofSciences).Moreover,wearehonouredtobesupportedbytheMinistry
ofScienceandHigherEducationoftheRepublicofPoland.
The attendance of specialists from variousresearch groupsaroundthe word as
wellasthesupportoftheinstitutionalorganizersandsponsorsmadetheworkshop
averysuccessfulevent.
Warszawa,Poland PiotrJaworski
Bolzano,Italy FabrizioDurante
Warszawa,Poland KrystynaJaworska
Berlin,Germany OstapOkhrin
January2013
Preface
Thenotionofcopulaprovidesanefficientwaytodescribetheinterrelationshipsof
random variables and offers a great flexibility in building multivariate stochastic
models. Since its discovery in the early 1950s, copulas have contributed to
understandbetter the variousfacets of stochastic dependenceand have allowed to
breakawayfromthestandardassumptions(likemultivariateGaussiandistribution),
whichgenerallyunderestimatetheprobabilityofjointextremerisks.
Nowadays, copula-based dependence models are rapidly gaining considerable
popularityinseveralfieldsandarebecomingindispensabletoolsnotonlyinfinance,
insurance,riskmanagementandeconometricsbutalsoinbiostatistics,hydrologyor
machinelearning.Forexample,theyarewidelyusedforthemodellingofmarket,
credit and operational risk, as well as for the aggregation of risks and portfolio
selection.Moreover,suchalargeinterestintheapplicationsofcopulashasspurred
researchersandscientistsin investigatinganddevelopingnewtheoreticalmethods
andtoolsforhandlingrandomnessanduncertaintyinpracticalsituations.
Theworkshop“CopulaeinMathematicalandQuantitativeFinance”,whichtook
place in Cracow (Poland) on 10th–11thJuly 2012, has representeda good oppor-
tunityforintensiveexchangeofideasaboutrecentdevelopmentsandachievements
thatcancontributetothegeneraldevelopmentofthefield.Thetalkspresentedatthis
eventhavefocusedonseveralinterestingtheoreticalproblemsaswellasempirical
applications.
In orderto makeallthese contributionsavailable to a largeraudience,we have
preparedthisvolumecollectingbothsurveysgivinganup-to-dateaccountofsome
aspectsofcopulamodelsandextendedversionsoftalkspresentedattheworkshop
inCracow.
Our special thanks go to the authors for their willingness to contribute to this
volumeandtoourcolleagueswhosecontributionasreviewerswasessentialinthe
preparationofthevolume.
vii
viii Preface
The professionalwork of the scientific and organizingcommittees was greatly
appreciated,aswellasthesupportoftheco-sponsorsofthisconference.
Finally,weareindebtedtoourpublisherSpringer,inparticulartoAliceBlanck
forherassistanceintheeditorialprocess.
Bolzano,Italy FabrizioDurante
Berlin,Germany WolfgangKarlHa¨rdle
Warszawa,Poland PiotrJaworski
January2013
Contents
1 AConvolution-BasedAutoregressiveProcess........................... 1
UmbertoCherubiniandFabioGobbi
2 SelectionofVineCopulas.................................................. 17
ClaudiaCzado,EikeChristianBrechmann,andLutzGruber
3 CopulasinMachineLearning............................................. 39
GalElidan
4 AnOverviewoftheGoodness-of-FitTestProblemforCopulas....... 61
Jean-DavidFermanian
5 Assessing and Modeling Asymmetry in Bivariate
ContinuousData............................................................ 91
ChristianGenestandJohannaG.Nesˇlehova´
6 Modeling Time-Varying Dependencies Between
Positive-ValuedHigh-FrequencyTimeSeries........................... 115
NikolausHautsch,OstapOkhrin,andAlexanderRistig
7 TheLimitingPropertiesofCopulasUnderUnivariate
Conditioning ................................................................ 129
PiotrJaworski
8 SingularMixtureCopulas................................................. 165
DominicLauterbachandDietmarPfeifer
9 TowardaCopulaTheoryforMultivariateRegularVariation ........ 177
HaijunLi
10 CIIDFrailtyModelsandImpliedCopulas .............................. 201
Jan-FrederikMai,MatthiasScherer,andRudiZagst
11 Copula-BasedModelsforMultivariateDiscreteResponseData...... 231
AristidisK.Nikoloulopoulos
ix
