Copulae in Mathematical and Quantitative Finance: Proceedings of the Workshop Held in Cracow, 10-11 July 2012 PDF
Preview Copulae in Mathematical and Quantitative Finance: Proceedings of the Workshop Held in Cracow, 10-11 July 2012
Lecture 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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) 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
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