... FIGURE1.7Three-levelfactorstructureinKMV’sGlobalCorrelationModelTM,seealsocomparablepresentationsintheliterature,e.g.Figure9.9.in[21].Firm Risk Systematic Risk Specific Risk Industry Risk Country Risk Industry-Specific Risk Country-Specific Risk Global Economic, Regional, and Industrial Sector Risk Level 1: Composite ... LLCReferences1.1.1TheDefaultProbabilityThetaskofassigningadefaultprobabilitytoeverycustomerinthebank’screditportfolioisfarfrombeingeasy.Thereareessentiallytwoapproachestodefaultprobabilities:•Calibrationofdefaultprobabilitiesfrommarketdata.Themostfamousrepresentativeofthistypeofdefaultprobabil-itiesistheconceptofExpectedDefaultFrequencies(EDF)fromKMV2Corporation.WewilldescribetheKMV-ModelinSection1.2.3andinChapter3.Anothermethodforcalibratingdefaultprobabilitiesfrommarketdataisbasedoncreditspreadsoftradedproductsbearingcredit risk, e.g.,corporatebondsandcreditderivatives(forexample,creditdefaultswaps;seethechapteroncreditderivatives).•Calibrationofdefaultprobabilitesfromratings.Inthisapproach,defaultprobabilitiesareassociatedwithratings,andratingsareassignedtocustomerseitherbyexternalratingagencieslikeMoody’sInvestorsServices,Standard&Poor’s(S&P),orFitch,orbybank-internalratingmethodologies.Be-causeratingsarenotsubjecttobediscussedinthisbook,wewillonlybrieflyexplainsomebasicsaboutratings.AnexcellenttreatmentofthistopiccanbefoundinasurveypaperbyCrouhyetal.[22].Theremainingpartofthissectionisintendedtogivesomebasicindicationaboutthecalibrationofdefaultprobabilitiestoratings.1.1.1.1RatingsBasicallyratingsdescribethecreditworthinessofcustomers.Herebyquantitativeaswellasqualitativeinformationisusedtoevaluateaclient.Inpractice,theratingprocedureisoftenmorebasedonthejudgementandexperienceoftheratinganalystthanonpuremathe-maticalprocedureswithstrictlydefinedoutcomes.ItturnsoutthatintheUSandCanada,mostissuersofpublicdebtareratedatleastbytwoofthethreemainratingagenciesMoody’s,S&P,andFitch.2KMVCorp.,founded13yearsago,headquarteredinSanFrancisco,developsanddis-tributescreditriskmanagementproducts;seewww.kmv.com.©2003 ... LLCInpractice,analyticalapproximationtechniquescanbeappliedquitesuccessfullytoso-calledhomogeneousportfolios.Theseareportfolioswherealltransactionsintheportfoliohavecomparableriskcharacter-istics,forexample,noexposureconcentrations,defaultprobabilitiesinabandwithmoderatebandwidth,onlyafew(better:onesingle!)industriesandcountries,andsoon.Therearemanyportfoliossatisfy-ingsuchconstraints.Forexample,manyretailbankingportfoliosandalsomanyportfoliosofsmallerbankscanbeevaluatedbyanalyticalapproximationswithsufficientprecision.Incontrast,afullMonteCarlosimulationofalargeportfoliocanlastseveralhours,dependingonthenumberofcounterpartiesandthenumberofscenariosnecessarytoobtainsufficientlyrichtailstatisticsforthechosenlevelofconfidence.ThemainadvantageofaMonteCarlosimulationisthatitaccuratelycapturesthecorrelationsinherentintheportfolioinsteadofrelyingonawholebunchofassumptions.Moreover,aMonteCarlosimulationtakesintoaccountallthedifferentriskcharacteristicsoftheloansintheportfolio.ThereforeitisclearthatMonteCarlosimulationisthe“state-of-the-art”increditriskmodeling,andwheneveraportfoliocon-tainsquitedifferenttransactionsfromthecreditriskpointofview,oneshouldnottrusttoomuchintheresultsofananalyticalapproximation.1.2.3ModelingCorrelationsbyMeansofFactorModelsFactormodelsareawellestablishedtechniquefrommultivariatestatistics,appliedincreditriskmodels,foridentifyingunderlyingdriversofcorrelateddefaultsandforreducingthecomputationaleffortregard-ingthecalculationofcorrelatedlosses.Westartbydiscussingthebasicmeaningofafactor.AssumewehavetwofirmsAandBwhicharepositivelycorrelated.Forexample,letAbeDaimlerChryslerandBstandforBMW.Then,itisquitenaturaltoexplainthepositivecorrelationbetweenAandBbythecorrelationofAandBwithanunderlyingfactor;seeFig-ure1.5.Inourexamplewecouldthinkoftheautomotiveindustryas...