Remember, all models,nomatterhow impressive their predictiveability,arestillmodels;
this isanabstractfromreality that needs externalverification.Therefore, it is importantto
vetandtestthe model particularlyforpolicy-orientedissues,suchascapitalallocationfor operationalrisk.Unfortunately, therealityisthat die dataissosparse thatestimatesarevery sensitive toincludingor removingevenasingle observation.
Practically speaking, itwill notbe possibletoadequately judge the predicative abilityof the modelbasedonexistingobservations.Noris it practical towaitfor additional annual observations,evenacrossseveralbanks, toapproach die 1,000-year mark tofit the99,9%
Basel mandate. Further, if such datawereavailable,itwould raise the question about the aggregadon procedureand consistency of the data.Hence,itappears thatwe areatan
impasse,exceptforgoodold-fashionedcommon sense.
©2013Kaplan,Inc.
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KEY CONCEPTS
AIM42.J
Operational lossesacrossmanybusinesslinesfollow heavy-taildistributions,suchas the lognormaldistribution. For reasonable-sizelosses, thedistributionfitisquitegood, but the tallestimation ismuch less precise*
AIM 42.2
Heavy-taildata suffers from:(1) significantvariation in quintileestimatesfrom the infrequentextremelosses,(2) thesum ofoperationallosses isdominated bythefew,large
observations,and (3)mixing heavy-tailandlight-tail distributions resultsinanessentially heavy-tail distribution.
AIM42.3
Heavy-taildatageneratessignificantly largerstandarderrorsof theextremequartile
estimate.Analogously, the confidence intervalsaresignificantly largerthan theyarefor light-taildistributions,all elseequal.
AIM42.4
EVTandGPDare bothvalid modelingchoicesforextremelosses and tailevents,EVT involvesasymptotic propertiesof thetails,whileGPDestimates atail parameter togenerate adistributionbeyondathreshold levelofextremeevents*
AIM42.5
Lossdistributions assumeindependentlyand identicallydistributed variablesacrossand within businesslines.The total loss distributionisthesumof business lineexposures,which
itselfIs thesumwithin each businessline.
AIM42.6
Model validationisnecessary to test theintegrityof themodelanditspredictions.
Unfortunately, theamountofnecessaryavailable data toreliably testmodelsatthe 99-9%
mandate level doesnotyetexist.
Topic
CrossReferencetoCARP Assigned Reading—Cape,Mignola,Antonini,&Ugoccioni
CONCEPT CHECKERS
Whenconsideringsimulated sampledata,toestimatethe 99.9%quantilelevelfor both heavy-tailedandlight-taileddistributions,whichof thefollowing conclusions will resultwhen attemptingtoequatethe confidencelevelsfrom bothtypesof distributions?
A. Light-tail distributions needsignificantly larger samplesizes.
B. Light-tail data willprovideless preciseconfidenceintervals,
C. Heavy-taildistributionsneedsignificandy largersamplesizes.
D. Heavy-taildatawillprovide moreprecise confidence intervals.
Statistical problemsresult whenapplyingtheheavy-tailed natureofoperadonal lossdata toestimate economiccapital.Whichof thefollowingstatementsdoesnot describea resultingstatisticalproblem?
A. The differences between diemeanand varianceof the distributioncan be dramatically differentfrom includingjustasingle,largeextremeloss.
B. Itisnot uncommon for thesingle,largestloss to accountfor the majority of totallossesacrosstheentirefinancialinstitution.
C- Widiin thesameprocess,thelargestfew observationsmayaccountfora
majority of the total lossesinabusinessline.
D. rfligfit-tailedand heavy-taileddistributionsareaggregated, thenit isclear that thelight-tailed distributionwill overwhelm die stable properties of theheavyơ
tailed distribution.
L
2.
Thedecision regardingwhich parametric model to usetolitoperational lossdata dependsondie assumptions of theloss-generatingprocess.Whichof thefollowing
statementsis not anecessary assumption for theloss-generating process?
A. Thereareseveralunderlying loss-gpneratingmechanisms, butsome are more
likely toyieldextreme events.
B. Lossesaregeneratedwhensimulatingeconomiccapitalrequirementsovertime.
C. Asingle loss-generatingmechanism isassumedfor all losses regardlessof source.
D. Theextremeeventsarenot drawnfromaknowndistribution anddonotoffer a patternforestimation.
Extremelosses in the tail of the operationalrisk lossdistribution mostlikely follow whichtypeofprocess/distribution?
A. Generalized Paretodistribution.
B. Historical simulationmethod, C. Poissondistribution,
D. Extremevalue theory.
TheMonteCarlosimulationtechniquefotmodelingtheoperationalloss distributionaggregatesdistribution componentsacrosseventtypesandbusiness lines,asindependenceamong tiiese distributionsis implied.Whichofthefollowing
itemscorrecdyidentifiesoneof theshortcomingsof dieindependenceassumption?
A. The underlyingdistributioncomponentsatestatic,
B. The underlying distributioncomponentsare time-varying.
C. Internal factors diatsimultaneouslyaffectmany large banksarepossible.
D. Changesin regulationwill not affectoperationalrisklosses, 3.
4.
5.
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CONCEPT CHECKER ANSWERS
1. C Toreach thesame jewelof confidence for the quantileestimate,which uses the standard
errorof thequantileestimate, heavy-taildistributions needsignificantly largersamplesizes.
Analogouslyfor thesamesamplesize,theheavy-taildatawillprovidelessprecise(wider) confidence intervalsfor thequantileestimate.
2. D The dominanceofmixtures isoneof theresultingstatisticalproblemswhen using
operationallossdata.Ifthelight-tailedandheavy-tailed distributionsareaggregated,then the heavy-taileddistribution willoverwhelmrhe stable properties of thelight-taileddistribution.
In feet,it isnotuncommonforthesingle, largestloss to accountfor themajorityoftotal lossesacrosstheentirefinancialinstitution.
3. B Three assumptions for the generatingloss dataareasfollows:(1)asingleloss-generating mechanism isassumedfor all lossesregardlessofsource, (2)thereareseveralunderlying loss-generatingmechanisms,hutsome are morelikelytoyieldextremeevents,and (3) the
extreme eventsarcnotdrawnfroma knowndistributionand/or donotoffera patternfor estimation.
4. A GPDaredescribed byatailparameterIfthe datacanreliablyestimatethe tailparameter,the distributionofestimatesbeyondthe threshold will followaGPDdistribution.
5. B Theassumptionofindependence impliesthat theunderlyingdistributioncomponentsarc static whentheyarcinsteadtime-varying. In addition,externalfactors,whichsimultaneously affect all banksarcpossible,suchasregulationimplementation, changesinexchangerates,
and othermacroeconomicfactors.
dieAIMstaiemeuLssetforthbyGART®.Thistopicis also covered in: