UnderstandingCredit DerivativesandRelated Instruments
AntulioN.Bomfim
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ICreditDerivatives:Definition,Market,Uses1
1CreditDerivatives:ABriefOverview 3
1.1WhatareCreditDerivatives?.................3
1.2Potential“GainsfromTrade”................5
1.3TypesofCreditDerivatives..................6
1.3.1Single-NameInstruments...............6
1.3.2Multi-NameInstruments...............7
1.3.3Credit-LinkedNotes ..................8
1.3.4Sovereignvs.OtherReferenceEntities........8
1.4ValuationPrinciples......................9
1.4.1FundamentalFactors .................10
1.4.2OtherPotentialRiskFactors.............11
1.4.3StaticReplicationvs.Modeling ............12
1.4.4ANoteonSupply,Demand,andMarketFrictions.14
1.5CounterpartyCreditRisk(Again) ..............15
2TheCreditDerivativesMarket 17
2.1EvolutionandSizeoftheMarket...............18
2.2MarketActivityandSizebyInstrumentType ........19
2.2.1Single-vs.Multi-nameInstruments.........20
2.2.2Sovereignvs.OtherReferenceEntities........21
6CreditDefaultSwaps
16.3ValuingaPrincipal-protectedNote ..............166
16.3.1Examples........................167
16.3.2PPNsvs.VanillaNotes ................168
16.4OtherApplicationsandSomeCaveats............169
17MainCreditModelingApproaches .............. 171
17.1StructuralApproach.....................172
17.1.1TheBlack-Scholes-MertonModel...........172
17.1.2SolvingtheBlack-Scholes-MertonModel .......176
17.1.3PracticalImplementationoftheModel .......178
17.1.4ExtensionsandEmpiricalValidation.........178
17.1.5CreditDefaultSwapValuation............181
17.2Reduced-formApproach...................183
17.2.1OverviewofSomeImportantConcepts........183
17.2.1.1StochasticInterestRates ..........184
17.2.1.2ForwardDefaultProbabilities .......185
17.2.1.3ForwardDefaultRates ...........186
17.2.2DefaultIntensity....................188
17.2.3UncertainTimeofDefault..............190
17.2.4ValuingDefaultableBonds..............191
17.2.4.1NonzeroRecovery.............192
17.2.4.2AlternativeRecoveryAssumptions....193
17.2.5ExtensionsandUsesofReduced-formModels....196
17.2.6CreditDefaultSwapValuation............197
17.3ComparingtheTwoMainApproaches............198
17.4Ratings-basedModels .....................200
18ValuingCreditOptions ..................... 205
18.1Forward-startingContracts..................205
18.1.1ValuingaForward-startingCDS...........206
18.1.2OtherForward-startingStructures..........207
18.2ValuingCreditDefaultSwaptions..............208
18.3ValuingOtherCreditOptions................210
18.4AlternativeValuationApproaches..............211
18.5ValuingBondOptions.....................211
IVIntroductiontoCreditModelingII: PortfolioCreditRisk213
19TheBasicsofPortfolioCreditRisk ............. 215 19.1DefaultCorrelation......................215
19.1.1PairwiseDefaultCorrelation.............216
19.1.2ModelingDefaultCorrelation.............219
19.1.3PairwiseDefaultCorrelationand“β ”........223
19.2TheLossDistributionFunction...............224
19.2.1ConditionalLossDistributionFunction.......225
19.2.2UnconditionalLossDistributionFunction......226
19.2.3Large-PortfolioApproximation............228
19.3DefaultCorrelationandLossDistribution..........230
19.4MonteCarloSimulation:BriefOverview...........231
19.4.1HowAccurateistheSimulation-Based Method?........................233
19.4.2EvaluatingtheLarge-PortfolioMethod.......235
19.5Conditionalvs.UnconditionalLossDistributions......237
19.6ExtensionsandAlternativeApproaches...........238
20ValuingBasketDefaultSwaps ................. 239
20.1BasicFeaturesofBasketSwaps................239
20.2ReexaminingtheTwo-AssetFTDBasket..........240
20.3FTDBasketwithSeveralReferenceEntities.........241
20.3.1ASimpleNumericalExample.............241
20.3.2AMoreRealisticValuationExercise.........243
20.4TheSecond-to-DefaultBasket................246
20.5BasketValuationandAssetCorrelation...........247
20.6ExtensionsandAlternativeApproaches...........248
21ValuingPortfolioSwapsandCDOs .............
21.1ASimpleNumericalExample.................249
21.2Model-basedValuationExercise...............252
21.3TheEffectsofAssetCorrelation...............255
21.4TheLarge-PortfolioApproximation.............257
21.5ValuingCDOs:SomeBasicInsights.............258
21.5.1SpecialConsiderationsforCDOValuation......258 21.6ConcludingRemarks.....................259
22AQuickTourofCommercialModels
22.1CreditMetrics.........................262
22.2TheKMVFramework.....................262
22.3CreditRisk
23ModelingCounterpartyCreditRisk .............
23.1TheSingle-NameCDSasa“Two-AssetPortfolio”.....268
23.2TheBasicModel.......................268
23.3ACDSwithNoCounterpartyCreditRisk..........270
23.4ACDSwithCounterpartyCreditRisk............272
23.4.1AnalyticalDerivationofJoint ProbabilitiesofDefault ................273
23.4.2Simulation-basedApproach..............277
23.4.3AnExample......................278
23.5OtherModelsandApproaches................280
23.6CounterpartyCreditRiskinMulti-nameStructures....281
23.7ConcludingThoughts.....................281
VABriefOverviewofDocumentationand RegulatoryIssues283
24AnatomyofaCDSTransaction 285
24.1StandardizationofCDSDocumentation ...........286
24.1.1EssentialTermsofaCDSTransaction........288
24.1.1.1TheReferenceEntity...........288
24.1.1.2ReferenceandDeliverableObligations..289
24.1.1.3SettlementMethod.............289
24.1.1.4CreditEvents................289
24.1.2OtherImportantDetailsofaCDSTransaction...290
24.1.3AFewWordsofCaution...............291
24.2WhenaCreditEventTakesPlace................291
24.2.1CreditEventNotificationandVerification ......291
24.2.2SettlingtheContract.................292
24.3TheRestructuringDebate..................293
24.3.1ACaseinPoint:Conseco...............294
24.3.2ModifiedRestructuring................295
24.3.3ABifurcatedMarket.................295
24.4ValuingtheRestructuringClause..............296
24.4.1ImplicationsforImpliedSurvivalProbabilities...296
25APrimeronBankRegulatoryIssues ............ 299
25.1TheBaselIICapitalAccord.................300
25.2BaselIIRiskWeightsandCreditDerivatives........302
25.3SuggestionsforFurtherReading...............303
AppendixABasicConceptsfromBondMath
305
A.1Zero-couponBonds......................305 A.2Compounding .........................306
A.3Zero-couponBondPricesasDiscountFactors........307 A.4Coupon-payingBonds.....................307
A.5InferringZero-couponYieldsfromtheCouponCurve....308 A.6ForwardRates .........................309
A.7ForwardInterestRatesandBondPrices ...........310
AppendixBBasicConceptsfromStatistics
B.1CumulativeDistributionFunction..............313
B.2ProbabilityFunction
B.3ProbabilityDensityFunction
B.4ExpectedValueandVariance.................315
B.5BernoulliTrialsandtheBernoulliDistribution.......316
B.6TheBinomialDistribution..................316
B.7ThePoissonandExponentialDistributions.........317
B.8TheNormalDistribution...................320
B.9TheLognormalDistribution
B.10JointProbabilityDistributions
B.11Independence.........................323 B.12TheBivariateNormalDistribution..............323
Definition,Market,Uses
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1 CreditDerivatives:ABriefOverview
Inthischapterwediscusssomebasicconceptsregardingcreditderivatives.Westartwithasimpledefinitionofwhatisacreditderivativeand thenintroducethemaintypesofcreditderivatives.Somekeyvaluation principlesarealsohighlighted.
1.1WhatareCreditDerivatives?
Mostdebtinstruments,suchasloansextendedbybanksorcorporate bondsheldbyinvestors,canbethoughtofasbasketsthatcouldpotentially involveseveraltypesofrisk.Forinstance,acorporatenotethatpromises tomakeperiodicpaymentsbasedonafixedinterestrateexposesitsholders tointerestraterisk.Thisistheriskthatmarketinterestrateswillchange duringthetermofthenote.Forinstance,ifmarketinterestratesincrease, thefixedratewrittenintothenotemakesitalessappealinginvestmentin thenewinterestrateenvironment.Holdersofthatnotearealsoexposedto creditrisk,ortheriskthatthenoteissuermaydefaultonitsobligations. Thereareothertypesofriskassociatedwithdebtinstruments,suchas liquidityrisk,ortheriskthatonemaynotbeabletosellorbuyagiven instrumentwithoutadverselyaffectingitsprice,andprepaymentrisk,or theriskthatinvestorsmayberepaidearlierthananticipatedandbeforced toforegofutureinterestratepayments.
Naturally,marketforcesgenerallyworksothatlenders/investorsare compensatedfortakingonalltheserisks,butitisalsotruethatinvestors havevaryingdegreesoftolerancefordifferenttypesofrisk.Forexample, agivenbankmayfeelcomfortablewiththeliquidityandinterestrate riskassociatedwithafixed-rateloanmadetoXYZCorp.,ahypothetical corporation,especiallyifitisplanningtoholdontotheloan,butitmay benervousaboutthecreditriskembeddedintheloan.Alternatively,an investmentfirmmightwantsomeexposuretothecreditriskassociated withXYZCorp.,butitdoesnotwanttohavetobotherwiththeinterest riskinherentinXYZ’sfixed-rateliabilities.Clearly,boththebankandthe investorstandtogainfromarelativelysimpletransactionthatallowsthe banktotransferatleastsomeofthecreditriskassociatedwithXYZCorp. totheinvestor.Intheend,theywouldeachbeexposedtothetypesofrisks thattheyfeelcomfortablewith,withouthavingtotakeon,intheprocess, unwantedriskexposures.
Assimpleastheaboveexampleis,itprovidesapowerfulrationalefor theexistenceofarapidlygrowingmarketforcreditderivatives.Indeed, creditderivativesarefinancialcontractsthatallowthetransferofcredit riskfromonemarketparticipanttoanother,potentiallyfacilitatinggreater efficiencyinthepricinganddistributionofcreditriskamongfinancialmarketparticipants.Letuscarryonwiththeaboveexample.Supposethebank entersintoacontractwiththeinvestmentfirmwherebyitwillmakeperiodicpaymentstothefirminexchangeforalumpsumpaymentinthe eventofdefaultbyXYZCorp.duringthetermofthederivativescontract.Asaresultofenteringintosuchacontract,thebankhaseffectively transferredatleastaportionoftheriskassociatedwithdefaultbyXYZ Corp.totheinvestmentfirm.(ThebankwillbepaidalumpsumifXYZ defaults.)Inreturn,theinvestmentcompanygetsthedesiredexposureto XYZcreditrisk,andthestreamofpaymentsthatitwillreceivefromthe bankrepresentscompensationforbearingsucharisk.
Itshouldbenotedthatthebasicfeaturesofthefinancialcontractjust describedarebecomingincreasinglycommonintoday’sfinancialmarketplace.Indeedthesearethemaincharacteristicsofoneofthemostprevalent typesofcreditderivatives,the creditdefaultswap.Intheparlanceof thecreditderivativesmarket,thebankintheaboveexampleistypically referredtoas thebuyerofprotection,theinvestmentfirmisknownas the protectionseller,andXYZCorp.iscalled thereferenceentity. 1
1 Thecontractmaybewritteneithertocoverdefault-relatedlossesassociatedwith aspecificdebtinstrumentofthereferenceentityoritmaybeintendedtocover defaultsbyarangeofdebtinstrumentsissuedbythatentity,providedthoseinstrumentsmeetcertaincriteria,whichmayberelatedtothelevelofseniorityinthecapital structureofthereferenceentityandtothecurrencyinwhichtheinstrumentsare denominated.
1.2Potential“GainsfromTrade”
Theprevioussectionillustratedonepotentialgainfromtradeassociated withcreditderivatives.Inparticular,creditderivativesareanimportant financialengineeringtoolthatfacilitatestheunbundlingofthevarioustypesofriskembedded,say,inafixed-ratecorporatebond.Asa result,thesederivativeshelpinvestorsbetteraligntheiractualanddesired riskexposures.Otherrelatedpotentialbenefitsassociatedwithcredit derivativesinclude:
• Increasedcreditmarketliquidity:Creditderivativespotentiallygive marketparticipantstheabilitytotraderisksthatwerepreviously virtuallyuntradeablebecauseofpoorliquidity.Forinstance,arepo marketforcorporatebondsis,atbest,highlyilliquideveninthe mostadvancedeconomies.Nonetheless,buyingprotectioninacredit derivativecontractessentiallyallowsonetoengineerfinanciallyashort positioninabondissuedbytheentityreferencedinthecontract. Anotherexampleregardstheroleofcredit-linkednotes,discussedin Chapter12,whichgreatlyfacilitatethetradingofbankloanrisk.
• Potentiallylowertransactioncosts:Onecreditderivativetransaction canoftenstandinfortwoormorecashmarkettransactions.For instance,ratherthanbuyingafixed-ratecorporatenoteandshortinga governmentnote,onemightobtainthedesiredcreditspreadexposure bysellingprotectioninthecreditderivativesmarket.2
• Addressinginefficienciesrelatedtoregulatorybarriers:Thistopicis particularlyrelevantforbanks.Aswillbediscussedlaterinthis book,bankshavehistoricallyusedcreditderivativestohelpbring theirregulatorycapitalrequirementscloserinlinewiththeireconomic capital.3
Theseandotherapplicationsofcreditderivativesarediscussedfurtherin Chapters2and3.Theyarelargelyresponsiblefortheimpressivegrowthof themarket,morethanoffsettingthepotentiallygrowth-inhibitinginfluence oftheso-calledasymmetric-informationproblemsthatareofteninherent inthetradingofcreditrisk.4
2 Animportantcaveatapplies.Obviously,whetherornotthesingletransactionactuallyresultsinlowercoststotheinvestorthanthetwocombinedtransactionsultimately dependsontherelativeliquidityofthecashandderivativesmarkets.
3 Thenotionsofregulatoryandeconomiccapitalarediscussedingreaterdetailin Chapters3and25.
4 Asymmetric-informationproblemsandtherelatedphenomenaofmoralhazardand adverseselectionarediscussedinChapters14and24.
1.3TypesofCreditDerivatives
Creditderivativescomeinmanyshapesandsizes,andtherearemany waysofgroupingthemintodifferentcategories.Thediscussionthatfollows focusesonthreedimensions:single-namevs.multi-namecreditderivatives, fundedvs.unfundedcreditderivativesinstruments,andcontractswritten oncorporatereferenceentitiesvs.contractswrittenonsovereignreference entities.
1.3.1Single-NameInstruments
Single-namecreditderivativesarethosethatinvolveprotectionagainst defaultbyasinglereferenceentity,suchasthesimplecontractoutlined inSection1.1.Theyarethemostcommontypeofcreditderivativeand accountforthemajorityofthetradingactivityinthemarketplace.Weshall analyzethemingreaterdetaillaterinthisbook.Inthischapter,weonly brieflydiscussthemaincharacteristicsofthemostubiquitoussingle-name instrument,thecreditdefaultswap.
Initsmostcommonor“vanilla”form,acreditdefaultswap(CDS)is aderivativescontractwheretheprotectionbuyeragreestomakeperiodic payments(theswap“spread”orpremium)overapredeterminednumber ofyears(thematurityoftheCDS)totheprotectionsellerinexchangefor apaymentintheeventofdefaultbythereferenceentity.CDSpremiums tendtobepaidquarterly,andthemostcommonmaturitiesarethree, five,andtenyears,withthefive-yearmaturitybeingespeciallyactive. Thepremiumissetasapercentageofthetotalamountofprotectionbought (thenotionalamountofthecontract).
Asanillustration,considerthecasewherethepartiesmightagreethat theCDSwillhaveanotionalamountof$100million:Iftheannualized swapspreadis40basispoints,thentheprotectionbuyerwillpay$100,000 everyquartertotheprotectionseller.Ifnodefaulteventoccursduringthe lifeoftheCDS,theprotectionsellersimplypocketsthepremiumpayments. Shouldadefaulteventoccur,however,theprotectionsellerbecomesliable forthedifferencebetweenthefacevalueofthedebtobligationsissuedby thereferenceentityandtheirrecoveryvalue.Asaresult,foracontractwith anotionalamountof$100,000,andassumingthatthereferenceentities’ obligationsareworth20centsonthedollarafterdefault,theprotection seller’sliabilitytotheprotectionbuyerintheeventofdefaultwouldbe $80,000.5
5 Intheeventofdefault,CDScanbesettledeitherphysically—theprotectionbuyer deliverseligibledefaultedinstrumentstotheprotectionsellersandreceivestheirpar value—orincash—theprotectionsellerpaysthebuyerthedifferencebetweentheface valueoftheeligibledefaultedinstrumentsandtheirperceivedpost-defaultvalue,where
Otherexamplesofsingle-namecreditderivativesincludeassetswaps, totalreturnswaps,andspreadandbondoptions,allofwhicharediscussed inPartIIofthisbook.
1.3.2Multi-NameInstruments
Multi-namecreditderivativesarecontractsthatarecontingentondefault eventsinapoolofreferenceentities,suchasthoserepresentedinaportfolioofbankloans.Assuch,multi-nameinstrumentsallowinvestorsand issuerstotransfersomeorallofthecreditriskassociatedwithaportfolio ofdefaultablesecurities,asopposedtodealingwitheachsecurityinthe portfolioseparately.
Arelativelysimpleexampleofamulti-namecreditderivativeisthefirstto-defaultbasketswap.Consideraninvestorwhoholdsaportfolioofdebt instrumentsissuedbyvariousentitiesandwhowantstobuysomeprotectionagainstdefault-relatedlossesinherportfolio.Theinvestorcanobtain thedesiredprotectionbyenteringintoafirst-to-defaultbasketwithacredit derivativesdealer.Inthiscase,the“basket”iscomposedoftheindividual referenceentitiesrepresentedintheinvestor’sportfolio.Theinvestoragrees tomakeperiodicpaymentstothedealerand,inreturn,thedealerpromises tomakeapaymenttotheinvestorshouldanyofthereferencenamesinthe basketdefaultonitsobligations.Becausethisisafirst-to-defaultbasket, however,thedealer’sobligationunderthecontractislimitedtothefirst default.Thecontractexpiresafterthefirstdefault,andthus,shouldasecondreferencenameinthebasketdefault,thedealerisundernoobligation tocometotheinvestor’srescue,i.e.,theinvestorsuffersthefullextentof anylossesbeyondthefirstdefault.Second-andthird-to-defaultproducts aredefinedinananalogousway.
Multi-namecreditderivativesmaybesetupasaportfoliodefaultswap, wherebythetransferofriskisspecifiednotintermsofdefaultsbyindividualreferenceentitiesrepresentedintheportfoliobutratherintermsof thesizeofthedefault-relatedlossintheoverallportfolio.Forinstance,in aportfoliodefaultswapwitha“first-losspiece”of,say,10percent,protectionsellersareexposedtohowevermanyindividualdefaultsarenecessary toleadtoa10percentlossintheoverallportfolio.Second-andthird-loss portfoliodefaultswapsaredefinedsimilarly.
Portfoliodefaultswapscanbethoughtofasthebuildingblocksfor syntheticcollateralizeddebtobligations(CDOs),whichhavebecomean increasinglyimportantsegmentofthecreditderivativesmarket.Synthetic CDOsandothermulti-namecreditderivativesarediscussedfurtherin Chapters9,10,and14,andinPartIVofthisbook.
thelatterisdeterminedbypollingothermarketparticipants.Chapters6and24take uptheseissuesingreaterdetail.
1.3.3Credit-LinkedNotes
Certaininvestorsarepreventedfromenteringintoderivativescontracts, eitherbecauseofregulatoryrestrictionsorowingtointernalinvestment policies.Credit-linkednotes(CLN)mayallowsuchinvestorstoderivesome ofthebenefitsofcreditderivatives,bothsingle-andmulti-name.
Credit-linkednotescanbebroadlythoughtofasregulardebtobligations withanembeddedcreditderivative.Theycanbeissuedeitherdirectlyby acorporationorbankorbyhighlyratedspecialpurposeentities,often sponsoredbydealers.ThecouponpaymentsmadebyaCLNeffectively transferthecashflowofacreditderivativescontracttoaninvestor.
Credit-linkednotesarebestunderstoodbyasimpleexample:AZZ Investmentswouldliketotakeontheriskassociatedwiththedebtof XYZCorp.,butallofXYZ’sdebtiscomposedofbankloansandAZZ Investmentscannotsimplysellprotectioninacreditdefaultswapbecause itsinvestmentguidelinespreventitfromenteringintoaderivativescontract.LetusassumethatthesizeofAZZInvestments’desiredexposure toXYZCorp.is$100million.OnewayofgainingthedesiredexposuretoXYZ’sdebtisforAZZInvestmentstopurchase$100millionin credit-linkednotesthatreferenceXYZCorp.Theissuerofthenotesmay takeAZZInvestments’$100millionandbuyhighlyrateddebtobligationstoserveascollateralforitsCLNliabilitytowardAZZInvestments. Atthesametime,theCLNissuerentersintoacreditdefaultswap withathirdparty,sellingprotectionagainstadefaultbyXYZCorp. Fromthatpointon,theCLNissuerwillsimplypassthroughthecash flowsassociatedwiththecreditdefaultswap—netofadministrativefees— toAZZinvestments.IntheeventofdefaultbyXYZCorp.,theCLN issuerwillpayitsdefaultswapcounterpartyandthecredit-linkednote terminateswithAZZInvestmentsreceivingonlytherecoveryvalueof XYZ’sdefaulteddebt.Ifnodefaultoccurs,AZZInvestmentswillcontinuetoreceivethecouponpaymentsassociatedwiththecredit-linked noteuntilitsmaturitydate,atwhichpointitwillalsoreceiveitsprincipalback.Itshouldthenbeclearthatacredit-linkednoteissimplya fundedwayofenteringintoacreditderivativescontract.(Indeed,CLNs canbewrittenbasedonmorecomplexcreditderivatives,suchasaportfolio defaultswap.)
1.3.4Sovereignvs.OtherReferenceEntities
Creditderivativescanreferenceeitheracorporateentityorasovereign nation.Forinstance,inadditiontobeingabletobuyandsellprotection againstdefaultbyXYZCorp.,oneisalsoabletobuyandsellprotection againstdefaultby,say,theBrazilianorChinesegovernments.Indeed,the
coremechanismofacreditdefaultswapmarketisessentiallythesame, regardlessofwhetherthereferenceentityisacorporateorasovereign debtor,withthedifferencesinthecontractsshowingupinsomeoftheir clauses.Forexample,contractswrittenonsovereigndebtorsmayinclude moratoriumanddebtrepudiationascreditevents(eventsthatwouldtriggerthepaymentbytheprotectionseller),whereascontractsthatreference corporatedebtgenerallydonotincludesuchevents.
Wherecreditderivativeswrittenonsovereignreferenceentitiesdiffer mostfromthosewrittenoncorporatesisinthegeneralcharacteristics ofthemarketsinwhichtheytrade.Inparticular,contractsthatreferencenon-sovereignnames,especiallythosewrittenoninvestment-grade corporates,arenegotiatedinamarketthatissubstantiallylargerthan thatforcontractsthatreferencesovereigncredits.Limitingfactorsfor themarketforcreditderivativeswrittenonsovereignentitiesincludethe factthattheinvestorbasefornon-sovereigndebtissignificantlylarger thanthatforsovereigndebt.Inaddition,modelingandquantifyingcredit riskassociatedwithsovereigndebtorscanbemorechallengingthandoing soforcorporateborrowers.Forinstance,sovereignentities,especiallyin someemergingeconomies,aremoresubjecttorisksassociatedwithpoliticalinstabilitythanaremostcorporationsbasedindevelopedeconomies. Inaddition,therearemorelimiteddefaultdataforsovereigndebtors thanforcorporations—inpartbecausetherearemorecorporationsthan countries—whichmakesithardertomakestatisticalinferencesbasedon historicalexperience.
1.4ValuationPrinciples
Tounderstandthemainfactorsthatenterintothepricingofcreditderivatives,weneedtoconsidertwobasicprinciples.First,eachpartyinacredit derivativecontractfacescertainrisks.Forinstance,theprotectionselleris exposedtotheriskthatthereferenceentitywilldefaultwhilethecontract isstillinforceandthatitwillhavetostepuptocovertheprotection buyer’sloss.Likewise,theprotectionbuyerisexposedtotheriskthatthe protectionsellermaybeunabletomakegoodonitscommitmentinthe eventofdefaultbythereferenceentity.
Thesecondbasicprincipleinthevaluationofcreditderivativesisthat, aswithanyotherfinancialmarketinstrument,marketforceswillbesuch thatthepartiesinthecontractwillgenerallybecompensatedaccordingto theamountofrisktowhichtheyareexposedunderthecontract.Thus,a firststeptounderstandbasicvaluationprinciplesforcreditderivativesis toexaminethenatureoftherisksinherentinthem.
1.4.1FundamentalFactors
Letusstartbyconsideringthefourmaintypesofriskregardingmostcredit derivativesinstruments:
• thecreditriskofthereferenceentity;
• thecreditriskoftheprotectionseller;
• thedefaultcorrelationbetweenthereferenceentityandtheprotection seller;
• theexpectedrecoveryratesassociatedwiththereferenceentityand theprotectionseller.
Theimportanceofthefirstfactorisclear:Otherthingsbeingequal,the greaterthelikelihoodofdefaultbythereferenceentity,themoreexpensive theprotection,andthusitshouldcomeasnosurprisethatbuyingprotectionagainstdefaultbyacompanywithalowcreditratingcostsmorethan buyingprotectionagainstdefaultbyanAAA-ratedfirm.
Thesecondandthirdfactorshighlightasignificantissueforpurchasers ofprotectioninthecreditdefaultswapsmarket:thecreditqualityofthe protectionseller.Theprotectionsellermayitselfgobankrupteitherbefore oratthesametimeasthereferenceentity.Inmarketparlance,thisiswhat iscalledcounterpartycreditrisk.
Asnotedlaterinthischapter,marketparticipantscommonlyusecreditenhancementmechanisms—suchasthepostingofcollateral—tomitigate theeffectsofcounterpartycreditriskinthedynamicsofthecreditderivativesmarket.Intheabsenceofthesemechanisms,however,otherthings beingequal,thehigherthecreditqualityofagivenprotectionsellerrelativetootherprotectionsellers,themoreitcanchargefortheprotectionit provides.
Regardingitscreditderivativescounterparty,theprotectionbuyeris subjecttotwotypesofrisk:Shouldtheprotectionsellerbecomeinsolvent beforethereferenceentity,theprotectionbuyerisexposedto“replacement risk”ortheriskthatthepriceofdefaultinsuranceonthereferenceentity mighthaverisensincetheoriginaldefaultswapwasnegotiated.Theprotectionbuyer’sgreatestloss,however,wouldoccurwhenboththeprotection sellerandthereferenceentitydefaultatthesametime,andhencethe importanceofhavingsomesenseofthedefaultcorrelationbetweenthe referenceentityandtheprotectionseller.6
Thefourthfactor—expectedrecoveryrates—isparticularlyrelevantfor creditderivativecontractsthatspecifyapayoffintheeventofthedefault
6 TheconceptofdefaultcorrelationisdiscussedinsomedetailinChapters9and10 andinPartIV.
thatdependsonthepost-defaultvalueofthereferenceentity’sdebt. (Thetypicalcreditdefaultswapexamplediscussedaboveisonesuch contract.)Undersuchcircumstances,thelowerthepost-defaultvalueof thedefaulteddebt—whichtheprotectionprovidermayhavetobuyforits parvalueintheeventofdefault—themoreexpensivetheprotection.Asa result,thelowertherecoveryvalueoftheliabilitiesofthereferenceentity, thehigherthecostofbuyingprotectionagainstadefaultbythatentity.
1.4.2OtherPotentialRiskFactors
Arethereotherrisksassociatedwithcreditderivatives?Ifso,howcanone protectoneselffromsuchrisks?Towhichextentdotheserisksaffectthe valuationofcreditderivativescontracts?Hereweshallbrieflydiscusstwo additionaltypesofrisk: • legalrisk • modelrisk
LegalRisk. Considerthecaseofacreditdefaultswap.Therightsand obligationsofeachpartyintheswaparespecifiedinalegallybinding agreementsignedbybothparties—thebuyerandthesellerofprotection. Forinstance,thecontractspecifieswhetherthepaymentsmadebythe protectionbuyerwillbe,say,quarterlyormonthly,andhow,intheevent ofdefault,thecontractwillbesettled.Justasimportant,thecontract willdeterminewhichkindsofeventswould“trigger”apaymentbythe protectionsellerandunderwhichcircumstances.Forexample,suppose thatthereferenceentityrenegotiatesthetermsofitsdebtwithitscreditors. Underwhichconditionswouldthatconstitutea“creditevent”?Arethese conditionsclearlyspecifiedinthecontract?Moregenerally,uncertainty abouthowthedetailsofthecontractwillapplytofutureunforeseenevents constitutes“legalrisk.”
Sincetheearlydaysofthecreditderivativesmarket,itwascleartothose involvedthat,ifthemarketweretoexperienceanymeasureofsuccess,the issueoflegalriskwasonethathadtobeaddressedheadon.Asdiscussedin Chapter24,marketparticipantshaveworkedtogethertocreateandadopt documentationstandardsforcreditderivativescontractswiththeaimof minimizingtheroleoflegalriskinthepricingofthecontracts.Onemight evensaythattheenormousgrowthofthismarketinrecentyearsattests thattheseeffortshavebeenlargelyfruitful.Wesaylargelybecausesome ofthefeaturesofearlycreditderivativescontracts,suchasthetreatment ofdebtrestructurings,mentionedabove,wouldlaterprovetobelessthan satisfactoryintheeyesofmanymarketparticipants.Asthemarkethas evolved,however,sohavedocumentationstandardsandmanyofthe“legal grayareas”ofearliertimeshavebeenworkedoutinmorerecentversions
121.CreditDerivatives:ABriefOverview
ofthecontracts,significantlyreducingthescopeforlegalrisktobean importantfactorinthepricingofcreditderivatives.
ModelRisk. Supposeaprospectiveprotectionbuyerhasgoodestimates ofthecreditqualityofboththeprotectionsellerandthereferenceentity. Assumefurtherthattheprospectivebuyerknowswithcertaintytherecoveryvalueoftheliabilitiesofthereferenceentityandprotectionseller,and thatthereisnolegalrisk.Howmuchshouldthisbuyerbewillingtopay forobtainingprotectionagainstdefaultbythereferenceentity?Likewise, consideraprotectionsellerwhoalsohasgoodestimatesofthecreditqualityandrecoveryrateofthesamereferenceentity.Howmuchshouldthis protectionsellercharge?
Whatthesetwopotentialcreditderivativescounterpartiesneedinorder toagreeonapriceforthecontractisawaytoquantifytheriskfactors inherentinthecontractandthentotranslatethosequantitiesintoa“fair” price.Inotherwords,whattheyneedisanapproachormethodforarriving atadollaramountthatisconsistentwiththeirperceptionoftherisks involvedinthecontract.
Wewillbrieflydiscussdifferentvaluationapproachesinthenextsubsectioninthischapterandthenlookatsomeofthemmorecarefullyin subsequentpartsofthisbook.Fornow,allthatweneedtoknowisthat themerefactthattherearedifferentwaystoarriveatafairvaluationof acreditderivativecontract—andthatdifferentwaysoftendeliverdifferentanswers—suggeststhatthereisalwayssomechancethatone’sfavorite approachormodelmaybewrong.Thisiswhatweshallrefertogenerically as“modelrisk,”ortheriskthatonemayendupunder-oroverestimating thefairvalueofthecontract,perhapsfindingoneselfwithalotmorerisk thanintended.
Weshouldpointoutthatevenifonehastherightmodelfortranslating riskfactorsintofairvaluations,itcouldwellbethatthebasicingredients thatgointothemodel,suchas,forexample,one’sestimateoftherecovery rateassociatedwiththereferenceentity,turnouttobewrong.Eventhe mostreliableofmodelswouldnotbefoolproofundersuchcircumstances. Howdoesoneprotectoneselffrommodelrisk?Onemightsaythatthe answerissimple.Comeupwithapricingmethodologythatisasfoolproof aspossible.Easiersaidthandone.Asweshallseethroughoutthisbook, thereisnoone“correct”method,andthereisneveraguaranteethatwhat workswelltodaywillcontinuetodosonextyearoreventomorrow ...
1.4.3StaticReplicationvs.Modeling
Wehavementionedmodelriskandthefactthatthereisnomagicformulathattellsushowtodeterminethefairvalueofacreditderivative. Thus,marketparticipantsusevariousapproachesforthevaluationofcredit
derivatives.Broadlyspeaking,themainapproachescanbegroupedintwo mainclasses:thosebasedon“staticreplication”methodsandthosethat relymoreheavilyoncreditriskmodels.Wewilldiscussthemainfeaturesoftheseapproachesthroughoutthebook,withtheexamplesofthe staticreplicationapproachshowingupinseveralchaptersinPartIIand thecreditriskmodelingapproachtakingcenterstageinPartsIIIandIV. Fornow,weshalllimitourselvestointroducingsomebasicterminology andtoprovidingthereaderwithaflavorofwhatistocome.
Thebasicideaofthestaticreplicationapproachisthatthepossible payoffsofcertaintypesofcreditderivativescan,inprinciple,bereplicated usingsimplefinancialmarketinstruments,thepricesofwhichmaybe readilyobservableinthemarketplace.7 Forinstance,asdiscussedinPart II,inaliquidmarketwithoutmajorfrictionsandcounterpartycreditrisk, arationalinvestorwouldbeindifferentbetweenbuyingprotectionina creditdefaultswapthatreferencesXYZCorp.orbuyingarisklessfloater whileshortingafloaterissuedbyXYZ—wherebothnoteshavethesame maturityandcashflowdatesasthecreditdefaultswap.Indeed,sucha riskyfloater/risklessfloatercombinationcanbeshowntobethereplicating portfolioforthisCDScontract.
Morespecifically,asdiscussedinChapter6,inafullyliquidmarketwith nocounterpartycreditrisk,allweneedtoknowtodeterminethefairvalue ofaCDSpremiumistheyieldspreadofacomparableriskyfloaterissued bythereferenceentityoverthatofarisklessfloater.Thatisall.Under theseidealizedmarketconditions,oncewedeterminethecompositionof thereplicatingportfolio,thevaluationexerciseisdone.Nocreditriskmodel isrequired!
Someoftheadvantagesofthestaticreplicationapproachincludethefact thatitiscompletelybasedonobservedmarketprices,thatreplicationargumentsarerelativelystraightforwardtounderstand,andthatreplication portfoliosare,inprinciple,easytoimplementformanycommonlynegotiatedcreditderivatives.Therelianceonobservedmarketpricesmeansthat oneshouldbeabletodeterminethefairmarketvalueofacreditdefault swapspreadwithouthavingtoknowthedefaultprobabilitiesassociated withthereferenceentity.Thisisindeedamajoradvantagegiventhatgood modelsofcreditriskcanbeverytechnicallydemanding,nottomention thefactthatnoteventhebestofmodelsisfoolproof.
Nonetheless,therearemanysituationswherethestaticreplication approachisofverylimitedpracticalvalue.Forinstance,considerthe casewheretherearenoreadilyobservedreliablepricesofnotesissued
7 Weusetheterm“staticreplication”torefertosituationswhere,oncethereplicating portfolioissetup,itrequiresnorebalancingduringtheentirelifeofthederivative. Incontrast,theconceptof“dynamicreplication”requiresfrequentrebalancingofthe portfolioifitistoreplicatethecashflowsofthederivative.
bythereferenceentity.Whatisthecreditdefaultswapmarketparticipanttodo?Totakeanotherexampleoflimitedapplicabilityofthe replicationapproach,consideracomplexmulti-namecreditderivative suchasasyntheticCDO.Withmanymulti-nameinstruments,creating thereplicatingportfoliocanbedifficultinpractice,ifnotimpossible. Whatelsecanbedone?Onemustventureintotheworldofcreditrisk modeling.
Creditriskmodelingisthescience,somemightsay“art,”ofwritingdown mathematicalandstatisticalmodelsthatcanbeusedtocharacterizethe fairmarketvalueofdifferentcreditinstrumentssuchascorporatebonds andloansandcreditderivatives.Modelshavetheadvantageofbeingmore widelyapplicablethanmethodsbasedonthestaticreplicationapproach. Forinstance,ifstaticreplicationisnotanoption,onecanpositamodel fortheevolutionofthecreditworthinessofthereferenceentityand,based onthatmodel,inferthecorrespondingprobabilitiesofdefaultandprotectionpremiums.Wehavealludedalreadytosomeofthedrawbacksofthe creditmodelingapproach.Creditmodelscanbedifficulttodevelopand implement,andtheirusersareclearlysubjecttomodelrisk,ortherisk thatthemodelmightfailtocapturesomekeyaspectofreality.
1.4.4ANoteonSupply,Demand,andMarketFrictions
Inprinciple,thepricingofacreditderivativeshouldessentiallyreflect theeconomicfundamentalsofthereferenceentity(ies)andofthecounterparty.Inpractice,however,otherfactorsalsoaffectderivativesprices, drivingawedgebetweenthetheoreticalpricessuggestedbyfundamentals andobservedmarketprices.Forinstance,liquidityinthemarketsforcorporatenotesandcreditderivativescanbesignificantlydifferentandsimple portfolioreplicationapproacheswouldmissthepricingoftheliquiditydifferentialacrossthetwomarkets.Thus,whatmaylooklikeanarbitrage opportunitymaybesimplyafunctionwiththerelativeeaseordifficultyof transactingincorporatenotesvs.increditderivatives.
Otherfactorsincludethefactthatitisoftendifficulttoshortacorporate bond—therepomarketforcorporatebondsisstillatarelativelyearlystage evenintheUnitedStates—andthefactthatthereisstillquiteabitof marketsegmentationwhencreditinstrumentsareconcerned.Forinstance, manyinstitutionsparticipateinthecorporatebondmarket,butnotinthe creditderivativesmarket.
Themainimplicationoftheseandothermarketfrictionsisthatobserved marketpricesforcreditderivativesmayatleasttemporarilydeviatefrom pricesimpliedbyeitherthestaticreplicationorcreditriskmodeling approaches.Thus,whileitistruethatthepriceofacreditderivativescontractshouldreflectthesupplyanddemandfordefaultprotectionregarding theentitiesreferencedinthecontract,becauseofilliquidityormarket
1.5CounterpartyCreditRisk(Again)15
segmentation,supplyanddemandthemselvesmaynotalwaysreflecta pureviewonthecreditriskassociatedwiththoseentities.Itshouldbe noted,however,thatlargediscrepanciesbetweenpricesofcreditderivativesandunderlyingcashinstrumentsareunlikelytopersist:Notonlyare arbitrageursexpectedtotakeadvantageofsuchdiscrepancies,butalsonew participantsmightbeenticedtoenterthemarket,reducingthelimitingrole ofmarketsegmentation.
1.5CounterpartyCreditRisk(Again)
Beforewemoveon,itisworthreturningbrieflytothesubjectofcounterpartycreditrisk.Howdomarketparticipantsaddressthisissue?First, justasonewouldnotbuylifeinsurancefromaninsurancecompanythatis teeteringonthevergeofbankruptcy,oneshouldnotbuydefaultprotection fromacreditderivativesdealerwithapoorcreditstanding.Thisobvious pointexplainswhythemajorsellersofprotectioninthecreditderivatives markettendtobelargehighlyratedfinancialinstitutions.
Second,andperhapsnotasself-evidentasthefirstpoint,potential buyersofdefaultprotectionmightwanttoassesstheextenttowhicheventualdefaultsbyprotectionsellerandthereferenceentityarecorrelated. Forinstance,otherthingsbeingequal,onemaynotwanttobuyprotectionagainstdefaultbyalargeindustrialconglomeratefromabankthat isknowntohaveahugeexposuretothatsameconglomerateinitsloan portfolio.Thebankmaynotbearoundwhenyouneeditmost!
Lastly,acommonapproachusedinthemarketplacetomitigateconcerns aboutcounterpartycreditriskisformarketparticipantstorequireeach othertopostcollateralagainstthemarketvaluesoftheircreditderivatives contracts.Thus,shouldtheprotectionsellerfailtomakegoodonitscommitmentunderthecontract,theprotectionbuyercanseizethecollateral. Indeed,whiletheorywouldsuggestatightlinkbetweenthecreditquality ofprotectionsellersandthepriceofdefaultprotection,inpractice,asis thecasewithothermajortypesofderivatives,suchasinterestrateswaps, theeffectofcounterpartycreditriskinthepricingofcreditdefaultswaps ismitigatedbytheuseofcollateralagreementsamongcounterparties. InChapter2wediscussthenatureoftheseagreementsandotherfactorsthathelpreduce(butnoteliminate)theimportanceofcounterparty creditriskinthevaluationofcreditderivatives.Inaddition,inChapter23 wediscussasimpleframeworkforanalyzingtheroleofcounterpartycredit riskonthevaluationofcreditdefaultswaps.
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“Why not? What is stirring you up to this? Be reasonable, for heaven’s sake. You’ve waited this long.”
“Not a day longer, my friend. Yes, we’ll say eight days, but not an hour longer. But can’t we rely any longer on—?”
“No names, Kesselmeyer.”
“No names. Good. But doesn’t some one rely any longer on his estimable Herr Pa—”
“No hints, either. My God, don’t be a fool.”
“Very good; no hints, either. But have we no claim any longer on the well-known firm with whom our credit stands and falls, my friend? How much did it lose by the Bremen failure? Fifty thousand? Seventy thousand? A hundred thousand? More? The sparrows on the housetops know that it was involved, heavily involved. Yesterday well, no names. Yesterday the well-known firm was good, and it was unconsciously protecting you against pressure. To-day its stock is flat and B. Grünlich’s stock is the flattest of the flat. Is that clear? Do you grasp it? You are the first man to notice a thing like that. How are people treating you? How do they look at you? Beck and Goudstikker are perfectly agreeable, give you the same terms as usual? And the bank?”
“They will extend.”
“You aren’t lying, are you? Oh, no! I know they gave you a jolt yesterday a very, very stimulating jolt eh? You see? Oh, don’t be embarrassed. It is to your interest, of course, to pull the wool over my eyes, so that the others will be quiet. Hey, my dear friend? Well, you’d better write to the Consul. I’ll wait a week.”
“A part payment, Kesselmeyer!”
“Part payment, rubbish! One accepts part payment to convince oneself for the time of a debtor’s ability to pay. Do I need to make experiments of that kind on you? I am perfectly well-informed about your ability to pay. Ah, ha, ah, ha! Part payment! That’s a very good joke.”
“Moderate your voice, Kesselmeyer. Don’t laugh all the time in that cursed way. My position is so serious—yes, I admit, it is serious. But I have such-and-such business in hand—everything may still come out all right. Listen, wait a minute: Give me an extension and I’ll sign it for twenty per cent.”
“Nothing in it, nothing in it, my friend. Very funny, very amusing. Oh, yes, I’m in favour of selling at the right time. You promised me eight per cent, and I extended. You promised me twelve and sixteen per cent, and I extended, every time. Now, you might offer me forty per cent, and I shouldn’t consider it—not for a moment. Since Brother Westfall in Bremen fell on his nose, everybody is for the moment freeing himself from the well-known firm and getting on a sound basis. As I say, I’m for selling at the right time. I’ve held your signatures as long as Johann Buddenbrook was good—in the meantime I could write up the interest on the capital and increase the per cent. But one only keeps a thing so long as it is rising or at least keeping steady. When it begins to fall, one sells—which is the same as saying I want my capital.”
“Kesselmeyer, you are shameless.”
“Ah, ha, a-ha! Shameless, am I? That’s very charming, very funny. What do you want? You must apply to your father-in-law. The Credit Bank is raging—and you know you are not exactly spotless.”
“No, Kesselmeyer. I adjure you to hear me quietly. I’ll be perfectly frank. I confess that my situation is serious. You and the Credit Bank are not the only ones—there are notes of hand—everything seems to have gone to pieces at once!”
“Of course—naturally. It is certainly a clean-up—a liquidation.”
“No, Kesselmeyer; hear me out. Do take another cigar.”
“This one is not half finished. Leave me alone with your cigars. Pay up.”
“Kesselmeyer, don’t let me smash!—You are a friend of mine—you have eaten at my table.”
“And maybe you haven’t eaten at mine?”
“Yes, yes—but don’t refuse me credit now, Kesselmeyer!”
“Credit? It’s credit, now, is it? Are you in your senses? A new loan?”
“Yes, Kesselmeyer, I swear to you— A little—a trifle. I only need to make a few payments and advances here and there to get on my feet again and restore confidence. Help me and you will be doing a big business. As I said, I have a number of affairs on hand. They may still all come out right. You know how shrewd and resourceful I am.”
“I know what a numbskull you are! A dolt, a nincompoop, my dear friend! Will you have the goodness to tell me what your resourcefulness can accomplish at this stage? Perhaps there is a bank somewhere in the wide world that will lend you a shilling? Or another father-in-law? Ah, no; you have already played your best card. You can’t play it twice. With all due respect, my dear fellow, and my highest regards.”
“Speak lower, devil take you!”
“You are a fool. Shrewd and resourceful, are you? Yes, to the other chap’s advantage. You’re not scrupulous, I’ll say that for you, but much good it’s done you! You have played tricks, and wormed capital out of people by hook or crook, just to pay me my twelve or sixteen per cent. You threw your honour overboard without getting any return. You have a conscience like a butcher’s dog, and yet you are nothing but a ninny, a scapegoat. There are always such people —they are too funny for words. Why is it you are so afraid to apply to the person we mean with the whole story? Isn’t it because there was crooked work four years ago? Perhaps it wasn’t all quite straight what? Are you afraid that certain things—?”
“Very well, Kesselmeyer; I will write. But suppose he refuses? Suppose he lets me down?”
“Oh—ah, ha! Then we will just have a bankruptcy, a highly amusing little bankruptcy. That doesn’t bother me at all. So far as I am
concerned, I have about covered my expenses with the interest you have scratched together, and I have the priority with the assets. Oh, you wait; I shan’t come short. I know everything pretty well, my good friend; I have an inventory already in my pocket. Ah, ha! We shall see that no dressing-gown and no silver bread-basket gets away.”
“Kesselmeyer, you have sat at my table—”
“Oh, be quiet with your table! In eight days I’ll be back for the answer. I shall walk in to town—the fresh air will do me good. Good morning, my friend, good morning!”
And Herr Kesselmeyer seemed to depart—yes, he went. She heard his odd, shuffling walk in the corridor, and imagined him rowing along with his arms....
Herr Grünlich entered the “pensée-room” and saw Tony standing there with the little watering-can in her hand. She looked him in the face.
“What are you looking at? Why are you staring like that?” he said to her. He showed his teeth, and made vague movements in the air with his hands, and wiggled his body from side to side. His rosy face could not become actually pale; but it was spotted red and white like a scarlet-fever patient’s.
CHAPTER VII
CONSUL JOHANN BUDDENBROOK arrived at the villa at two o’clock in the afternoon. He entered the Grünlich salon in a grey travelling-cloak and embraced his daughter with painful intensity. He was pale and seemed older. His small eyes were deep in their sockets, his large pointed nose stuck out between the fallen cheeks, his lips seemed to have grown thinner, and the beard under his chin and jaws halfcovered by his stiff choker and high neck-band,—he had lately ceased to wear the two locks running from the temples half-way down the cheeks—was as grey as the hair on his head.
The Consul had hard, nerve-racking days behind him. Thomas had had a haemorrhage; the Father had learned of the misfortune in a letter from Herr van der Kellen. He had left his business in the careful hands of his clerk and hurried off to Amsterdam. He found nothing immediately dangerous about his son’s illness, but an openair cure was necessary, in the South, in Southern France; and as it fortunately happened that a journey of convalescence had been prescribed for the young son of the head of the firm, the two young men had left for Pau as soon as Thomas was able to travel.
The Consul had scarcely reached home again when he was attacked by a fresh misfortune, which had for the moment shaken his firm to its foundations and by which it had lost eighty thousand marks at one blow. How? Discounted cheques drawn on Westfall Brothers had come back to the firm, liquidation having begun. He had not failed to cover them. The firm had at once showed what it could do, without hesitation or embarrassment. But that could not prevent the Consul from experiencing all the sudden coldness, the reserve, the mistrust at the banks, with “friends,” and among firms abroad, which such an event, such a weakening of working capital, was sure to bring in its train.
Well, he had pulled himself together, and had reviewed the whole situation; had reassured, reinforced, made head. And then, in the
midst of the struggle, among telegrams, letters, and calculations, this last blow broke upon him as well: B. Grünlich, his daughter’s husband, was insolvent. In a long, whining, confused letter he had implored, begged, and prayed for an assistance of a hundred to a hundred and twenty thousand marks. The Consul replied curtly and non-committally that he would come to Hamburg to meet Herr Grünlich and Kesselmeyer the banker, made a brief, soothing explanation to his wife, and started off.
Tony received him in the salon. She was fond of receiving visits in her brown silk salon, and she made no exception now; particularly as she had a very profound impression of the importance of the present occasion, without comprehending in the least what it was about. She looked blooming and yet becomingly serious, in her pale grey frock with its laces at breast and wrists, its bell-shaped sleeves and long train, and little diamond clasp at the throat. “How are you, Papa? At last you have come to see us again. How is Mamma? Is there good news from Tom? Take off your things, Father dear. Will you dress? The guest-room is ready for you. Grünlich is dressing.”
“Don’t call him, my child. I will wait for him here. You know I have come for a talk with your husband—a very, very serious talk, my dear Tony. Is Herr Kesselmeyer here?”
“Yes, he is in the pensée-room looking at the album.”
“Where is Erica?”
“Up in the nursery with Tinka. She is very well. She is bathing her doll—of course, not in real water; I mean—she is a wax-doll, she only—”
“Of course.” The Consul drew a deep breath and went on: “Evidently you have not been informed as to—to the state of affairs with your husband.”
He had sat down in an arm-chair near the large table, and Tony placed herself at his feet on a little seat made of three cushions on top of one another. The finger of her right hand toyed gently with the diamond at her throat.
“No, Papa,” answered Tony. “I must confess I know nothing. Heavens, I am a goose!—I have no understanding at all. I heard Kesselmeyer talking lately to Grünlich—at the end it seemed to me he was just joking again—he always talks so drolly. I heard your name once or twice—”
“You heard my name? In what connection?”
“Oh, I know nothing of the connection, Papa. Grünlich has been insufferably sulky ever since that day, I must say. Until yesterday yesterday he was in a good mood, and asked me a dozen times if I loved him, and if I would put in a good word for him with you if he had something to ask you.”
“Oh!”
“Yes, he told me he had written you and that you were coming here. It is good you have. Everything is so queer. Grünlich had the cardtable put in here. There are a lot of paper and pencils on it—for you to sit at, and hold a council together.”
“Listen, my dear child,” said the Consul, stroking her hair. “I want to ask you something very serious. Tell me: you love your husband with your whole heart, don’t you?”
“Of course, Papa,” said Tony with a face of childlike hypocrisy— precisely the face of the child Tony when she was asked: “You won’t tease the old doll-woman again, Tony?” The Consul was silent a minute.
“You love him so much,” he asked again, “that you could not live without him, under any circumstances, even if by God’s will your situation should alter so that he could no longer surround you with all these things?” And his hand described a quick movement over the furniture and portières, over the gilt clock on the étagère, and finally over her own frock.
“Certainly, Papa,” repeated Tony, in the soothing tone she nearly always used when any one spoke seriously to her. She looked past her father out of the window, where a heavy veil of rain was silently
descending. Her face had the expression children wear when some one tells them a fairy story and then tactlessly introduces a generalization about conduct and duty—a mixture of embarrassment and impatience, piety and boredom.
The Consul looked at her without speaking for a minute. Was he satisfied with her response? He had weighed everything thoroughly, at home and during the journey.
It is comprehensible that Johann Buddenbrook’s first impulse was to refuse his son-in-law any considerable payment. But when he remembered how pressing—to use a mild word—he had been about this marriage; when he looked back into the past, and recalled the words: “Are you satisfied with me?” with which his child had taken leave of him after the wedding, he gave way to a burdensome sense of guilt against her and said to himself that the thing must be decided according to her feelings. He knew perfectly that she had not made the marriage out of love, but he was obliged to reckon with the possibility that these four years of life together and the birth of the child had changed matters; that Tony now felt bound body and soul to her husband and would be driven by considerations both spiritual and worldly to shrink from a separation. In such a case, the Consul argued, he must accommodate himself to the surrender of whatever sum was necessary. Christian duty and wifely feeling did indeed demand that Tony should follow her husband into misfortune; and if she actually took this resolve, he did not feel justified in letting her be deprived of all the ease and comfort to which she had been accustomed since childhood. He would feel himself obliged to avert the catastrophe, and to support B. Grünlich at any price. Yet the final result of his considerations was the desire to take his daughter and her child home with him and let Grünlich go his own way. God forbid that the worst should happen!
In any case, the Consul invoked the pronouncement of the law that a continued inability to provide for wife and children justified a separation. But, before everything, he must find out his daughter’s real feelings.
“I see,” he said, “my dear child, that you are actuated by good and praiseworthy motives. But—I cannot believe that you are seeing the thing as, unhappily, it really is—namely, as actual fact. I have not asked what you would do in this or that case, but what you to-day, now, will do. I do not know how much of the situation you know or suspect. It is my painful duty to tell you that your husband is obliged to call his creditors together; that he cannot carry on his business any longer. I hope you understand me.”
“Grünlich is bankrupt?” Tony asked under her breath, half rising from the cushions and seizing the Consul’s hand quickly.
“Yes, my child,” he said seriously. “You did not know it?”
“My suspicions were not definite,” she stammered. “Then Kesselmeyer was not joking?” she went on, staring before her at the brown carpet. “Oh, my God!” she suddenly uttered, and sank back on her seat.
In that minute all that was involved in the word “bankrupt” rose clearly before her: all the vague and fearful hints which she had heard as a child. “Bankrupt”—that was more dreadful than death, that was catastrophe, ruin, shame, disgrace, misery, despair. “He is bankrupt,” she repeated. She was so cast down and shaken by the fatal word that the idea of escape, of assistance from her father, never occurred to her. He looked at her with raised eyebrows, out of his small deep-set eyes, which were tired and sad and full of an unusual suspense. “I am asking you,” he said gently, “my dear Tony, if you are ready to follow your husband into misery?” He realized at once that he had used the hard word instinctively to frighten her, and he added: “He can work himself up again, of course.”
“Certainly, Papa,” answered she. But it did not prevent her from bursting into tears. She sobbed into her batiste handkerchief, trimmed with lace and with the monogram A. G. She still wept just like a child; quite unaffectedly and without embarrassment. Her upper lip had the most touching expression.
Her father continued to probe her with his eyes. “That is your serious feeling, my child?” he asked. He was as simple as she.
“I must, mustn’t I?” she sobbed. “Don’t I have to—?”
“Certainly not,” he said. But with a guilty feeling he added: “I would not force you to it, my dear Tony. If it should be the case that your feelings did not bind you indissolubly to your husband—”
She looked at him with uncomprehending, tear-streaming eyes. “How, Papa?”
The Consul twisted and turned, and found a compromise. “My dear child, you can understand how painful it would be for me to have to tell you all the hardships and suffering that would come about through the misfortune of your husband, the breaking-up of the business and of your household. I desire to spare you these first unpleasantnesses by taking you and little Erica home with me. You would be glad of that, I think?”
Tony was silent a moment, drying her tears. She carefully breathed on her handkerchief and pressed it against her eyes to heal their inflammation. Then she asked tn a firm tone, without lifting her voice: “Papa, is Grünlich to blame? Is it his folly and lack of uprightness that has brought him to this?”
“Very probably,” said the Consul. “That is—no, I don’t know, my child. The explanation with him and the banker has not taken place yet.”
She seemed not to be listening. She sat crouched on her three silk cushions, her elbow on her knee, her chin in her hand, and with her head bowed looked dreamily into the room.
“Ah, Papa,” she said softly, almost without moving her lips, “wouldn’t it have been better—?”
The Consul could not see her face—but it had the expression it often wore those summer evenings at Travemünde, as she leaned at the window of her little room. One arm rested on her Father’s knee, the hand hanging down limply. This very hand was expressive of a sad
