Credit risk 1.1~1.2

1. Credit risk1.1~1.2 指導教授:戴天時 學 生:施嘉紋

2. IntroductiontoCreditRisk • Defaultrisk aprobabilitythatacounterpartyinafinancialcontractwillnotfulfillacontractualcommitmenther/hisobligationsstatedinthecontract. • Creditrisk theriskassociatedwithanykindofcredit-linkedevents. • Spreadrisk anothercomponentsofcreditrisk

3. IntroductiontoCreditRisk • Reference(credit)risk assumebothpartiesofacontracttobedefault-free It’sapartyofthecontract’sriskwhichisassociatedwiththethirdparty(thereferenceentityofagivencontract). • Creditderivatives developedfinancialinstrumentsthatallowmarketparticipantstoisolateandtradethereferencerisk. main:transferthereferenceriskbetweenthecounterparties. • sellerofreferencerisk buyerofaninsuranceagainstthereferencerisk. • buyerofreferencerisk bearthereferencerisk.

4. IntroductiontoCreditRisk • Counterparty(credit)risk 1.over-thecounterderivativesisunlikethe exchange-tradecontracts,theyarenot backedbytheguaranteeofaclearinghouse oranexchange. 2.Itemergesinaclearwayinsuchcontractsasvulnerableclaimsanddefaultableswaps. • vulnerableclaimsanddefaultabnleswapsneedtoquantifythedefaultriskofbothparties. • unilateral(one-sided)/bilateral(two-sided)risk thedefaultrisktakesintoaccountoneortwoparties.

5. 1.1CorporateBonds • CorporateBonds 1.debtinstrumentsissuedbycorporate 2.apartofthecapitalstructureofthefirm(justliketheequity). 3.makespecifiedpaymentstothebondholder 4.corporatemaydefaultwhichthebondholderswillnotreceivethepromisedpaymentinfull,theywillsufferafinancialloss. • theoccurrenceofdefault, possiblycausedbythefirm’sbankruptcy,ismeaningfulduringthethetimeperiodbetweenthebond’sinceptionanditsmaturity. • Acorporatebondisanexampleofadefaultableclaim

6. 1.1CorporateBonds • 符號介紹 Facevalue=L,maturity=T D(t,T):thearbitragepriceattimetofaT- maturitydefaultablebond B(t,T):thearbitragepriceattimetofaT- maturitydefault-freebondwithfacevalue=1 D(T,T)=LB(T,T)=1 • Discountbond thebondpaysnocoupons • thedefaultabletermstructure thetermstructureofinterestratesimpliedbytheyieldsonthedefaultpronecorporatebondsoronthedefaultpronesovereignbonds

7. 1.1CorporateBonds • Thedefault-freebond payssurelyboththecouponsandthefacevaluetothebondholderspredetermineddates. • 1.Thedefaultbond:riskybonds 2.Thedefault-freebond:risk–freebondsorTreasurybonds. theyexposedtothemarket(interestrate)risk 3. adjectivedefault-free referstopresumedabsenceofthecreditriskinbondsof highestcreditquality. • themathematicaltechniquespresentedinthisareapplicabletothevaluationofgeneralcorporateliabilities,suchascorporatebonds.Butcorporateloansisanotherone.

8. 1.1.1RecoveryRules • Thespecificrecoveryruleswilltypicallyincludeclausessuchasprioritypaymentsupondefaultbasedonthedebt’sseniority(seniorityrulesorprioritystructure) • Recoveryschemes(orrecoverycovenantsorrecoveryrules) determinethetimingandtheamountofrecoverypaymentsthatispaidtocreditorsifthedefaultoccursbeforethebond’smaturity.

9. 1.1.1RecoveryRules

10. 1.1.1RecoveryRules

11. 1.1.1RecoveryRules • LGD:lossgivendefault LGD=1-δ • workonthecreditrisk assumption: thebonddefaultduringitslifetimethentherecoverypaymentismadeeitheratτoratT 1. recoverypaymentdeterminedatτand determinedbythevalueZτatτoftherecoveryprocess Ztermeddefaultableclaimswithrecoveryatdefault 2. recoverypaymentdeterminedatTand determinedbyrecoveryclaim termeddefaultableclaimswithrecoveryatmaturity

12. 1.1.1RecoveryRules • Itshouldbestressedrecoveryprocessand/ortherecoveryvaluemaybespecificeitherexogenouslyorendogenouslywithrespecttothecurrentmarketvalueofthebond.

13. 1.1.2SafetyCovenants • Bankruptcy firm’sbondholdertakecontroloverthefirmandthefirmundergoesareorganization. • Forthesakeofsimplicity,thisparticularaspectisnottakenintoaccountthebargainingprocess. • Exogenousbankruptcy bankruptcyisspecifiedinformofsome protectivecovenants. • Endogenousbankruptcy coverthesituationswhenbankruptcyisdeclared bythefirm’s stockholderifthefirm’svaluefalls belowcertainpre-specifiedlevel. (max.equity,mindebt)

14. 1.1.2SafetyCovenants • Dealwithacorporatedebtwiththestructuralapproachtocreditriskinordertospecifythedefaultevent. • SafetyCovenantismodeledasabarrierprocess(alsocalledthresholdprocess),usuallydenotedasυinwhatfollows. • Defaultevent:firmvalueprocessVfallsbelowbarrierprocessυpriororatthematurityT. • Proposeofsafetycovenants:describeanymechanismwhichtriggersdefaulteventbeforethematurityofthedebt

15. 1.1.3CreditSpread • Creditspread measurestheexcessreturnonacorporate bondoverthereturnonaequivalent Treasurybond,i.e., abondwhichisassumed tobefreeofthecreditrisk. • Express: differencebetweenrespectiveyieldstomaturityordifferencebetweenrespectiveinstantaneousforwardrates. • Thedeterminationofthecreditspreadsisinfacttheultimategoalofmostcreditriskmodels.

16. 1.1.3CreditSpread • Distressedsecurities highlevelofcreditspreadsyieldedbysomecorporatesecurities,shouldtheynotdefault. Orencompassespubliclyheldandtradeddebtorequitysecuritiesoffirmsthathavedefaultedorhavefiledforprotectionunderthebankruptcycode.

17. 1.1.4CreditRatings • Afirm’screditratingsisameasureofthefirm’spropensitytodefault. • Typicallyidentifiedwithelementsofafiniteset,alsoreferredtoasthesetofcreditclassesorcreditgrades. • Moody’sInvestmentService,Standard&Poor’sCorporation,FitchIBCA,Duff&Phelps. • Internalratings: basedoninternallydevelopedmethodologies. • officialcreditratings: primarilyreflectthelikelihoodofdefault • Theimprovementofthefirm’screditqualitytypicallydoesnotresultinanimmediateupgrade(ordowngrade)ofitsratings.

18. 1.1.5CorporateCouponBonds • Discretetimecouponpayment 1.paymentsareonlypriortothedefaulttime 2.thecouponbondmaybeconsideredasa portfoliocomposedofthedefaultable couponsanddefaultablefacevalue.

19. 1.1.5CorporateCouponBonds

20. 1.1.5CorporateCouponBonds

21. 1.1.6FixedandFloatingRateNotes • Fixed-couponbond contractstipulatescouponpaymentsarefixed • Fixed-couponbond risk-freebond defaultablebond • Iftradeatpar,thecouponrateofacorporatebondwouldbegreaterthanarisk-freebondtocompensateaninvestorforthedefaultrisk. • Thecorrespondingdiscrepancyisreferredasfixed-ratecreditspreadoverTreasuryforagivencorporatebond • Creditspreadreflectsthecreditqualityoftheissuer. • Financialmarketrequiresahigherriskpremiumforalowerqualitydebt,sothecostofcapitalforadebtoroflowercreditqualityishigher.

23. 1.1.6FixedandFloatingRateNotes • CreditspreadvarieswithbothtimetandthematurityT=Tntherebygivingrisetoaparticulartermstructureofcreditspreads. • Floatingratenote(FRNs,forshort) couponpaymentismadeaccordingtothefloatinginterestrateprevailingonthiscoupon’sdate(resetdate)

24. 1.1.6FixedandFloatingRateNotes

25. 1.1.6FixedandFloatingRateNotes

27. 1.1.6FixedandFloatingRateNotes • CallableFRN hastherighttoredeemthenotebefore maturity. • PutableFRN hastherighttoforceanearlyredeemption • Thechangesincreditqualitydeterminewhetheroptionexerciseisadvantageous.

28. 1.1.7BankLoansandSovereignDebt • Syndicatedbankloans(SBLs) primarilylarge,highgradecommercialloans secondarytrading paralleledbytheemergenceofbankloanratings substitutesorcomplementsofcorporatebonds • SovereignDebt(Bradybonds) issuedbyseveraldevelopedcountries denominatedinU.S.dollars containvariousformsofcreditguaranteesandprotections,soitishardtoisolatethecountry-specificcreditspreadthatisembeddedinyieldsonBradybonds.

29. 1.1.8CrossDefault • Basicallycorrespondstoprovisioninloanagreementsorbondindentures,whichtriggeraneventofdefaultifthecounterparty(borrowerorissue)defaultsonanotherobligation. • Aprovisionofaloanorswapagreementstatingthatanydefaultonanotherloanorswapwillbeconsideredadefaultontheissuewithcross- defaultprovision. • Protectacreditororcounterpartyfromactionsfavoringanothercreditor

30. 1.1.9DefaultCorrelations

31. 1.1.9DefaultCorrelations • Thedefaultcorrelationbetweenthetwodefaultableclaimsisdefinedasthe correlationcoefficientbetweentherandomvariableXandY • Defaultcorrelationareanimportantbuildingblockofcreditriskmeasurementandmanagementmethodologiesforcredit-risksensitiveportfolio.

32. 1.2VulnerableClaims • Tradeover-the-counterbetweendefault-proneparties;eachsideofthecontractisthusexposedtothecounterpartyriskoftheotherparty. • theunderlying(reference)assetsareassumedtobeinsensitivetothecreditrisk. • Creditderivatives allowsecludedtradinginthereferencerisk handleortransferthereferencecreditrisk alsoaVulnerableclaim

33. 1.2.1VulnerableClaimswithUnilateralDefaultRisk

34. 1.2.1VulnerableClaimswithUnilateralDefaultRisk

35. 1.2.1VulnerableClaimswithUnilateralDefaultRisk

36. 1.2.1VulnerableClaimswithUnilateralDefaultRisk

37. 1.2.2VulnerableClaimswithbiilateralDefaultRisk • Contractsinwhichbothcounterpartiesaresusceptibletodefaultrisk. • defaultswaps insuranceagainstreferencerisk • defaultableswaps 1.swapagreementsbetweentwodefault-prone entities 2.alternativesettlementrules in case of default may largely influence the valuation of defaultable swap 3.need to specify the debt’sseniority 4.assumeswapsaresubordinatedtodebtinbankruptcy

38. 1.2.2VulnerableClaimswithbiilateralDefaultRisk • Ifthepartyindefaultduetoreceiveaswappayment,twoalternativesettlementrulescanbeexamined: (1) theswappaymentisreceived option-likefeatures totalvalueofaswapcontractdependsonthevalueoftheembeddedoption (2) theswappaymentiswithheld becomevaluelessincaseofdefault

39. 1.2.3DefaultableInterestRateContracts • (default-free)spotinterestrateagreement (oracreditagreement) notionalamount=L nominalinterestrate=κ accrualperiod=[T,U] refertoTastheresetdate; Uasthesettlementdate • Aninterestrateagreementcanbedescribedasafinancialcontractbetweenreceiverandpayer,whichissubjecttothefollowingcovenants: -attimeTthereceiverpassesthenotionalamountLtothepayer - hereceivesfromthepayertheaccruedamountL(1+ κ(U-T))at timeU Assumption:thepayer(ofthefixedrateκ)iscertaintodeliverthepromisedpaymenttothereceiverattimeU

40. 1.2.3DefaultableInterestRateContracts • Default-freefeatures 1.theactualtimingofthepaymentisnotessential 見P.14例子 2.thecovenantsoftheinterestrateagreementdescribed aboveinvokeexchangeofprincipalpayments.Itis equivalenttoaloansubjecttoafixedinterestrateκ,where thereceiveristhelendingparty,andthepayeristhe borrowing party.Suchagreementgivesriseto(default-free) spotLIBORrate

41. 1.2.3DefaultableInterestRateContracts

42. Defaultableinterestrateagreement • Defaultableinterestrateagreement (or,adefaultablecreditagreement) payerpartyispronetodefault • assumption: noneofpartieshasgonebankruptcybeforethedateT • Convenants -attimeTthereceiverpassesthenotionalamountL - ifthepayerdoesn’tdefault inthetimeinterval(T,U]thenatthesettlementdateUhepaystothereceivertheaccruedamountL(1+ κ(U-T)) - ifthepayerdefaults in(T,U]thenhepaysthereceiverattimeUthereducedamountδ L(1+ κ(U-T)), δisrecoveryrate • wedealherewithaloaninwhichthedebtormaydefaultonhis • obligationtorepaythedebt.

43. 1.2.3DefaultableInterestRateContracts • Thebasictypeofaspotdefault-freeinterestrateswapisthefixed-for-floatingswapfortheaccrualperiod[T,U],settledinarrears,withthespotdefault-freeLIBORrateL(T)beingthereferencefloatingrate. • OnepartyisthepayerofthefixedrateκandtheotheristhepayerofthefloatingrateL(T);thepartiesagreetoexchangeatthesettlementdateUthenominalpaymentsbasedonthenominalamountL. • IfL=1thenetcashflowatthecontract’ssettlementdateUtooneofoneoftheparties,tothepayerofthefixedrateκ says,isequalto(L(T)- κ)(U-T)

44. 1.2.3DefaultableInterestRateContracts • Thevalueofthefixedrateκ,whichmakesthiscashflowhaveavaluezeroattheinceptionT,iscalledthe(default-free)spotswaprate. • Inthedefault-freeenvironmentthespotswaprateandthespotLIBORratecoincide • Inthedefault-freeenvironment,theloanagreementsandtheinterestrateswapsareequivalent

45. Example -thereceiverpassesatsettlementdateUtothepayerthefullfloatingamountdue:L(T)(U-T) • ifthepayerdoesn’tdefault inthetimeperiod(T,U],thereceivercollectsatthesettlementdateUthefullfixedamountdue:κ(U-T) • ifthepayerdefaults in(T,U],thereceivergetsatthetimeUthereducedamountdue:δκ(U-T) • κ:defaultablespotswaprate,whichmakestheabovecontractvaluelessattheinceptiontimeT.ItdiffersfromthedefaultablespotLIBORrate. inthepresenceofacounterpartyrisk,theloanandtheswapcontractarenotequivalenttoeachother.