Table Of Content“This impressive book covers an important and highly complex area of quantitative
finance dealing with counterparty credit risk. It covers many vital topics and demon-
strates in great detail how to compute Credit, Debt, and Funding Value Adjustments.
Writtenbysomeofthebestexpertsinthefield,itprovidesimportantinsightsinitssubject
matter,whichwillbeofgreatvalueforpractitioners,academics,andregulators.”
Alexander Lipton, Co-Head of Global Quantitative Group at Bank of America
MerrillLynchandHonoraryProfessoratImperialCollege
“This book could rightly be called The Encyclopaedia of Credit Value Adjustments,
althoughitisbothmoredetailedandmorepleasantlyreadablethananencyclopaedia.
Itistheone-stopCVA(andmore)referenceforpractitionersandacademicsalike.”
(This endorsement is a personal opinion and does not represent the view of the
FinancialServicesAuthority)
Dirk Tasche, Technical Specialist, Risk Specialists Division, Financial Services
Authority
“There are many books in Finance. This one is different. It focuses on CVA (Credit
Valuation Adjustment), a topic related to counterparty risk. The first chapter alone
is worth the price of the book. This chapter is an ‘extended dialogue,’ where Brigo
uses a question and answer format to teach, in an entertaining manner, a lot of the
fundamentalideas,aswellasthejargonwithitsalphabet-cityinnumerableacronyms,
of modern financial mathematics, both as it is practiced in industry and in academia.
Hisapproachiscreativeandoriginal;itcouldbeactedoutbytwoperformersinfront
ofaliveaudience.Thebookisurgentlyneededatatimewhencreditriskhasemerged
astheissueofthetimes.”
Professor Philip Protter, Professor of Statistics, Statistics Department, Columbia
University
Counterparty Credit Risk,
Collateral and Funding
ForothertitlesintheWileyFinanceseries
pleaseseewww.wiley.com/finance
Counterparty Credit Risk,
Collateral and Funding
With Pricing Cases for All Asset Classes
Damiano Brigo
Massimo Morini
Andrea Pallavicini
©2013JohnWiley&SonsLtd
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LibraryofCongressCataloging-in-PublicationData
Brigo,Damiano,1966–
Counterpartycreditrisk,collateralandfunding:withpricingcasesforallassetclasses/DamianoBrigo,
MassimoMorini,AndreaPallavicini.
1onlineresource.
Includesbibliographicalreferencesandindex.
DescriptionbasedonprintversionrecordandCIPdataprovidedbypublisher;resourcenotviewed.
ISBN978-0-470-66167-3(ebk)–ISBN978-0-470-66178-9(ebk)–ISBN978-0-470-66249-6(ebk)–
ISBN978-0-470-74846-6(cloth) 1.Finance–Mathematicalmodels. 2.Credit–Mathematicalmodels.
3.Creditderivatives–Mathematicalmodels. 4.Financialrisk–Mathematicalmodels. I.Morini,Massimo.
II.Pallavicini,Andrea. III.Title.
HG106
332.701′5195–dc23
2013001506
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN978-0-470-74846-6(hbk)ISBN978-0-470-66249-6(ebk)
ISBN978-0-470-66167-3(ebk)ISBN978-0-470-66178-9(ebk)
CoverimagesreproducedbypermissionofShutterstock.com
Setin10/12ptTimesbyAptara,Inc.,NewDelhi,India
PrintedinGreatBritainbyCPIGroup(UK)Ltd,Croydon,CR04YY
Contents
Ignition xv
AbbreviationsandNotation xxiii
PARTI COUNTERPARTYCREDITRISK,COLLATERALANDFUNDING
1 Introduction 3
1.1 ADialogueonCVA 3
1.2 RiskMeasurement:CreditVaR 3
1.3 Exposure,CE,PFE,EPE,EE,EAD 5
1.4 ExposureandCreditVaR 7
1.5 Interlude:PandQ 7
1.6 Basel 8
1.7 CVAandModelDependence 9
1.8 InputandDataIssuesonCVA 10
1.9 EmergingAssetClasses:LongevityRisk 11
1.10 CVAandWrongWayRisk 12
1.11 BaselIII:VaRofCVAandWrongWayRisk 13
1.12 DiscrepanciesinCVAValuation:ModelRiskandPayoffRisk 14
1.13 BilateralCounterpartyRisk:CVAandDVA 15
1.14 First-to-DefaultinCVAandDVA 17
1.15 DVAMark-to-MarketandDVAHedging 18
1.16 ImpactofClose-OutinCVAandDVA 19
1.17 Close-OutContagion 20
1.18 CollateralModellinginCVAandDVA 21
1.19 Re-Hypothecation 22
1.20 Netting 22
1.21 Funding 23
1.22 HedgingCounterpartyRisk:CCDS 25
1.23 RestructuringCounterpartyRisk:CVA-CDOsandMarginLending 26
viii Contents
2 Context 31
2.1 DefinitionofDefault:SixBasicCases 31
2.2 DefinitionofExposures 32
2.3 DefinitionofCreditValuationAdjustment(CVA) 35
2.4 CounterpartyRiskMitigants:Netting 37
2.5 CounterpartyRiskMitigants:Collateral 38
2.5.1 TheCreditSupportAnnex(CSA) 39
2.5.2 TheISDAProposalforaNewStandardCSA 40
2.5.3 CollateralEffectivenessasaMitigant 40
2.6 Funding 41
2.6.1 AFirstAttackonFundingCostModelling 42
2.6.2 TheGeneralFundingTheoryanditsRecursive
Nature 42
2.7 ValueatRisk(VaR)andExpectedShortfall(ES)ofCVA 43
2.8 TheDilemmaofRegulatorsandBaselIII 44
3 ModellingtheCounterpartyDefault 47
3.1 FirmValue(orStructural)Models 47
3.1.1 TheGeometricBrownianAssumption 47
3.1.2 Merton’sModel 48
3.1.3 BlackandCox’s(1976)Model 50
3.1.4 CreditDefaultSwapsandDefaultProbabilities 54
3.1.5 BlackandCox(B&C)ModelCalibrationtoCDS:Problems 55
3.1.6 TheAT1PModel 57
3.1.7 ACaseStudywithAT1P:LehmanBrothersDefault
History 58
3.1.8 Comments 60
3.1.9 SBTVModel 61
3.1.10 ACaseStudywithSBTV:LehmanBrothersDefaultHistory 62
3.1.11 Comments 64
3.2 FirmValueModels:HintsattheMultinamePicture 64
3.3 ReducedForm(Intensity)Models 65
3.3.1 CDSCalibrationandIntensityModels 66
3.3.2 ASimplerFormulaforCalibratingIntensitytoaSingleCDS 70
3.3.3 StochasticIntensity:TheCIRFamily 72
3.3.4 TheCox-Ingersoll-RossModel(CIR)Short-RateModelforr 72
3.3.5 Time-InhomogeneousCase:CIR++Model 74
3.3.6 StochasticDiffusionIntensityisNotEnough:AddingJumps.The
JCIR(++)Model 75
3.3.7 TheJump-DiffusionCIRModel(JCIR) 76
3.3.8 MarketIncompletenessandDefaultUnpredictability 78
3.3.9 FurtherModels 78
3.4 IntensityModels:TheMultinamePicture 78
3.4.1 ChoiceofVariablesfortheDependenceStructure 78
3.4.2 FirmValueModels? 80
3.4.3 CopulaFunctions 80
3.4.4 CopulaCalibration,CDOsandCriticismofCopulaFunctions 86
Description:The book’s content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterpa
