XVA: Credit, Funding and Capital Valuation Adjustments

539 Pages·2015·7.24 MB·English

by  Andrew Green

XVA: Credit, Funding
and Capital Valuation
Adjustments
ForothertitlesintheWileyFinanceseries
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XVA: Credit, Funding
and Capital Valuation
Adjustments
ANDREW GREEN
Thiseditionfirstpublished2016
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Green,Andrew,
XVA:credit,fundingandcapitalvaluationadjustments/AndrewGreen.
pagescm.—(Thewileyfinanceseries)
Includesbibliographicalreferencesandindex.
ISBN978-1-118-55678-8(hardback)—ISBN978-1-118-55675-7(ebk)—
ISBN978-1-118-55676-4(ebk)—ISBN978-1-119-16123-3(ebk) 1.Finance.
2.Derivativesecurities. I.Title.
HG173.G7442015
332.64′57–dc23
2015019353
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN978-1-118-55678-8(hardback) ISBN978-1-118-55675-7(ebk)
ISBN978-1-118-55676-4(ebk) ISBN978-1-119-16123-3(obk)
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ForSimone

Contents
ListofTables xvii
ListofFigures xxi
Acknowledgements xxv
CHAPTER1
Introduction:TheValuationofDerivativePortfolios 1
1.1 Whatthisbookisabout 1
1.2 PricesandValues 4
1.2.1 BeforetheFall... 4
1.2.2 ThePost-CrisisWorld... 5
1.3 TradeEconomicsinDerivativePricing 6
1.3.1 TheComponentsofaPrice 6
1.3.2 Risk-NeutralValuation 8
1.3.3 HedgingandManagementCosts 11
1.3.4 CreditRisk:CVA/DVA 11
1.3.5 FVA 13
1.3.6 RegulatoryCapitalandKVA 14
1.4 Post-CrisisDerivativeValuationorHowILearnedtoStopWorryingand
LoveFVA 16
1.4.1 TheFVADebateandtheAssaultonBlack-Scholes-Merton 16
1.4.2 DifferentValuesforDifferentPurposes 19
1.4.3 Summary:TheValuationParadigmShift 21
1.5 ReadingthisBook 21
PARTONE
CVAandDVA:CounterpartyCreditRiskandCreditValuationAdjustment
CHAPTER2
IntroducingCounterpartyRisk 25
2.1 DefiningCounterpartyRisk 25
2.1.1 Wrong-wayandRight-wayRisk 27
vii
viii CONTENTS
2.2 CVAandDVA:CreditValuationAdjustmentandDebitValuation
AdjustmentDefined 27
2.3 TheDefaultProcess 28
2.3.1 ExampleDefault:TheCollapseofLehmanBrothers 30
2.4 CreditRiskMitigants 30
2.4.1 Netting 30
2.4.2 Collateral/Security 31
2.4.3 CentralClearingandMargin 34
2.4.4 Capital 35
2.4.5 BreakClauses 35
2.4.6 BuyingProtection 37
CHAPTER3
CVAandDVA:CreditandDebitValuationAdjustmentModels 39
3.1 Introduction 39
3.1.1 Close-outandCVA 40
3.2 UnilateralCVAModel 42
3.2.1 UnilateralCVAbyExpectation 42
3.2.2 UnilateralCVAbyReplication 43
3.3 BilateralCVAModel:CVAandDVA 48
3.3.1 BilateralCVAbyExpectation 48
3.3.2 BilateralCVAbyReplication 50
3.3.3 DVAandControversy 53
3.4 ModellingDependencebetweenCounterparties 55
3.4.1 GaussianCopulaModel 55
3.4.2 OtherCopulaModels 56
3.5 ComponentsofaCVACalculationEngine 57
3.5.1 MonteCarloSimulation 57
3.5.2 TradeValuationandApproximations 57
3.5.3 ExpectedExposureCalculation 59
3.5.4 CreditIntegration 59
3.6 CounterpartyLevelCVAvs.TradeLevelCVA 59
3.6.1 IncrementalCVA 60
3.6.2 AllocatedCVA 60
3.7 RecoveryRate/Loss-Given-DefaultAssumptions 63
CHAPTER4
CDSandDefaultProbabilities 65
4.1 SurvivalProbabilitiesandCVA 65
4.2 HistoricalversusImpliedSurvivalProbabilities 66
4.3 CreditDefaultSwapValuation 67
4.3.1 CreditDefaultSwaps 67
4.3.2 PremiumLeg 69
4.3.3 ProtectionLeg 71
4.3.4 CDSValueandBreakevenSpread 72
Contents ix
4.4 BootstrappingtheSurvivalProbabilityFunction 72
4.4.1 UpfrontPayments 74
4.4.2 ChoiceofHazardRateFunctionandCVA:CVACarry 75
4.4.3 CalibrationProblems 76
4.5 CDSandCapitalRelief 77
4.6 LiquidandIlliquidCounterparties 78
4.6.1 MappingtoRepresentativeCDS 79
4.6.2 MappingtoBasketsandIndices 80
4.6.3 Cross-sectionalMaps 81
CHAPTER5
AnalyticModelsforCVAandDVA 83
5.1 AnalyticCVAFormulae 83
5.2 InterestRateSwaps 84
5.2.1 UnilateralCVA 84
5.2.2 BilateralCVA 86
5.3 Options:InterestRateCapletsandFloorlets 86
5.4 FXForwards 88
CHAPTER6
ModellingCreditMitigants 91
6.1 CreditMitigants 91
6.2 Close-outNetting 91
6.3 BreakClauses 93
6.3.1 MandatoryBreakClauses 93
6.3.2 OptionalBreakClauses 93
6.4 VariationMarginandCSAAgreements 97
6.4.1 SimpleModel:ModifyingthePayoutFunction 97
6.4.2 ModellingCollateralDirectly 99
6.4.3 LookbackMethod 101
6.4.4 ModellingDowngradeTriggersinCSAAgreements 102
6.5 Non-financialSecurityandtheDefaultWaterfall 107
CHAPTER7
Wrong-wayandRight-wayRiskforCVA 109
7.1 Introduction:Wrong-wayandRight-wayRisks 109
7.1.1 ModellingWrong-wayRiskandCVA 110
7.2 DistributionalModelsofWrong-way/Right-wayRisk 111
7.2.1 SimpleModel:IncreasedExposure 111
7.2.2 CopulaModels 111
7.2.3 LinearModelsandDiscreteModels 114
7.3 AGeneralisedDiscreteApproachtoWrong-wayRisk 116
7.4 StochasticCreditModelsofWrong-way/Right-wayRisk 118
7.4.1 SovereignWrong-wayRisk 119
7.5 Wrong-way/Right-wayRiskandDVA 119