Correlation Risk Modeling and Management, + Website: An Applied Guide including the Basel III Correlation Framework - With Interactive Models in Excel / VBA

352 Pages·2014·4.296 MB·English

by  Gunter Meissner

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Correlation Risk
Modeling and
Management
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Correlation Risk
Modeling and
Management
An Applied Guide Including the
—
Basel III Correlation Framework
with Interactive Correlation Models

in Excel /VBA
GUNTER MEISSNER
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Contents
Preface xiii
Acknowledgments xvii
AbouttheAuthor xix
CHAPTER1
SomeCorrelationBasics:Properties,Motivation,Terminology 1
1.1 WhatAreFinancialCorrelations? 1
1.2 WhatIsFinancialCorrelationRisk? 2
1.3 Motivation:CorrelationsandCorrelationRiskAre
EverywhereinFinance 5
1.3.1 InvestmentsandCorrelation 6
1.3.2 TradingandCorrelation 8
1.3.3 RiskManagementandCorrelation 14
1.3.4 TheGlobalFinancialCrisisof2007to2009
andCorrelation 18
1.3.5 RegulationandCorrelation 23
1.4 HowDoesCorrelationRiskFitintotheBroaderPicture
ofRisksinFinance? 24
1.4.1 CorrelationRiskandMarketRisk 24
1.4.2 CorrelationRiskandCreditRisk 25
1.4.3 CorrelationRiskandSystemicRisk 27
1.4.4 CorrelationRiskandConcentrationRisk 30
1.5 AWordonTerminology 33
1.6 Summary 34
Appendix1A:DependenceandCorrelation 35
Dependence 35
Correlation 36
IndependenceandUncorrelatedness 37
Appendix1B:OnPercentageandLogarithmicChanges 38
v
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vi CONTENTS
PracticeQuestionsandProblems 39
ReferencesandSuggestedReadings 40
CHAPTER2
EmpiricalPropertiesofCorrelation:HowDoCorrelationsBehave
intheRealWorld? 43
2.1 HowDoEquityCorrelationsBehaveinaRecession,
NormalEconomicPeriod,orStrongExpansion? 43
2.2 DoEquityCorrelationsExhibitMeanReversion? 46
2.2.1 HowCanWeQuantifyMeanReversion? 47
2.3 DoEquityCorrelationsExhibitAutocorrelation? 50
2.4 HowAreEquityCorrelationsDistributed? 51
2.5 IsEquityCorrelationVolatilityanIndicatorfor
FutureRecessions? 52
2.6 PropertiesofBondCorrelationsandDefault
ProbabilityCorrelations 53
2.7 Summary 54
PracticeQuestionsandProblems 55
ReferencesandSuggestedReadings 55
CHAPTER3
StatisticalCorrelationModels—CanWeApplyThemtoFinance? 57
3.1 AWordonFinancialModels 57
3.1.1 TheFinancialModelItself 58
3.1.2 TheCalibrationoftheModel 59
3.1.3 MindfulnessaboutModels 60
3.2 StatisticalCorrelationMeasures 60
3.2.1 ThePearsonCorrelationApproachandIts
LimitationsforFinance 60
3.2.2 Spearman’sRankCorrelation 62
3.2.3 Kendall’st 64
3.3 ShouldWeApplySpearman’sRankCorrelation
andKendall’stinFinance? 65
3.4 Summary 66
PracticeQuestionsandProblems 67
ReferencesandSuggestedReadings 68
CHAPTER4
FinancialCorrelationModeling—Bottom-UpApproaches 69
4.1 CorrelatingBrownianMotions(Heston1993) 69
4.1.1 ApplicationsoftheHestonModel 72
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Contents vii
4.2 TheBinomialCorrelationMeasure 72
4.2.1 ApplicationoftheBinomial
CorrelationMeasure 73
4.3 CopulaCorrelations 74
4.3.1 TheGaussianCopula 76
4.3.2 SimulatingtheCorrelatedDefaultTime
forMultipleAssets 81
4.3.3 FindingtheCorrelatedDefaultTimeina
ContinuousTimeFrameworkUsing
SurvivalProbabilities 82
4.3.4 CopulaApplications 85
4.3.5 LimitationsoftheGaussianCopula 85
4.4 ContagionCorrelationModels 88
4.5 Summary 90
Appendix4A:CholeskyDecomposition 91
Example:CholeskyDecompositionforThreeAssets 92
Appendix4B:AShortProofoftheGaussianDefault
TimeCopula 93
PracticeQuestionsandProblems 93
ReferencesandSuggestedReadings 94
CHAPTER5
ValuingCDOswiththeGaussianCopula—WhatWentWrong? 101
5.1 CDOBasics—WhatIsaCDO?WhyCDOs?Types
ofCDOs 101
5.1.1 WhatIsaCDO? 101
5.1.2 WhyCDOs? 102
5.1.3 TypesofCDOs 103
5.2 ValuingCDOs 105
5.2.1 DerivingtheDefaultProbabilityforEachAsset
inaCDO 106
5.2.2 DerivingtheDefaultCorrelationoftheAssets
inaCDO 110
5.2.3 RecoveryRate 113
5.3 Conclusion:TheGaussianCopulaandCDOs—What
WentWrong? 113
5.3.1 ComplexityofCDOs 114
5.3.2 TheGaussianCopulaModeltoValueCDOs 114
5.4 Summary 115
PracticeQuestionsandProblems 116
ReferencesandSuggestedReadings 117
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viii CONTENTS
CHAPTER6
TheOne-FactorGaussianCopula(OFGC)Model—TooSimplistic? 119
6.1 TheOriginalOne-FactorGaussianCopula
(OFGC)Model 121
6.2 ValuingTranchesofaCDOwiththeOFGC 122
6.2.1 RandomnessintheOFGCModel 127
6.3 TheCorrelationConceptintheOFGCModel 128
6.3.1 TheLossDistributionoftheOFGCModel 129
6.3.2 TheTrancheSpread–CorrelationRelationship 130
6.4 TheRelationshipbetweentheOFGCandthe
StandardCopula 131
6.5 ExtensionsoftheOFGC 132
6.5.1 FurtherExtensionsoftheOFGCModel:
HybridCID–ContagionModeling 134
6.6 Conclusion—IstheOFGCTooSimplistictoEvaluate
CreditRiskinPortfolios? 135
6.6.1 BenefitsoftheOFGCModel 135
6.6.2 LimitationsoftheOFGCModel 136
6.7 Summary 138
PracticeQuestionsandProblems 139
ReferencesandSuggestedReadings 140
CHAPTER7
FinancialCorrelationModels—Top-DownApproaches 143
7.1 Vasicek’s1987One-FactorGaussianCopula(OFGC)
ModelRevisited 144
7.2 MarkovChainModels 146
7.2.1 InducingCorrelationviaTransition
RateVolatilities 146
7.2.2 InducingCorrelationviaStochastic
TimeChange 148
7.3 ContagionDefaultModelinginTop-DownModels 150
7.4 Summary 153
PracticeQuestionsandProblems 154
ReferencesandSuggestedReadings 154
CHAPTER8
StochasticCorrelationModels 157
8.1 WhatIsaStochasticProcess? 157
8.2 SamplingCorrelationfromaDistribution(Hulland
White2010) 159
8.3 DynamicConditionalCorrelations(DCCs)(Engle2002) 160