Table Of ContentDominique Guégan · Bertrand K. Hassani
Risk
Measurement
From Quantitative Measures to
Management Decisions
Risk Measurement
Dominique Guégan (cid:129) Bertrand K. Hassani
Risk Measurement
From Quantitative Measures
to Management Decisions
123
DominiqueGuégan BertrandK.Hassani
UniversityParis1Panthéon-Sorbonne DepartmentofComputerScience
LabExReFiandIPAG UniversityCollegeLondon
Paris,France London,UK
UniversityCa’Foscari DepartmentofFinance
Venezia,Italy UniversitéParis1Panthéon-Sorbonne
Paris,France
DepartmentofFinancialRegulation
LabeXRefi(ESCP-ENA-Paris1)
Paris,France
ISBN978-3-030-02679-0 ISBN978-3-030-02680-6 (eBook)
https://doi.org/10.1007/978-3-030-02680-6
LibraryofCongressControlNumber:2018959149
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Amodest contributionto theworld ofrisk
measurement,openingthewayforpossible
alternativesinthefieldoffinancialregulation
andotherareas.
Ihopemyformer studentswillfind inthis
booka sourceofreflection.
DominiqueGuéganFebruary 2019
To mysunshines,Lila,Liam andJihane.
To myparents,mybrother,myfamilyandmy
friends.
Iamgratefulfor yourcontinuoussupport
andencouragement.WithLove,
Bertrand KianHassani February 2019
Preface
The purpose of this book is to discuss how risk measures can be leveraged for
riskmanagementpurposesandinthemeantimeaddresstheregulatoryrequirements
concerningtheevaluationoftheriskassociatedwithanyfinancialinstitution.Even
if regulation is seen as a necessity for financial institutions, financial institutions
shouldbeinterestedinriskcontrolaspartoftheircorebusinessandshouldnotonly
addresstheissuebecauseofregulatoryrequirement.Itisimportanttorememberat
that stage that financial institutions are generating profit by a risk transformation
mechanism, and as such risk measurement is key. This book will address the
differentriskmeasuresthroughthisangle.
The objective is to provide an adequate framework for risk managers to reach
the objectives set by regulatory guidelines while controlling internal risks in the
bestpossibleway,inparticularwheninstabilityispresentonthemarkets,orwhen
specificeventsaregeneratingturmoilthatcouldengenderbiglosses,illiquidityor
bankruptcy. In order to meet that goal, the process is broken down into several
compulsory elements required to obtain an appropriate value associated with all
the risks faced by financial institutions, i.e. a value deemed representative of
the exposure. The measures associated with all these risks depend on various
mathematicalcomponentsthat risk managersneed to be aware of:the importance
and the influence of these tools on the results are illustrated in this book. At the
sametime,wealsodemonstratethatthecomputationoftherisksneedstolieonthe
realityoftheriskstomeasure,andnotonsomeaprioriconcerningthechoiceofthe
mathematicaltoolsweneedtousetogetthismeasure.Ourpointswillbeillustrated
withexamplesallowingustounderstandthelinksbetweentheconceptsdiscussed
withinthebookandtheriskmanagementreality.
Indeed,riskmeasurementraisesanumberofquestionswhichwe addresspoint
by point in the following chapters. After introducing a discussion on the Basel’s
guidelinesaroundthe question of risk measure, we recall the classic modelsused
in finance (variance, CAPM, APT, etc.) for measuring the risks and discuss their
limits. Then, we address the characterisation of a risk factor using an unimodal
distributionanddeveloptherisk measuresassociatedwiththisapproach(classical
VaR, TVaR and ES). We extend the discussion to the risk measures computed
ix
x Preface
usingmulti-modaldistributions(distortion,combination,etc.).We thenextendthe
discussiontomultivariateapproaches,introducingtheKendallriskmeasureamong
others.Finally,newroutesareexploredconcerningspectralmeasures,spectrumof
riskmeasuresandspatialrisk measures.We concludethisbookshowinghowrisk
measurescan be used as alert proceduresin case of fire in the banksor insurance
companieswiththestressapproach.Butbeforegoingintothetechnicalaspectsof
theriskmeasures,wefocusontheevolutionoftheregulationsince1968.
Paris,France DominiqueGuégan
Paris,France BertrandK.Hassani
Contents
1 Introduction .................................................................. 1
1.1 1968–1988:Premises................................................... 1
1.1.1 TheTriggeringElements....................................... 1
1.2 BaselI ................................................................... 4
1.3 BaselII .................................................................. 4
1.3.1 BaselII.5........................................................ 6
1.4 BaselIII.................................................................. 7
1.5 SolvencyIIDirectives .................................................. 11
1.6 SuccessiveCriticisms................................................... 12
1.6.1 BaselI........................................................... 12
1.6.2 BaselII.......................................................... 13
1.6.3 BaselIII ......................................................... 13
1.6.4 SolvencyII...................................................... 14
References..................................................................... 15
2 FinancialInstitutions:ARegulationReviewThroughtheRisk
MeasurementPrism ......................................................... 17
2.1 CreditRisk .............................................................. 17
2.1.1 StandardisedApproach......................................... 18
2.1.2 InternalRatings-BasedApproach.............................. 19
2.2 CreditValueAdjustment................................................ 21
2.3 OperationalRisk ........................................................ 22
2.3.1 BasicIndicatorApproach ...................................... 23
2.3.2 StandardisedApproach......................................... 23
2.3.3 TheAdvancedMeasurementApproach(AMA) .............. 24
2.3.4 Standardised Measurement Approach or New
StandardizedApproach......................................... 25
2.4 MarketRisk ............................................................. 27
2.4.1 TheFundamentalReviewoftheTradingBook ............... 27
2.4.2 StandardisedApproach......................................... 28
2.4.3 InternalModelsApproach...................................... 29
xi
xii Contents
2.5 IFRS9asaRiskRegulation ............................................ 31
2.6 TheStress-TestingFramework......................................... 33
References..................................................................... 35
3 TheTraditionalRiskMeasures............................................. 37
3.1 MeasuresofDispersion................................................. 37
3.1.1 DistanceBetweenRepresentativeValues...................... 38
3.1.2 DeviationfromaCentralValue................................ 39
3.1.3 MeanAbsoluteDifference ..................................... 45
3.2 RiskMeasurement:PortfolioTheoryPhilosophy..................... 46
3.2.1 ModernPortfolioTheory....................................... 46
3.2.2 Efficient Frontier with No Risk-Free Asset:
RiskManagementinEssence.................................. 48
3.2.3 Risk-FreeAssetandtheCapitalAllocationLine ............. 49
3.2.4 Risk ManagementThroughMPT:SystematicRisk
andSpecificRisk ............................................... 49
3.2.5 CapitalAssetPricingModel ................................... 50
3.2.6 ArbitragePricingTheory....................................... 51
3.2.7 DownsideRiskMeasures....................................... 53
3.2.8 DownsideDeviation............................................ 55
3.2.9 SortinoRatio.................................................... 56
3.3 QuantileRiskMeasureandAffiliated.................................. 56
3.3.1 VaR.............................................................. 56
3.3.2 ExpectedShortfall.............................................. 58
3.3.3 TailValueatRisk............................................... 59
3.3.4 CoVaR........................................................... 60
3.3.5 EntropicRiskMeasures:ρermandEVaR...................... 61
3.4 DistortionRiskMeasure................................................ 64
References..................................................................... 65
4 UnivariateandMultivariateDistributions................................ 69
4.1 UnivariateDistributions ................................................ 69
4.1.1 Some Recalls on the Probabilistic Characteristic
ofaRiskFactor................................................. 69
4.1.2 ExamplesofParametricDistributions......................... 70
4.1.3 Non-parametricModellingforaDistribution................. 77
4.1.4 DistortedDistributions ......................................... 80
4.2 MultivariateApproach.................................................. 92
4.2.1 DefinitionofaCopula.......................................... 93
4.2.2 Properties........................................................ 94
4.2.3 ExamplesofCopulas........................................... 98
4.2.4 TailDependenceConcept ...................................... 103
References..................................................................... 112
