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Risk management in banking





About the AuthorBASIC POSTULATES OF THIS TEXTThe Financial CrisisScope and Goals of this TextPOSITIONING OF THE TEXTThe "Model Divide"Risk Management versus Risk InstrumentsReverting to Better Risk Practices and Lessons of the CrisisBOOK STRUCTURETHE THIRD EDITIONSection 1. The Financial CrisisThe 2007-2008 Financial CrisisTHE SUB-PRIME CRISISCLASSICAL CONTAGION MECHANISMSFINANCIAL RISKSREGULATIONSRisk RegulationsAccounting StandardsCONTAGION THROUGH SECURITIZATIONSLIQUIDITY CONTAGIONCONTAGION AND PROCYCLICALITYTHROUGH FAIR VALUE RULESCONTAGION THROUGH RATING DOWNGRADESCONTAGION AND PROCYCLICALITY IN A LEVERAGED INDUSTRYSOME IMPLICATIONSSection 2. Business Lines, Risks, and Risk ManagementBanking Business LinesBUSINESS POLES IN THE BANKING INDUSTRYMANAGEMENT PRACTICES DIFFER ACROSS AND WITHIN BUSINESS LINESBANKING REGULATIONS AND ACCOUNTING STANDARDSRisks and Risk ManagementUNCERTAINTY, RISK,AND EXPOSURETO RISKTYPES OF RISKSCREDIT RISKDefault RiskMigration RiskExposure RiskCounterparty Risk of DerivativesRecovery RiskCorrelation and Concentration RisksCredit Risk in the Trading PortfolioSpread RiskCountry RiskLIQUIDITY RISK: FUNDINGINTEREST RATE RISKMISMATCH RISKMARKET LIQUIDITY RISKMARKET RISKFOREIGN EXCHANGE RISKSOLVENCY RISKOPERATIONAL RISKRisk ManagementRISK OVERSIGHT CHALLENGESMotivations for Risk OversightRisk Oversight: Banks' ChallengesRisk Oversight: Regulators' ChallengesRISK MANAGEMENT PROCESSESThe "Three Lines of Defense" PrincipleRisk Management Organization and Central FunctionsLimits and DelegationsSETTING-UP LIMITSCredit Risk and Lending ActivitiesMarket Risk and Trading ActivitiesAsset-liability Management (ALM)ENTERPRISE-WIDE RISK MANAGEMENT (ERM)Top-down and Bottom-up Risk Management Processes and SystemsEarnings Allocation and Fund Transfer Pricing (FTP) SystemCapital and Risk Allocation SystemSection 3. Financial ProductsBanking and Financial ProductsCLASSIFICATION OF LENDING PRODUCTS AND BASEL 2 CRITERIASOVEREIGN, BANK, AND EQUITY EXPOSURESBank ExposuresSovereign ExposuresEquity ExposuresRETAIL PORTFOLIO IN BASEL 2Nature of Borrower or Low Value of Individual ExposuresLarge Number of ExposuresRetail Portfolio: Further Differentiation for Capital TreatmentTRANSACTION-SPECIFIC CREDIT RISKCredit Risk MitigantsCredit Risk Mitigation under Basel 2SECURITY LENDING AND BORROWINGSPECIALIZED LENDINGProject FinanceObject FinanceCommodities FinanceIncome-producing Real EstateHigh-volatility Commercial Real EstateSECURITIZATIONSSecuritizations: TraditionalSecuritizations: SyntheticOFF-BALANCE SHEET ITEMSEssentials on Derivative ProductsASSETS AND POSITIONSDERIVATIVES: BASIC DEFINITIONS AND PRINCIPLESFORWARD CONTRACTSA Simple Example of a Forward ContractSpot and Forward PricesHedging and Speculating with Forward ContractsPayoff of a Forward ContractFORWARD CONTRACTS VERSUS OPTIONSOPTIONSOptions Allow Hedging RisksThe Payoff of Option ContractsSellers of OptionsRisk and Return of Option ContractsOption PricingUnderlying of OptionsInterest Rate Risk and Interest. Rate DerivativesINTEREST RATE RISK FOR BORROWERS AND LENDERSINTEREST RATES AND TERM STRUCTURELending, Borrowing and the Term Structure of Interest RatesFixed and Variable RatesFORWARD RATES: DEFINITIONSReplicating a Forward LoanForward and Spot Rates: No ArbitrageExample of Calculations of the Forward Yield CurvesUsages of Forward Rate ContractsValuation of a Forward Contract or FRAINTEREST RATE SWAPS (IRS)Definition of Interest Rate SwapReplicating an Interest Rate SwapAsset Swaps: GeneralizationMark-to-market Value of an IRSDerivatives and P & LINTEREST RATE OPTIONS: CAPS AND FLOORSPayoff of Interest Rate OptionsCollarOptions as Volatility InstrumentsHEDGING INTEREST RATE RISK BY CORPORATE BORROWER (CASE STUDY)WHERE DO INTEREST RATES COME FROM?Foreign Exchange Risk and Foreign Exchange DerivativesFOREIGN EXCHANGE RATES AND FORWARD CONTRACTSReplicating a Forward Exchange RateMark-to-market Valuation of Forward ContractsFOREIGN EXCHANGE OPTIONSHEDGING A CORPORATE LONG EXPOSURE IN FOREIGN CURRENCY (CASE STUDY)THE FOREIGN EXCHANGE MARKET AND RATESCredit DerivativesDEFINITIONS OF CREDIT DERIVATIVESCREDIT DEFAULT SWAPS (CDS)TOTAL RETURN SWAPSCREDIT SPREAD PRODUCTSBASKET SWAPS, FIRST-TO-DEFAULT, N-TO-DEFAULTSOVEREIGN RISK CREDIT DERIVATIVESMAIN SPECIFICS AND KEYTERMSThe Underlying AssetsPayment TermsLegal IssuesPayments under a Credit EventCredit EventsMaterializationPRICING CREDIT DERIVATIVESSection 4. ValuationDistribution FunctionsRANDOM VARIABLES AND PROBABILITY DISTRIBUTION FUNCTIONSDiscrete VariablesContinuous VariablesINVERSE FUNCTIONSTHE MOMENTS OF A DISTRIBUTIONExpectationsVariance and VolatilityUNIFORM DISTRIBUTIONAPPLICATION TO LOSS DISTRIBUTIONS AND LOSS PERCENTILESBERNOULLI VARIABLEINDICATOR FUNCTIONBERNOULLI DISTRIBUTIONBINOMIAL DISTRIBUTION OF SUM OF BERNOULLI VARIABLESNORMAL DISTRIBUTIONLOGNORMAL DISTRIBUTIONTHE POISSON DISTRIBUTIONDefinitionFinancial ApplicationsNumber of Default Events over a Given HorizonTHE EXPONENTIAL DISTRIBUTION AND TIME TO DEFAULTTHE BETA DISTRIBUTIONTHE STUDENT DISTRIBUTIONA SUMMARYAPPENDIX: CALCULATION OF STANDARD DEVIATION FROM TIME SERIESDiscrete and Continuous ReturnsDISCRETE AND CONTINUOUS RETURNSSingle Period Discrete ReturnCompounding Discrete Returns over Multiple PeriodsFrom Discrete to Continuous ReturnsLogarithmic ReturnsCompounding Continuous ReturnsComparing Continuous and Discrete ReturnsTHE DISCOUNTED CASH FLOW MODELValuation in Discrete Time and the Rationale of DiscountingThe Case of FloatersContinuous TimeAsset Value and Market Required ReturnYield-to-Maturity and Zero-coupon RatesVALUATION UNDER UNCERTAINTYAPPENDIX:THE TAYLOR EXPANSION FORMULAStochastic ProcessesSTOCHASTIC PROCESSESCOMMON STOCHASTIC PROCESSESThe Wiener ProcessApplication: The Square Root of Time Rule for the Simple Wiener ProcessThe Generalized Wiener ProcessThe Ito ProcessThe Stock Price ProcessThe Mean Reverting ProcessThe "Rare Event" ProcessAPPLICATION: STOCK VALUE DISTRIBUTIONINTEREST RATE PROCESSESSPECIFICS OF STOCHASTIC PROCESSES AND ITO LEMMADeterministic CalculusStochastic CalculusIto LemmaExample: Stock Price DistributionValuation and Pricing RiskCONSTRUCTING A RISK-FREE PORTFOLIOHow to Form Risk-free PortfoliosHow to Derive the Pricing PDEHow to Solve Numerically a PDERISK-NEUTRAL VALUATION:THE CASE OF A STOCK PRICERisk-neutral ProbabilityStock Price Dynamics under Risk-neutral ProbabilitiesVALUATION: END RESULTSSome Applications of Valuation TechniquesVALUATION OF RISKY DEBT FROM CREDIT SPREADS AND RISK-NEUTRAL PROBABILITIESVALUATION OF AN OPTION UNDER RISK-NEUTRAL PROBABILITIESTHE VASICEK MODELSection 5. Risk ModelingSensitivitySENSITIVITY DEFINITIONSCOMMON SENSITIVITIESStocksBonds and LoansOptionsForward Contracts and Interest Rate SwapsSENSITIVITY AND RISK FACTORSSENSITIVITIES AND RISK CONTROLLINGVolatilityVOLATILITYEQUALLY WEIGHTED HISTORICAL VOLATILITYContinuous Returns and VarianceHistorical Volatility with Equally Weighted ObservationsEXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA) MODELGARCH MODELSMAXIMUM LIKELIHOOD METHODOLOGYESTIMATING EWMA VOLATILITYThe Value-at-Risk MeasureMODELING POTENTIAL VARIATIONS AND PERCENTILESModeling Potential Variations of ValueValue PercentileTHE VAR METHODOLOGY: MARKET RISKSensitivityFrom Sensitivity to VolatilityFrom Daily Volatility of the Position to Daily VaRVaR at Different HorizonsSummary and ExtensionsCREDIT RISK VARThe Firm ValueThe Distribution of Firm ValueVaR and CapitalTHE CONTRIBUTIONS OF VAR-BASED MEASURESLOSS DISTRIBUTIONSMEASURES OF POTENTIAL LOSSESExpected LossLoss PercentilesUnexpected Loss and VaRExceptional LossesLoss Distributions, Potential Losses and VaRVAR AND ECONOMIC CAPITALEARNINGS-AT-RISK ("EAR")Section 6. RegulationsBanking Regulations: Basel I and Market RiskREGULATORY ISSUESTHE DILEMMAS OF THE REGULATORRegulation and CompetitionPreemptive Risk Control versus Risk InsuranceCAPITAL ADEQUACYRisk-based Capital RegulationsCapital RequirementsRisk-based Capital and GrowthTHE "BASEL I ACCORD" FOR CREDIT RISKThe Cooke Ratio and Credit RiskDerivatives and Credit RiskBasel I DrawbacksTHE ACCORD FOR MARKET RISKThe Standardized ApproachProprietary Models of Market Risk VaRBanking Regulations: The Basel 2 AccordTHE NEW BASEL ACCORDASSET CLASSESCREDIT RISK COMPONENTSProbability of Default (DP) and Default EventExposure at Default (EAD)Loss Given Default (LGD)Credit Conversion Factors (CCFs)Credit Components and Risk WeightsTHE STANDARDIZED APPROACHRegulatory Risk Weights for Corporates, Sovereigns and BanksThe Retail PortfolioEffective Maturity (M)Off Balance Sheet ItemsINTERNAL RATINGS BASED FRAMEWORKCREDIT RISK MITIGATIONCredit Risk Mitigation: Guarantees and Credit DerivativesCredit Risk Mitigation: Collateral TreatmentCollateral: Haircut CalculationsEffective LGD for Collateral-based TransactionsCOUNTERPARTY CREDIT RISKCAPITAL CALCULATIONRisk-Weighted Assets for Corporate, Sovereign, and Bank ExposuresInterpretation of Basel 2 Formulas for Risk WeightsRetail PortfolioEquity ExposuresSAMPLE COMPARISON BETWEEN BASEL I AND BASEL 2 CAPITAL FOR CORPORATE ASSET CLASS CREDIT RISKSPECIALIZED LENDINGSECURITIZATIONSStandardized ApproachIRB ApproachesINTEREST RATE RISKOPERATIONAL RISKPILLAR 2: SUPERVISORY REVIEW PROCESSPILLAR 3: MARKET DISCIPLINEADDITIONAL PROPOSALSAccounting StandardsBANKS'FINANCIAL STATEMENTSINITIAL RECOGNITION OF FINANCIAL ASSETS AND LIABILITIESFinancial Assets and Liabilities at Fair Value through Profit or LossLoans and ReceivablesHeld-to-maturity Financial AssetsAvailable-for-sale Financial AssetsVALUATION RULESAmortized CostMethod of Determining Fair ValueInstruments Traded in Active MarketsInstruments Traded in Inactive MarketsIMPAIRMENT OF FINANCIAL ASSETSHEDGE ACCOUNTINGTypes of Hedges"Effectiveness" of HedgeCOMPARISONS OF CLASSIFICATIONS: RISK REGULATIONS AND IFRSSection 7. Asset Liability Management (ALM)ALM GOALSALM SCOPE AND STRUCTURE OF THE SECTIONTHE ALM FUNCTIONLiquidity Management and Liquidity GapsLIQUIDITY DEFINITIONSLIQUIDITY GAP TIME PROFILESThree Basic Liquidity PositionsMismatch RiskLIQUIDITY GAP CALCULATIONSStatic Liquidity GapsDynamic Liquidity GapsHow Gaps Change Through TimeFixed Assets and EquityLIQUIDITY MANAGEMENTStructuring Debt MaturitiesNumerical ExampleSTRUCTURAL EXCESSES OF LIQUIDITYISSUES FOR DETERMINING THE LIQUIDITY GAP TIME PROFILELines without MaturityDemand DepositsContingencies Given (Off-balance Sheet)Amortizing LoansMultiple ScenariosLIQUIDITY SCENARIOSLiquid AssetsLiquidity Crises and Stress Test ScenariosInterest Rate GapsDEFINITION OF INTEREST RATE GAPSCALCULATIONS OF INTEREST RATE GAPSInterest Rate Gap and Liquidity GapsSample Gap ReportsTHE GAP MODELNET INTEREST INCOME AND INTEREST RATE GAPSProjected GapsProjected Net Interest IncomeCommercial SpreadsThe Sensitivity of Nil and Interest Rate GapSTATIC VERSUS DYNAMIC GAPSLIMITATIONS OF INTEREST RATE GAPSEmbedded Options in Banking ProductsLines without MaturityMapping Interest Rates to Selected Risk FactorsRegulated RatesMark-ups and Mark-downs over Reference RatesIntermediate Flows and NIL CalculationsFROM GAPS TO SIMULATIONSALM and Hedging PoliciesMANAGING GAPS: SETTING UP LIMITSThe Basic Mechanism of LimitsLimits and "Nil at Risk"HEDGING: CLOSING INTEREST RATE GAPSSingle PeriodHedging Over Multiple PeriodsHEDGING THE VARIATIONS OF THE TERM STRUCTURE OF INTEREST RATES (CASE STUDY)HEDGING BUSINESS RISK AND INTEREST RATE RISKMultiple Business and Interest Rate ScenariosMatrix Methodology and The Risk-Return Profile of the Balance SheetImplementing the Matrix ApproachHedging both Interest Rate and Business RisksThe Matrices of Net Interest IncomeImplicit Options RiskOPTIONAL RISKOptional Risk is Always Adverse to the BankOptional Risk and HedgingMODELING PREPAYMENTSPAYOFF OF PREPAYMENTTHE VALUE OF IMPLICIT OPTIONSTHE SIMPLE "BINOMIALTREE" TECHNIQUE APPLIED TO INTEREST RATESThe Binomial Tree for Interest RateValuation of a BondThe Global Calibration of the Binomial TreeThe Valuation of American OptionsThe Current Value of the Prepayment OptionThe Original LoanBinomial Tree of Interest RatesThe Market Value of LoanThe Exercise Price and the Payoff of the OptionPayoffs of the Option under Differed ExerciseOption-adjusted SpreadEconomic Value of the Balance SheetECONOMIC VALUE (EV)ECONOMIC VALUE AND NET INTEREST INCOME FOR A BANK WITHOUT CAPITALSample Bank Balance SheetEV and Projected Interest Income at Risk-free RateNIL AND EVIDENTITY BETWEEN EV AND "ALL-IN" CASH FLOWS (CAPITAL AND INTEREST)Separating All-in Flows into Capital and Interest FlowsEconomie Value and NiL: General ExampleEconomic Value and Convexity RiskDURATION PROPERTIESSENSITIVITY OF ECONOMIC VALUE AND DURATION GAPSDuration GapControlling Duration with DerivativesDuration Gap and Sensitivity of EVECONOMIC VALUE, DURATION AND CONVEXITYConvexitySources of ConvexityMeasure of ConvexityEconomic Value and Convexity GapsCONVEXITY GAPS AND OPTIONSOPTIONAL RISK AND OPTIONAL GAPSHedging Caps Sold to ClientsHedging Implicit Options to Renegotiate Fixed RatesSection 8. Funds Transfer Pricing SystemsFunds Transfer Pricing SystemsTHE ORGANIZATION OF FTP SYSTEMSExchanging Net Balances of Funds between UnitsExchanging all Outstanding BalancesCALCULATING INCOME WITHIN A FTP SYSTEMAllocating Income through the FTP SystemThe Accounting N11 of the BankBreaking Down the Bank Margin into Contributions of Business UnitsEconomic Transfer PricesCOMMERCIAL SPREADS AND MATURITY SPREADECONOMIC TRANSFER PRICES FOR LOANSThe Cost of Existing ResourcesThe "Notional" Funding of LoansThe Cost of the Mirror DebtThe Benefits from the Mirror DebtECONOMIC TRANSFER PRICES FOR RESOURCESTRANSFERRING LIQUIDITY AND INTEREST RATE RISK TO ALM THROUGH THE FTP SYSTEMPRICING FOR LENDINGThe All-in Cost of Funds of the Mirror DebtThe Cost of Credit Risk and the Risk PremiumTransaction Versus Client Revenues and PricingEconomic and Commercial Transfer PricesSection 9. Dependencies and Portfolio RiskDEPENDENCIES MODELING ASA KEY BUILDING BLOCK FOR RISK MODELINGMEASURES OF DEPENDENCIESSIMULATIONSSECTION ORGANIZATIONCorrelations and CovariancesCORRELATIONS AND COVARIANCESCorrelations, Variances, and CovariancesCorrelation and Volatility of a Sum of Random VariablesVisual Representation of the Diversification EffectExtension to any Number of VariablesTHE VARIANCE-COVARIANCE MATRIXMatrix Notations Variance-Covariance Matrix of Portfolio ReturnsThe Variance-Covariance Matrix of Portfolio ReturnPortfolio Return VolatilityPORTFOLIO RETURN RISK AND CORRELATIONAPPENDIX: MATRIX NOTATIONS AND FORMULASTranspose MatrixVariance-Covariance Matrix and Correlation MatrixVariance Formula and Correlation MatrixConditional ProbabilitiesDEFINITION OF CONDITIONAL AND JOINT PROBABILITIESConditional ProbabilitiesConditional and Joint ProbabilitiesDEFAULT PROBABILITY OF A FIRM DEPENDENT ON THE STATE OF THE ECONOMYTHE TWO-OBLIGOR PORTFOLIO AND CONDITIONAL PROBABILITIESThe Independence CaseThe Dependent CaseAPPENDIX: CONDITIONING, EXPECTATION AND VARIANCEFactor ModelsFACTOR MODELSTHE GENERIC FORM OF FACTOR MODELSExample of a One-factor ModelThe Single-factor ModelThe Generic Form of Multiple-factor ModelsRISK OF A TWO-STOCK PORTFOLIO WITH THE ONE-FACTOR MODELThe One-factor ModelThe Vanance-Covanance MatrixVanance-Covanance Matrices of Asset Returns and of FactorsPORTFOLIO RISK WITH MULTIPLE-FACTOR MODELSRISK FOR A SINGLE ASSET AND TWO-FACTOR MODELSATWO-ASSET PORTFOLIO WITH TWO-FACTOR MODELSThe Two-factor Model Applied to a Two-asset PortfolioThe Two-asset Portfolio ReturnPortfolio Systematic Risk: Two-factor ModelsPortfolio Systematic Risk Decomposition into Additive ItemsTwo-asset Portfolio and Two-factor Model: Specific RiskPortfolio Total Risk and Two-factor ModelORTHOGONAL MULTIPLE FACTOR MODELS AND PCAUsing PCA for Single AssetsTwo-asset Portfolio and Two Orthogonal FactorsPORTFOLIO RISK: SUMMARY OF MATRIX FORMAT CALCULATIONSAPPENDIX I:THE CONCEPTUAL FOUNDATIONS OF PCAAPPENDIX 2: PORTFOLIO GENERAL RISK, ORTHOGONAL FACTORSDependencies and Copula FunctionsKEY BENEFITS OF COPULA DEPENDENCYREMINDERS AND NOTATIONSDEFINITION OF COPULA FUNCTIONSBivariate CopulaProperties of Copula FunctionsDistribution Functions and PercentilesVarious Forms of Bivariate Copula FunctionsThe Bivariate Copula Function: Expanded FormThe Copula Density FunctionGeneralization to Several VariablesBIVARIATE NORMAL STANDARD DISTRIBUTIONSUnivariate and Bivariate Normal DistributionsBivariate Normal Standard DensityThe Bivariate Normal CopulaForms of the Gaussian CopulaThe Normal Standard Copula Density and the Joint Density of Two VariablesCONDITIONAL PROBABILITY FROM THE COPULA DENSITYConditional Density of Normal BivariateConditional Distributions and SimulationsApplication: Simulating Two Uniform Standard Variables with Conditional CopulaAPPENDIX: COPULA FUNCTION AND COPULA DENSITYDeriving the Copula Density from Copula FunctionJoint Probability Density Functions with Two VariablesDerivation of the Normal Copula DensityJoint Density of a Bivariate Normal Distribution and the Copula Density FunctionConditional Distributions and CopulaSimulations with Factor Models or the Copula ApproachSIMULATIONS AND INVERSE FUNCTIONSSIMULATION OF CORRELATED NORMAL VARIABLES WITH FACTOR MODELSStandardizing the Single-factor ModelThe Simulation Algorithm for Standardized Normal Variables using Single-factor ModelsThe Cholesky Decomposition Method: Two VariablesTwo Random Normal VariablesApplication of Cholesky DecompositionClassical Methodology: SummarySIMULATION OF DEPENDENT VARIABLES WITH THE COPULA APPROACHMain PrincipleSimulation AlgorithmSIMULATION OF TWO DEPENDENT UNIFORM STANDARD VARIABLESSIMULATION OF TWO DEPENDENT NORMAL STANDARD VARIABLESSIMULATION OF TWO DEPENDENT TIMES TO DEFAULTSimulation of Time to Default for a Single ObligorSimulation of Two Exponentially Distributed Dependent Times to DefaultAPPENDIX:THE CHOLESKY DECOMPOSITION METHODSection 10. Market RiskDelta-normal VaRPORTFOLIO DELTA-NORMAL VARSteps for Determining VaRA Simple Portfolio of Two Zero-coupon BondsMAPPING AN INSTRUMENTTO RISK FACTORSInterpolation of Interest Rate from Selected Risk FactorsValue PreservationVolatility PreservationMapping and AllocationTHE EXAMPLE OF A FORWARD FOREIGN EXCHANGE RATETHE CONCEPTUAL FRAMEWORK OF DELTA-NORMAL VARDeriving SensitivitiesMathematical SensitivitiesNumerical SensitivitiesDecomposition of the Forward as a Linear Function of Elementary PositionsVOLATILITY AND DELTA-NORMAL VAR OF THE FORWARD VALUETHE DELTA-VAR OF THE FORWARD CONTRACT: SUMMARYHistorical and Hypothetical SimulationsHISTORICAL SIMULATIONSPrinciplesHistorical VaR: Forward Contract ExampleMONTE CARLO SIMULATIONSGrid SimulationsFull Monte Carlo SimulationsExample: Option ContractEXTENSIONS OF THE MARKET VAR METHODOLOGYE-VaR or Expected ShortfallHypothetical Scenarios, Stress-tests and Extreme VaRSimulation of Interest RatesINTEREST RATES AND FACTOR MODELSPRINCIPAL COMPONENT ANALYSIS AND THE TERM STRUCTURE OF INTEREST RATESINTEREST RATE SIMULATIONS WITH PCAAPPLICATION TO MARKET VARALM APPLICATIONSBack Tests, Benchmarks and Stress Tests BACK TESTINGBENCHMARKINGSTRESS TESTING, HYPOTHETICAL SCENARIOS AND SENSITIVITY ANALYSESDirect Effects or "Factor-push" TechniquesIndirect Effects and Factor-push ScenariosVALIDATIONSection 11. Credit Risk: StandaloneCredit Risk DataDEFAULT STATISTICSAnnual Default RatesCumulative Default RatesRECOVERY STATISTICSTRANSITION MATRICESRating SystemsCREDIT RATINGSCREDIT RATINGS AND LINKS BETWEEN COUNTERPARTIESINTERNAL CREDIT RATINGS AND BUSINESS RULESBUILDING BLOCKS OF THE INTERNAL CREDIT RATING SYSTEMRATING GRIDSJudgmental Ratings versus "Rating Models"Corporate Sample Rating GridBanks: Sample Rating GridMAPPING RATINGS TO DEFAULT PROBABILITIESAPPENDIX: RATING SCALES OF RATING AGENCIESStatistical and Scoring ModelsSCORINGTHE ECONOMICS OF SCORING SYSTEMSLOGIT MODELSThe "Basic" Linear Model DrawbacksLogit Model FamilySCORING IN RETAIL BANKING: BEHAVIORAL VERSUS ORIGINATION MODELSIMPLEMENTATION OF SCORING IN RETAIL BANKINGDiscriminating VariablesIdentification of Potentially Significant AttributesNon-linear Relationship between Selected Attributes and Credit StateConstructing Attributes from Observed CharacteristicsFitting and Back Testing Scoring ModelsACCURACY OF SCORING MODELS:THE "CAP"MAPPING SCORING MODELS TO A MASTER SCALE OF DEFAULT PROBABILITIESThe Option Approach to Defaults and MigrationsHOW FIRMS DEFAULTTHE OPTION THEORETIC FRAMEWORK OF VALUATION OF EQUITY AND DEBTIMPLEMENTING THE STRUCTURAL MODEL OF DEFAULTMODELING DEFAULT PROBABILITY AND CREDIT STANDING AT HORIZONIMPLEMENTING THE EDF© MODELTHEORETICAL VALUES OF THE OPTION TO DEFAULT ANDTHE EDF©Valuation of the Put Option to DefaultDetermination of the Default ProbabilityDetermining the Percentile of the Final Asset ValueSAMPLE CALCULATIONS OF EDF© AND OF THE PUT AND CALL VALUESVARIATIONS ON THE MERTON'S MODELMAPPING DEFAULT PROBABILITY TO THE STANDARDIZED NORMAL DISTANCE TO DEFAULTDefault Probability and Default IntensityCUMULATIVE DEFAULT AND SURVIVAL PROBABILITIESFORWARD DEFAULT AND SURVIVAL PROBABILITIESBasic FormulasCalculating Marginal Default ProbabilitiesMIGRATION MATRICESMigration Matrices and Cumulative Default ProbabilitiesDirect Calculation of Default Probability over Two PeriodsGeneral Calculation of Default Probability over Two PeriodsGenerator MatricesCREDIT INTENSITY MODELSDefault Intensity ModelsForward Default IntensityTime to DefaultAPPENDIX: MATRIX DIAGONALIZATIONCredit Risk Potential ExposureBANKING PORTFOLIO EXPOSURESOn Balance SheetOff Balance Sheet CommitmentsMARKET INSTRUMENTS AND POTENTIAL FUTURE EXPOSURES (PFES)Interest Rate SwapsForeign Exchange SwapsOptionsREGULATORY ADD-ONS FOR DERIVATIVESCREDIT RISK FOR DERIVATIVES: METHODOLOGYCALCULATING THE PFE FOR AN INTEREST RATE SWAPCREDIT RISK EXPOSURE FOR PORTFOLIOS OF DERIVATIVESModeling RecoveriesCOLLATERALIZED SECURITIES LENDING/BORROWINGEconomic Derivation of Minimum Over-collateralizationBasel 2 Treatment of Collateralized TransactionsVALUATION OF CREDIT RISK GUARANTEES, INSURANCE OR CREDIT DERIVATIVESSUPPORTDISTRIBUTION OF RANDOM RECOVERIESCOVENANTSCredit Risk Valuation and Credit SpreadsCREDIT SPREAD, IMPLIED DEFAULT INTENSITY AND RECOVERY RATECREDIT VAR AND MATRIX VALUATIONCREDIT VAR AND MATRIX VALUATION: APPLICATIONMIGRATIONS AND VAR UNDERTHE STRUCTURAL MODELFORWARD VALUATION AND EXCESS SPREADSSection 12. Credit Portfolio RiskCredit Event DependenciesMODELING JOINT MIGRATIONS AND DEFAULTS WITH THE STRUCTURAL MODELDependency and Joint Default ProbabilityDependency and Joint Migration ProbabilitiesJOINT DEFAULT PROBABILITY USING DISCRETE VARIABLESCONDITIONAL PROBABILITIES AND CORRELATIONJOINT MIGRATION MATRICESSIMULATION OF JOINT DEFAULTS AND MIGRATIONSExample of Portfolio Loss Distribution PORTFOLIO OF TWO OBLIGORSPORTFOLIO OF TWO INDEPENDENT OBLIGORSThe Loss DistributionThe Loss StatisticsDEPENDENT DEFAULT EVENTSCalculation of Joint Default and Conditional ProbabilitiesLoss DistributionLoss StatisticsCOMPARISON OF THE DEPENDENT AND THE INDEPENDENT CASESAnalytical Loss DistributionsINDEPENDENT DEFAULT EVENTS:THE BINOMIAL DISTRIBUTIONSimulating Increased Diversification with Loss IndependenceThe Effect of DiversificationTHE "STANDARDIZED" STANDALONE STRUCTURAL MODELA Single Obligor Dependent on the State of the EconomyThe Asset Value and Default Probability Conditional on the State of the EconomyThe Default Probability Conditional on The State of the EconomyApplication: The Stressed Default Probability under Basel 2MODELING DEFAULTS IN A UNIFORM PORTFOLIO:THE LIMIT DISTRIBUTIONThe Uniform Granular PortfolioModeling Defaults under the Structural ModelThe Limit DistributionApplication: Finding the Factor Value Matching a Given Portfolio Loss PercentileSimulation of Credit Portfolio Loss DistributionsPRINCIPLES OF SAMPLE SIMULATIONSMONTE CARLO SIMULATIONS OF DEFAULT EVENTS BASED ON THE STRUCTURAL MODEL OF DEFAULTAsset Distribution and Default ProbabilityThe Multiple SimulationsThe Simulation AlgorithmSimulations of Default DistributionsDealing with Different Default Probabilities and Discrepancies of ExposuresSIMULATIONS OF TIMES TO DEFAULTThe Simulation AlgorithmDealing with Different Default Probabilities and Discrepancies of ExposuresCredit Portfolio ModelsCREDIT PORTFOLIO MODEL OVERVIEWMOODY'S-KMV CREDIT MONITOR AND MOODY'S-KMV PORTFOLIO MANAGERConceptual FrameworkCredit Events and Credit State at HorizonRisk Factors and Dependence StructureRevaluation of Facilities at HorizonGeneration of Portfolio Value DistributionPortfolio OptimizationCREDIT METRICSCREDIT PORTFOLIO VIEW: ECONOMETRIC MODELSCredit Portfolio View Conceptual FrameworkCredit Events and Credit State at HorizonRisk Factors and Dependence StructureRevaluation of Facilities at HorizonGeneration of Portfolio Value DistributionCREDITRISK+AND ANALYTICAL DISTRIBUTIONSConceptual FrameworkCredit Events and Credit State at HorizonRisk FactorsDependency StructureGeneration of Portfolio Value DistributionAPPENDIX:THE GAMMA DISTRIBUTIONSection 13. Capital AllocationEconomic Capital and Credit Risk VaRHORIZON FOR CREDIT CAPITALFROM PORTFOLIO VALUE DISTRIBUTION TO CREDIT CAPITALCapital Under Default ModeCapital Under Full Migration ModeExpected LossEconomic Capital and Loss VolatilityFrom Future Values to Current CapitalRAROC CALCULATIONS AT PORTFOLIO AND FACILITY LEVELSCapital Allocation and Risk ContributionsNORMATIVE CAPITAL ALLOCATIONS AND CAPITAL EFFECTIVE UTILIZATIONSNormative Risk Allocations Versus Capital UtilizationsCapital UtilizationsDEFINITIONS OF RISK CONTRIBUTIONSSTANDALONE INDIVIDUAL LOSSESRISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONS TO PORTFOLIO LOSS VOLATILITY AND TO CAPITALRisk Contributions, Portfolio Loss Volatility and CapitalMarginal Risk ContributionsUsages of Risk Contributions and of Marginal Risk ContributionsBASIC PROPERTIES OF RISK CONTRIBUTIONSTHE CAPITAL ALLOCATION MODEL AND RISK CONTRIBUTIONSRisk Contributions to Portfolio Loss VolatilitySpecific CasesFrom Risk Contributions to Capital AllocationSAMPLE CALCULATIONS OF RISK CONTRIBUTIONSStandalone Expected Loss and Portfolio Expected LossStandalone Loss Volatilities and Portfolio Loss VolatilityThe Portfolio Loss VolatilityRisk Contributions to VolatilityCapital AllocationAPPENDIX: CALCULATION OF ABSOLUTE RISK CONTRIBUTIONS FROM THE VARIANCE-COVARIANCE MATRIXMarginal Risk ContributionsMARGINAL RISK CONTRIBUTIONS TO LOSS VOLATILITYMARGINAL RISK CONTRIBUTIONS TO CAPITALGENERAL PROPERTIES OF RISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONSMARGINAL RISK CONTRIBUTIONS TO VOLATILITY VERSUS RISK CONTRIBUTIONSMARGINAL RISK CONTRIBUTION AND SIZE OF AN EXISTING EXPOSURESection 14. Risk-adjusted PerformanceRaRoC and Shareholders' Value Added RISK-ADJUSTED MEASURES OF PERFORMANCEDefinitionsThe Hurdle Rate and the Cost of CapitalThe "Ex Ante" and the "Ex Post" ViewsThe Reference Capital for Risk ContributionsRISK-BASED PRICING AND MARGINAL RISK CONTRIBUTIONSRisk-based Pricing and Marginal Risk Contribution to CapitalRisk-based Pricing and Risk Contribution to CapitalThe Pricing Paradox with Marginal Risk ContributionsRisk-adjusted Performance versus Risk-based PricingRAROC CALCULATIONSRevenuesExpected LossOther CostsExpanded RaRoC FormulaTHE RISK PREMIUM EMBEDDED IN RISK-BASED PRICINGSVA MEASURESTHE PRICE OF RISK AND ARBITRAGEEconomic Income StatementsTHE CALCULATION OF RAROC AND SVA FOR CREDIT RISKCalculation of RaRoC and SVARISK-BASED PRICINGRISK-BASED PERFORMANCE, PRICING AND CAPITAL ALLOCATIONRisk-based PricingRisk-based PerformanceORIGINATION AND POST-ORIGINATION FOLLOW UPSection 15. Credit Portfolio ManagementPortfolio AnalysisTHE SAMPLE PORTFOLIO AND THE SIMULATIONSPortfolio DataPortfolio SimulationsPORTFOLIO LOSS DISTRIBUTIONPORTFOLIO OVERVIEWLoss Statistics and CapitalPortfolio Risk Return ProfilePortfolio Concentration and Correlation RiskFrom Portfolio Risk to Individual FacilitiesREPORTING ALTERNATE METRICS OF RISKExposures, Default Probability and Loss Given DefaultExposure and Expected LossExposure and Capital Allocation or Loss VolatilityRISK-ADJUSTED PERFORMANCE AND MISPRICING REPORTSBook Measures of Profitability versus Risk-adjusted MeasuresMispricing ReportsREPORTING RISK AND RETURN VERSUS BUSINESS DIMENSIONSAPPENDIX I: SAMPLE PORTFOLIO INPUTSAPPENDIX 2: SAMPLE PORTFOLIO OUTPUTSAPPENDIX 3: PORTFOLIO ANALYSIS AND REPORTING ISSUESTraceability of Aggregated Measures and Risk ManagementDealing with Multiple DimensionsPORTFOLIO ANALYSIS AND REPORTING TECHNICAL CHALLENGESBasic Specifications of Reporting SystemsStress Testing and What-if AnalysesInteractive Implementation of Risk SystemsSecuritization and Capital ManagementECONOMICS OF SECURITIZATIONSExpected Return on Assets and Compensations to InvestorsVariety of SecuritizationsRationales For SecuritizationsThe Securitization OrganizationSTRUCTURING AND THE WATERFALL MECHANISMStructuring of NotesThe Waterfalls of Cash Flows and LossesECONOMICS OF SECURITIZATION FORTHE BANKAnalysis of a Securitization Transaction (Case Study)The Costs of Funding On Balance Sheet and through SecuritizationThe Effective Return on Capital for the BankThe Cost of Financing through SecuritizationThe Annualized All-in Cost of Financing through SecuritizationThe Pricing of Assets Sold to the SPEThe All-in Cost of Funding through SecuritizationSecuritization Economics and the Return on EquityEnhancing the Bank's Return on Capital through SecuritizationASSESSING THE RISK OF ASSET-BACKED NOTESRating Methodologies for Structured NotesCredit Portfolio Models and SecuritizationsTranches are Subject to Correlation RiskCredit Portfolio ManagementTHE RATIONALE FOR CREDIT PORTFOLIO MANAGEMENTTRADING CREDIT RISKAPPLICATIONS OF CREDIT DERIVATIVESHedging Credit RiskTrading Credit RiskCustomizing Credit RiskApplications for Credit Portfolio ManagementEvolution of Credit Risk ModelsPORTFOLIO CREDIT RISK MANAGEMENT (CASE STUDY)Buying Protection for the Portfolio from Another BankBuying Protection for the Portfolio and Selling ProtectionOTHER ARBITRAGE BETWEEN ECONOMIC PRICES AND RATING-BASED PRICESThe Financial System and Reforms THE FINANCIAL STABILITY FORUM RECOMMENDATIONSCapitalProvisioningValuation and LeverageTHE WHITE PAPER FROM THE WHITE HOUSESupervisionEstablish Comprehensive Supervision and Regulation of Financial MarketsProtect Consumers and Investors from Financial AbuseImprove Tools for Managing Financial CrisesRaise International Regulatory Standards and Improve International CooperationAREAS UNDER SCRUTINY BY FINANCIAL AUTHORITIES: SUMMARY
 
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