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«Risk management in banking»





APPENDIX 3: PORTFOLIO ANALYSIS AND REPORTING ISSUESEXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA) MODELAbout the AuthorNumerical SensitivitiesEARNINGS-AT-RISK ("EAR")APPENDIX: RATING SCALES OF RATING AGENCIESConvexityPRICING FOR LENDINGSection 12. Credit Portfolio RiskCREDIT SPREAD PRODUCTSApplications for Credit Portfolio ManagementExposure at Default (EAD)Credit Portfolio View Conceptual FrameworkCorrelation and Volatility of a Sum of Random VariablesVariance and VolatilityGeneration of Portfolio Value DistributionThe Matrices of Net Interest IncomeRISK MANAGEMENT PROCESSESFrom Discrete to Continuous ReturnsSection 13. Capital AllocationCredit Risk Mitigation: Collateral TreatmentCAPITAL CALCULATIONJOINT DEFAULT PROBABILITY USING DISCRETE VARIABLESVAR AND ECONOMIC CAPITALSTATIC VERSUS DYNAMIC GAPSLOGIT MODELSLIQUIDITY GAP TIME PROFILESMAPPING SCORING MODELS TO A MASTER SCALE OF DEFAULT PROBABILITIESLarge Number of ExposuresMarginal Risk ContributionsSENSITIVITY AND RISK FACTORSJudgmental Ratings versus "Rating Models"Optional Risk is Always Adverse to the BankSection 2. Business Lines, Risks, and Risk ManagementSIMULATIONS OF TIMES TO DEFAULTCalculation of RaRoC and SVASection 1. The Financial CrisisINTEREST RATE RISKESTIMATING EWMA VOLATILITYTHE "STANDARDIZED" STANDALONE STRUCTURAL MODELMAPPING RATINGS TO DEFAULT PROBABILITIESLIQUIDITY RISK: FUNDINGFORWARD CONTRACTS VERSUS OPTIONSThe Cholesky Decomposition Method: Two VariablesOption-adjusted SpreadAccounting StandardsMatrix Methodology and The Risk-Return Profile of the Balance SheetRATING GRIDSThe Cost of the Mirror DebtSecuritizations: SyntheticMarket Risk and Trading ActivitiesRisk Management versus Risk InstrumentsRating SystemsBanking Business LinesUNIFORM DISTRIBUTIONRaRoC and Shareholders' Value Added THE ALM FUNCTIONREGULATIONSCOLLATERALIZED SECURITIES LENDING/BORROWINGProprietary Models of Market Risk VaRThe Bivariate Normal CopulaMark-to-market Value of an IRSStochastic ProcessesHow to Derive the Pricing PDEThe Pricing Paradox with Marginal Risk ContributionsASSET CLASSESINTEREST RATE RISK FOR BORROWERS AND LENDERSAnnual Default RatesProvisioningSCORINGSimulating Increased Diversification with Loss IndependenceDependency StructureRisk-based Capital RegulationsDistribution Functions and PercentilesThe "Rare Event" ProcessAPPENDIX I: SAMPLE PORTFOLIO INPUTSINTEREST RATE PROCESSESRAROC CALCULATIONSOptions Allow Hedging RisksInterest Rate GapsTHE VARIANCE-COVARIANCE MATRIXContinuous TimeImplementing the Matrix ApproachNIL AND EVStatistical and Scoring ModelsTrading Credit RiskVolatilityInterest Rate Risk and Interest. Rate DerivativesTHE VAR METHODOLOGY: MARKET RISKCredit Risk Mitigation: Guarantees and Credit DerivativesOPTIONAL RISK AND OPTIONAL GAPSRANDOM VARIABLES AND PROBABILITY DISTRIBUTION FUNCTIONSComparing Continuous and Discrete ReturnsAccounting StandardsBank ExposuresORIGINATION AND POST-ORIGINATION FOLLOW UPECONOMIC VALUE AND NET INTEREST INCOME FOR A BANK WITHOUT CAPITALEmbedded Options in Banking ProductsSIMULATIONS AND INVERSE FUNCTIONSThe Option Approach to Defaults and MigrationsGeneration of Portfolio Value DistributionStandalone Loss Volatilities and Portfolio Loss VolatilityDefault Probability and Default IntensityDerivatives and Credit RiskLimits and DelegationsMEASURES OF POTENTIAL LOSSESSection 9. Dependencies and Portfolio RiskTHE CONTRIBUTIONS OF VAR-BASED MEASURESStandalone Expected Loss and Portfolio Expected LossINDEPENDENT DEFAULT EVENTS:THE BINOMIAL DISTRIBUTIONConditional ProbabilitiesContinuous Returns and VarianceTwo-asset Portfolio and Two-factor Model: Specific RiskFOREIGN EXCHANGE OPTIONSCredit Events and Credit State at HorizonPayoff of a Forward ContractPreemptive Risk Control versus Risk InsuranceThe "Three Lines of Defense" PrincipleThe Multiple SimulationsSOLVENCY RISKAPPENDIX: CALCULATION OF ABSOLUTE RISK CONTRIBUTIONS FROM THE VARIANCE-COVARIANCE MATRIXThe Global Calibration of the Binomial TreeSection 15. Credit Portfolio ManagementOPERATIONAL RISKSECURITIZATIONSInteractive Implementation of Risk SystemsThe Portfolio Loss VolatilityVALUATION RULESVaR at Different HorizonsAPPLICATION: STOCK VALUE DISTRIBUTIONVALUATION OF CREDIT RISK GUARANTEES, INSURANCE OR CREDIT DERIVATIVESCREDIT RISK FOR DERIVATIVES: METHODOLOGYRISK-ADJUSTED PERFORMANCE AND MISPRICING REPORTSScope and Goals of this TextUNCERTAINTY, RISK,AND EXPOSURETO RISKCredit Risk in the Trading PortfolioFROM GAPS TO SIMULATIONSHedging both Interest Rate and Business RisksTHE GAP MODELConditional Distributions and SimulationsUnderlying of OptionsMigration Matrices and Cumulative Default ProbabilitiesRAROC CALCULATIONS AT PORTFOLIO AND FACILITY LEVELSTime to DefaultPOSITIONING OF THE TEXTForward and Spot Rates: No ArbitragePRINCIPAL COMPONENT ANALYSIS AND THE TERM STRUCTURE OF INTEREST RATESThe Original LoanFrom Portfolio Risk to Individual FacilitiesForeign Exchange SwapsCONTAGION THROUGH SECURITIZATIONSExpected LossINTEREST RATE RISKNumerical ExampleThe Payoff of Option ContractsPayment TermsCAPITAL ADEQUACYTRANSACTION-SPECIFIC CREDIT RISKEconomic Capital and Loss VolatilityVarious Forms of Bivariate Copula FunctionsHEDGING INTEREST RATE RISK BY CORPORATE BORROWER (CASE STUDY)Raise International Regulatory Standards and Improve International CooperationPortfolio DataLIQUIDITY DEFINITIONSASSETS AND POSITIONSCorrelations and CovariancesApplication: Simulating Two Uniform Standard Variables with Conditional CopulaAPPENDIX:THE TAYLOR EXPANSION FORMULAStatic Liquidity GapsRevenuesDeriving SensitivitiesGeneration of Portfolio Value DistributionBERNOULLI DISTRIBUTIONOPTIONAL RISKECONOMIC TRANSFER PRICES FOR LOANSPORTFOLIO ANALYSIS AND REPORTING TECHNICAL CHALLENGESThe Loss StatisticsCREDIT METRICSDEFINITIONS OF CREDIT DERIVATIVESHedging Over Multiple PeriodsConditional Distributions and CopulaRISK-BASED PRICING AND MARGINAL RISK CONTRIBUTIONSOn Balance SheetHEDGING THE VARIATIONS OF THE TERM STRUCTURE OF INTEREST RATES (CASE STUDY)Transpose MatrixCUMULATIVE DEFAULT AND SURVIVAL PROBABILITIESMAPPING DEFAULT PROBABILITY TO THE STANDARDIZED NORMAL DISTANCE TO DEFAULTDISTRIBUTION OF RANDOM RECOVERIESMEASURES OF DEPENDENCIESThe Basic Mechanism of LimitsALM APPLICATIONSHEDGING BUSINESS RISK AND INTEREST RATE RISKSimulation of Interest RatesTHE "BASEL I ACCORD" FOR CREDIT RISKBack Tests, Benchmarks and Stress Tests SupervisionRISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONS TO PORTFOLIO LOSS VOLATILITY AND TO CAPITALProject FinanceBasel I DrawbacksEnhancing the Bank's Return on Capital through SecuritizationThe Loss DistributionTHE CONCEPTUAL FRAMEWORK OF DELTA-NORMAL VARMARGINAL RISK CONTRIBUTIONS TO VOLATILITY VERSUS RISK CONTRIBUTIONSNORMAL DISTRIBUTIONCREDIT PORTFOLIO MODEL OVERVIEWRisk Oversight: Regulators' ChallengesRisk-based Pricing and Risk Contribution to CapitalAPPENDIX: COPULA FUNCTION AND COPULA DENSITYMultiple Business and Interest Rate ScenariosLOGNORMAL DISTRIBUTIONPORTFOLIO RISK WITH MULTIPLE-FACTOR MODELSSTRESS TESTING, HYPOTHETICAL SCENARIOS AND SENSITIVITY ANALYSESTHE NEW BASEL ACCORDCapital AllocationRisk ManagementTHE RATIONALE FOR CREDIT PORTFOLIO MANAGEMENTHEDGING: CLOSING INTEREST RATE GAPSMigration RiskVALUATION OF RISKY DEBT FROM CREDIT SPREADS AND RISK-NEUTRAL PROBABILITIESADDITIONAL PROPOSALSHEDGING A CORPORATE LONG EXPOSURE IN FOREIGN CURRENCY (CASE STUDY)Expected LossMapping and AllocationThe Cost of Credit Risk and the Risk PremiumHow to Solve Numerically a PDEIMPLEMENTING THE EDF© MODELTRADING CREDIT RISKDetermination of the Default ProbabilityLoans and ReceivablesValue PercentileMark-ups and Mark-downs over Reference RatesThe Valuation of American OptionsLegal IssuesCommercial SpreadsSecuritization and Capital ManagementWHERE DO INTEREST RATES COME FROM?BINOMIAL DISTRIBUTION OF SUM OF BERNOULLI VARIABLESREMINDERS AND NOTATIONSConceptual FrameworkThe Securitization OrganizationCOMPARISONS OF CLASSIFICATIONS: RISK REGULATIONS AND IFRSCredit Portfolio Models and SecuritizationsDEPENDENT DEFAULT EVENTSDURATION PROPERTIESHow to Form Risk-free PortfoliosLoss Given Default (LGD)The All-in Cost of Funding through SecuritizationFORWARD RATES: DEFINITIONSMark-to-market Valuation of Forward ContractsALM and Hedging PoliciesVariety of SecuritizationsFrom Future Values to Current CapitalSpot and Forward PricesForeign Exchange Risk and Foreign Exchange DerivativesRisk Factors and Dependence StructureThe Sensitivity of Nil and Interest Rate GapDEFINITIONS OF RISK CONTRIBUTIONSAsset Swaps: GeneralizationTHE FOREIGN EXCHANGE MARKET AND RATESThe Generic Form of Multiple-factor ModelsDetermining the Percentile of the Final Asset ValueEvolution of Credit Risk ModelsTHE SIMPLE "BINOMIALTREE" TECHNIQUE APPLIED TO INTEREST RATESCONTAGION AND PROCYCLICALITY IN A LEVERAGED INDUSTRYORTHOGONAL MULTIPLE FACTOR MODELS AND PCAMODELING POTENTIAL VARIATIONS AND PERCENTILESFOREIGN EXCHANGE RATES AND FORWARD CONTRACTSAsset Value and Market Required ReturnDemand DepositsSimulation of Time to Default for a Single ObligorDISCRETE AND CONTINUOUS RETURNSFrom Daily Volatility of the Position to Daily VaRPORTFOLIO OF TWO OBLIGORSTRANSFERRING LIQUIDITY AND INTEREST RATE RISK TO ALM THROUGH THE FTP SYSTEMCOMMON STOCHASTIC PROCESSESSIMULATION OF DEPENDENT VARIABLES WITH THE COPULA APPROACHPayments under a Credit EventOPTIONSIncome-producing Real EstateTHE ECONOMICS OF SCORING SYSTEMSTHE EXPONENTIAL DISTRIBUTION AND TIME TO DEFAULTKEY BENEFITS OF COPULA DEPENDENCYMotivations for Risk OversightProjected Net Interest IncomeFactor ModelsHigh-volatility Commercial Real EstateCONTAGION AND PROCYCLICALITYTHROUGH FAIR VALUE RULESSingle Period Discrete ReturnSPECIFICS OF STOCHASTIC PROCESSES AND ITO LEMMAMAPPING AN INSTRUMENTTO RISK FACTORSModeling Defaults under the Structural ModelThe Wiener ProcessSIMULATION OF CORRELATED NORMAL VARIABLES WITH FACTOR MODELSMODELING DEFAULTS IN A UNIFORM PORTFOLIO:THE LIMIT DISTRIBUTIONNumber of Default Events over a Given HorizonTHE ACCORD FOR MARKET RISKAvailable-for-sale Financial AssetsThe Effect of DiversificationFINANCIAL RISKSPILLAR 2: SUPERVISORY REVIEW PROCESSDEFINITION OF INTEREST RATE GAPSVOLATILITY AND DELTA-NORMAL VAR OF THE FORWARD VALUEAsset-liability Management (ALM)Measure of ConvexityECONOMICS OF SECURITIZATION FORTHE BANKOption PricingTYPES OF RISKSThe Uniform Granular PortfolioMODELING JOINT MIGRATIONS AND DEFAULTS WITH THE STRUCTURAL MODELPORTFOLIO DELTA-NORMAL VARMispricing ReportsValuation of the Put Option to DefaultBOOK STRUCTUREHOW FIRMS DEFAULTSection 5. Risk ModelingDependency and Joint Default ProbabilityTraceability of Aggregated Measures and Risk ManagementCALCULATIONS OF INTEREST RATE GAPSThe Copula Density FunctionCalculation of Joint Default and Conditional ProbabilitiesObject FinanceLIMITATIONS OF INTEREST RATE GAPSBANKING REGULATIONS AND ACCOUNTING STANDARDSDEFAULT PROBABILITY OF A FIRM DEPENDENT ON THE STATE OF THE ECONOMYBENCHMARKINGLending, Borrowing and the Term Structure of Interest RatesVolatility PreservationPortfolio Systematic Risk: Two-factor ModelsInterpretation of Basel 2 Formulas for Risk WeightsExample: Stock Price DistributionCredit DerivativesRISK OF A TWO-STOCK PORTFOLIO WITH THE ONE-FACTOR MODELSENSITIVITIES AND RISK CONTROLLINGExposures, Default Probability and Loss Given DefaultALM GOALSMARGINAL RISK CONTRIBUTIONS TO CAPITALVariance-Covariance Matrix of Portfolio ReturnsCalculating Marginal Default ProbabilitiesSTOCHASTIC PROCESSESThe Exercise Price and the Payoff of the OptionDirect Effects or "Factor-push" TechniquesTHE BETA DISTRIBUTIONCountry RiskSIMULATIONSCONVEXITY GAPS AND OPTIONSCREDIT VAR AND MATRIX VALUATIONIMPAIRMENT OF FINANCIAL ASSETSECONOMIC TRANSFER PRICES FOR RESOURCESRationales For SecuritizationsRisk FactorsOptional Risk and HedgingCredit Risk Valuation and Credit SpreadsAPPLICATION TO LOSS DISTRIBUTIONS AND LOSS PERCENTILESEconomic Capital and Credit Risk VaRLiquidity Management and Liquidity GapsCALCULATING INCOME WITHIN A FTP SYSTEMMONTE CARLO SIMULATIONSEssentials on Derivative ProductsAPPENDIX 2: SAMPLE PORTFOLIO OUTPUTSRISK OVERSIGHT CHALLENGESALM SCOPE AND STRUCTURE OF THE SECTIONThe Mean Reverting ProcessA Simple Portfolio of Two Zero-coupon BondsEconomic Value and Convexity GapsHedging Implicit Options to Renegotiate Fixed RatesBASIC POSTULATES OF THIS TEXTDerivation of the Normal Copula DensityThe Firm ValueA Single Obligor Dependent on the State of the EconomySOME IMPLICATIONSEconomic Value and Convexity RiskLoss DistributionCommodities FinanceHypothetical Scenarios, Stress-tests and Extreme VaRUnivariate and Bivariate Normal DistributionsCapital RequirementsProtect Consumers and Investors from Financial AbuseCREDIT RISK MITIGATIONThe Two-factor Model Applied to a Two-asset PortfolioSingle PeriodBanking Regulations: Basel I and Market RiskIDENTITY BETWEEN EV AND "ALL-IN" CASH FLOWS (CAPITAL AND INTEREST)Two Random Normal VariablesINTEREST RATES AND FACTOR MODELSThe Independence CaseRegulation and CompetitionThe "Ex Ante" and the "Ex Post" ViewsSellers of OptionsINTEREST RATE OPTIONS: CAPS AND FLOORSRisk Contributions, Portfolio Loss Volatility and CapitalOther CostsRisk Factors and Dependence StructureCapital Allocation and Risk ContributionsTHEORETICAL VALUES OF THE OPTION TO DEFAULT ANDTHE EDF©Standardized ApproachSensitivityFORWARD CONTRACTSCredit Risk DataAmortizing LoansRisk-adjusted Performance versus Risk-based PricingPORTFOLIO OF TWO INDEPENDENT OBLIGORSVARIATIONS ON THE MERTON'S MODELTHE VALUE OF IMPLICIT OPTIONSEconomic Derivation of Minimum Over-collateralizationSTRUCTURING AND THE WATERFALL MECHANISMCollarIMPLEMENTATION OF SCORING IN RETAIL BANKINGUnexpected Loss and VaRPortfolio Risk Return ProfileCredit Portfolio ManagementFrom Risk Contributions to Capital AllocationLIQUIDITY SCENARIOSLiquidity Crises and Stress Test ScenariosConstructing Attributes from Observed CharacteristicsRISK-NEUTRAL VALUATION:THE CASE OF A STOCK PRICEBreaking Down the Bank Margin into Contributions of Business UnitsContinuous VariablesVALUATION OF AN OPTION UNDER RISK-NEUTRAL PROBABILITIESProperties of Copula FunctionsBASKET SWAPS, FIRST-TO-DEFAULT, N-TO-DEFAULTExample of a One-factor ModelExtension to any Number of VariablesInterpolation of Interest Rate from Selected Risk FactorsConditional ProbabilitiesRisk Oversight: Banks' ChallengesCORRELATIONS AND COVARIANCESCREDIT RISK COMPONENTSDefault RiskVariance Formula and Correlation MatrixTransaction Versus Client Revenues and PricingSAMPLE CALCULATIONS OF RISK CONTRIBUTIONSMAIN SPECIFICS AND KEYTERMSThe Simulation AlgorithmPORTFOLIO CREDIT RISK MANAGEMENT (CASE STUDY)RISK-BASED PERFORMANCE, PRICING AND CAPITAL ALLOCATIONHow Gaps Change Through TimeHedging and Speculating with Forward ContractsThe Costs of Funding On Balance Sheet and through SecuritizationHEDGE ACCOUNTINGDERIVATIVES: BASIC DEFINITIONS AND PRINCIPLESSUPPORTSETTING-UP LIMITSDiscrete VariablesVisual Representation of the Diversification EffectValuation and LeverageSection 8. Funds Transfer Pricing SystemsMarginal Risk ContributionsRisk RegulationsThe Simulation Algorithm for Standardized Normal Variables using Single-factor ModelsCorrelation and Concentration RisksCLASSIFICATION OF LENDING PRODUCTS AND BASEL 2 CRITERIASection 7. Asset Liability Management (ALM)Options as Volatility InstrumentsBasel 2 Treatment of Collateralized TransactionsMANAGEMENT PRACTICES DIFFER ACROSS AND WITHIN BUSINESS LINESCONTAGION THROUGH RATING DOWNGRADESTHE RISK PREMIUM EMBEDDED IN RISK-BASED PRICINGAsset Distribution and Default ProbabilityBasic FormulasSENSITIVITY OF ECONOMIC VALUE AND DURATION GAPSREGULATORY ISSUESTHE VASICEK MODELEconomic Transfer PricesBivariate CopulaExchanging all Outstanding BalancesHedging Credit RiskLIQUIDITY CONTAGIONRisk-based PricingRisk and Return of Option ContractsDealing with Different Default Probabilities and Discrepancies of ExposuresBasic Specifications of Reporting SystemsVariance-Covariance Matrix and Correlation MatrixLiquid AssetsMOODY'S-KMV CREDIT MONITOR AND MOODY'S-KMV PORTFOLIO MANAGERGenerator MatricesINVERSE FUNCTIONSImprove Tools for Managing Financial CrisesOptionsSeparating All-in Flows into Capital and Interest FlowsMaterializationATWO-ASSET PORTFOLIO WITH TWO-FACTOR MODELSOPERATIONAL RISKInstruments Traded in Inactive MarketsTHE WHITE PAPER FROM THE WHITE HOUSEMONTE CARLO SIMULATIONS OF DEFAULT EVENTS BASED ON THE STRUCTURAL MODEL OF DEFAULTTHE ORGANIZATION OF FTP SYSTEMSACCURACY OF SCORING MODELS:THE "CAP"GARCH MODELSDEFINITION OF COPULA FUNCTIONSPORTFOLIO LOSS DISTRIBUTIONTRANSITION MATRICESJOINT MIGRATION MATRICESLoss PercentilesTHE POISSON DISTRIBUTIONFOREIGN EXCHANGE RISKSECTION ORGANIZATIONThe Generalized Wiener ProcessApplication: The Stressed Default Probability under Basel 2Simulation of Two Exponentially Distributed Dependent Times to DefaultExceptional LossesDuration Gap and Sensitivity of EVSensitivityBonds and LoansRisk-neutral ProbabilityRisk Contributions to Portfolio Loss VolatilityE-VaR or Expected ShortfallThe Normal Standard Copula Density and the Joint Density of Two VariablesREGULATORY ADD-ONS FOR DERIVATIVESLIQUIDITY GAP CALCULATIONSThe Cost of Financing through SecuritizationPortfolio Concentration and Correlation RiskHistorical VaR: Forward Contract ExampleAPPLICATIONS OF CREDIT DERIVATIVESBUILDING BLOCKS OF THE INTERNAL CREDIT RATING SYSTEMExpected LossCollateral: Haircut CalculationsNORMATIVE CAPITAL ALLOCATIONS AND CAPITAL EFFECTIVE UTILIZATIONSSample Gap ReportsThe Cooke Ratio and Credit RiskTop-down and Bottom-up Risk Management Processes and SystemsDeterministic CalculusExposure and Capital Allocation or Loss VolatilityCompounding Discrete Returns over Multiple PeriodsRetail PortfolioRisk-based Pricing and Marginal Risk Contribution to CapitalContingencies Given (Off-balance Sheet)Economic Value of the Balance SheetSpecific CasesINTERNAL CREDIT RATINGS AND BUSINESS RULESDynamic Liquidity GapsSIMULATION OF TWO DEPENDENT TIMES TO DEFAULTTHE PRICE OF RISK AND ARBITRAGEDefault Intensity ModelsNET INTEREST INCOME AND INTEREST RATE GAPSBIVARIATE NORMAL STANDARD DISTRIBUTIONSInterest Rate SwapsCONDITIONAL PROBABILITIES AND CORRELATIONUsages of Forward Rate ContractsBivariate Normal Standard DensityCredit Risk and Lending ActivitiesSTRUCTURAL EXCESSES OF LIQUIDITYDEPENDENCIES MODELING ASA KEY BUILDING BLOCK FOR RISK MODELINGGeneralization to Several VariablesModeling RecoveriesBACK TESTINGDEFINITION OF CONDITIONAL AND JOINT PROBABILITIESBUSINESS POLES IN THE BANKING INDUSTRYHORIZON FOR CREDIT CAPITALDefinitionDiscriminating VariablesCapitalThe Accounting N11 of the BankREPORTING ALTERNATE METRICS OF RISKProjected GapsThe Effective Return on Capital for the BankRecovery RiskSection 3. Financial ProductsNature of Borrower or Low Value of Individual ExposuresStructuring of NotesHISTORICAL SIMULATIONSCustomizing Credit RiskBASIC PROPERTIES OF RISK CONTRIBUTIONSFrom Sensitivity to VolatilityMARGINAL RISK CONTRIBUTION AND SIZE OF AN EXISTING EXPOSUREBanks: Sample Rating GridCREDIT INTENSITY MODELSThe Variance-Covariance Matrix of Portfolio ReturnCOMPARISON OF THE DEPENDENT AND THE INDEPENDENT CASESINITIAL RECOGNITION OF FINANCIAL ASSETS AND LIABILITIESSOVEREIGN, BANK, AND EQUITY EXPOSURESLogit Model FamilyCREDIT PORTFOLIO VIEW: ECONOMETRIC MODELSThe Value-at-Risk MeasureMISMATCH RISKThe "Basic" Linear Model DrawbacksDerivatives and P & LECONOMICS OF SECURITIZATIONSEquity ExposuresThe Distribution of Firm ValueCredit Conversion Factors (CCFs)The Underlying AssetsENTERPRISE-WIDE RISK MANAGEMENT (ERM)THE THIRD EDITIONPORTFOLIO OVERVIEWBANKS'FINANCIAL STATEMENTSCapital Under Default ModeSection 4. ValuationRevaluation of Facilities at HorizonTranches are Subject to Correlation RiskCREDIT RISK VARTHE CAPITAL ALLOCATION MODEL AND RISK CONTRIBUTIONSCONSTRUCTING A RISK-FREE PORTFOLIOThe Benefits from the Mirror DebtMODELING PREPAYMENTSLoss Statistics and CapitalRegulated RatesDefinition of Interest Rate SwapControlling Duration with DerivativesRECOVERY STATISTICSSimulations with Factor Models or the Copula ApproachSample Bank Balance SheetSpread RiskECONOMIC VALUE, DURATION AND CONVEXITYAPPENDIX: MATRIX DIAGONALIZATIONEffective LGD for Collateral-based TransactionsTHE GENERIC FORM OF FACTOR MODELSCredit Portfolio ModelsFORWARD VALUATION AND EXCESS SPREADSCONDITIONAL PROBABILITY FROM THE COPULA DENSITYThe Stock Price ProcessPRINCIPLES OF SAMPLE SIMULATIONSImplicit Options RiskMIGRATION MATRICESThe Asset Value and Default Probability Conditional on the State of the EconomyIto LemmaThree Basic Liquidity PositionsRETAIL PORTFOLIO IN BASEL 2CALCULATING THE PFE FOR AN INTEREST RATE SWAPIdentification of Potentially Significant AttributesFORWARD DEFAULT AND SURVIVAL PROBABILITIESThe Current Value of the Prepayment OptionReverting to Better Risk Practices and Lessons of the CrisisGENERAL PROPERTIES OF RISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONSSPECIALIZED LENDINGOff Balance Sheet ItemsEconomie Value and NiL: General ExampleThe Two-asset Portfolio ReturnDealing with Different Default Probabilities and Discrepancies of ExposuresThe 2007-2008 Financial CrisisPortfolio Return VolatilityValuation of a Forward Contract or FRABook Measures of Profitability versus Risk-adjusted MeasuresMultiple ScenariosConceptual FrameworkSection 14. Risk-adjusted PerformanceRISK-ADJUSTED MEASURES OF PERFORMANCESection 11. Credit Risk: StandaloneBanking Regulations: The Basel 2 AccordMapping Interest Rates to Selected Risk FactorsSOVEREIGN RISK CREDIT DERIVATIVESAPPENDIX: CONDITIONING, EXPECTATION AND VARIANCESECURITY LENDING AND BORROWINGApplication: The Square Root of Time Rule for the Simple Wiener ProcessThe Financial CrisisPRICING CREDIT DERIVATIVESDealing with Multiple DimensionsSIMULATION OF JOINT DEFAULTS AND MIGRATIONSExpected Return on Assets and Compensations to InvestorsFixed and Variable RatesThe Case of FloatersTOTAL RETURN SWAPSMismatch RiskLIQUIDITY MANAGEMENTTHE DISCOUNTED CASH FLOW MODELValuation and Pricing RiskExample of Calculations of the Forward Yield CurvesThe Waterfalls of Cash Flows and LossesDependency and Joint Migration ProbabilitiesSovereign ExposuresFixed Assets and EquityPayoff of Interest Rate OptionsYield-to-Maturity and Zero-coupon RatesCounterparty Risk of DerivativesA Simple Example of a Forward ContractTHE OPTION THEORETIC FRAMEWORK OF VALUATION OF EQUITY AND DEBTForward Default IntensitySIMULATION OF TWO DEPENDENT NORMAL STANDARD VARIABLESPORTFOLIO RETURN RISK AND CORRELATIONCREDITRISK+AND ANALYTICAL DISTRIBUTIONSSECURITIZATIONSCapital Under Full Migration ModeSVA MEASURESVALIDATIONEconomic Income StatementsRISK FOR A SINGLE ASSET AND TWO-FACTOR MODELSThe Ito ProcessRISK-BASED PRICINGStress Testing and What-if AnalysesTHE TWO-OBLIGOR PORTFOLIO AND CONDITIONAL PROBABILITIESHedging Caps Sold to ClientsUsing PCA for Single AssetsIMPLEMENTING THE STRUCTURAL MODEL OF DEFAULTCREDIT DEFAULT SWAPS (CDS)Modeling Potential Variations of ValueDuration GapValuation in Discrete Time and the Rationale of DiscountingUsages of Risk Contributions and of Marginal Risk ContributionsSecuritizations: TraditionalINTEREST RATE SIMULATIONS WITH PCAValue PreservationMethod of Determining Fair ValueRevaluation of Facilities at HorizonForward Contracts and Interest Rate SwapsMARKET LIQUIDITY RISKExample of Portfolio Loss Distribution INDICATOR FUNCTIONStock Price Dynamics under Risk-neutral ProbabilitiesVaR and CapitalDelta-normal VaREstablish Comprehensive Supervision and Regulation of Financial MarketsPAYOFF OF PREPAYMENTCredit Risk Mitigation under Basel 2THE SUB-PRIME CRISISECONOMIC VALUE (EV)Instruments Traded in Active MarketsSimulation AlgorithmNormative Risk Allocations Versus Capital UtilizationsConditional and Joint ProbabilitiesCredit EventsASSESSING THE RISK OF ASSET-BACKED NOTESIRB ApproachesThe Standardized ApproachVALUATION: END RESULTSMARKET INSTRUMENTS AND POTENTIAL FUTURE EXPOSURES (PFES)Stochastic CalculusISSUES FOR DETERMINING THE LIQUIDITY GAP TIME PROFILEINTERNAL RATINGS BASED FRAMEWORKAPPENDIX: CALCULATION OF STANDARD DEVIATION FROM TIME SERIESCorrelations, Variances, and CovariancesExample: Option ContractStructuring Debt MaturitiesEffective Maturity (M)Forms of the Gaussian CopulaBanking and Financial ProductsStandardizing the Single-factor ModelCredit Event DependenciesPILLAR 3: MARKET DISCIPLINERegulatory Risk Weights for Corporates, Sovereigns and BanksHistorical and Hypothetical SimulationsThe One-factor ModelDirect Calculation of Default Probability over Two PeriodsThe Limit DistributionMatrix Notations Financial ApplicationsThe Pricing of Assets Sold to the SPEMathematical SensitivitiesEV and Projected Interest Income at Risk-free RateGrid SimulationsLogarithmic ReturnsCredit Events and Credit State at HorizonLines without MaturityLines without MaturityRetail Portfolio: Further Differentiation for Capital TreatmentCumulative Default RatesBuying Protection for the Portfolio from Another BankThe Reference Capital for Risk ContributionsNon-linear Relationship between Selected Attributes and Credit StateThe Cost of Existing ResourcesFROM PORTFOLIO VALUE DISTRIBUTION TO CREDIT CAPITALCompounding Continuous ReturnsRisk Management Organization and Central FunctionsThe Retail PortfolioFACTOR MODELSAPPLICATION TO MARKET VARRating Methodologies for Structured NotesLoss Distributions, Potential Losses and VaRINTEREST RATE SWAPS (IRS)STANDALONE INDIVIDUAL LOSSESLimits and "Nil at Risk"Corporate Sample Rating GridRisks and Risk ManagementBuying Protection for the Portfolio and Selling ProtectionThe Hurdle Rate and the Cost of CapitalOff Balance Sheet CommitmentsPortfolio Systematic Risk Decomposition into Additive ItemsTHE STUDENT DISTRIBUTIONValuation of a BondPrinciplesEQUALLY WEIGHTED HISTORICAL VOLATILITYTHE EXAMPLE OF A FORWARD FOREIGN EXCHANGE RATEApplication of Cholesky DecompositionDependencies and Copula FunctionsCapital UtilizationsMARKET RISKAPPENDIX:THE GAMMA DISTRIBUTIONAnalytical Loss DistributionsSome Applications of Valuation TechniquesEconomic and Commercial Transfer PricesRisk-based PerformanceProbability of Default (DP) and Default EventThe All-in Cost of Funds of the Mirror DebtStocksDecomposition of the Forward as a Linear Function of Elementary PositionsMAXIMUM LIKELIHOOD METHODOLOGYThe Dependent CaseThe Default Probability Conditional on The State of the EconomyCredit Risk Potential ExposureRisk-based Capital and GrowthSteps for Determining VaRTHE CALCULATION OF RAROC AND SVA FOR CREDIT RISKPortfolio SimulationsReplicating a Forward Exchange RateMARGINAL RISK CONTRIBUTIONS TO LOSS VOLATILITYFull Monte Carlo SimulationsTHE DILEMMAS OF THE REGULATORSimulations of Default DistributionsCredit Events and Credit State at HorizonFitting and Back Testing Scoring ModelsCREDIT RISKPortfolio Total Risk and Two-factor ModelIndirect Effects and Factor-push ScenariosThe Bivariate Copula Function: Expanded FormAPPENDIX:THE CHOLESKY DECOMPOSITION METHODEarnings Allocation and Fund Transfer Pricing (FTP) SystemSCORING IN RETAIL BANKING: BEHAVIORAL VERSUS ORIGINATION MODELSCOUNTERPARTY CREDIT RISKEquity ExposuresPortfolio OptimizationThe "Model Divide"VALUATION UNDER UNCERTAINTYTwo-asset Portfolio and Two Orthogonal FactorsCOMMON SENSITIVITIESJoint Density of a Bivariate Normal Distribution and the Copula Density FunctionCREDIT RISK EXPOSURE FOR PORTFOLIOS OF DERIVATIVESIntermediate Flows and NIL CalculationsSENSITIVITY DEFINITIONSTHE MOMENTS OF A DISTRIBUTIONExpanded RaRoC FormulaThe Market Value of LoanAllocating Income through the FTP SystemLoss StatisticsOFF-BALANCE SHEET ITEMSCREDIT SPREAD, IMPLIED DEFAULT INTENSITY AND RECOVERY RATECapital and Risk Allocation SystemOptionsThe "Notional" Funding of LoansSimulation of Credit Portfolio Loss DistributionsREPORTING RISK AND RETURN VERSUS BUSINESS DIMENSIONSExposure RiskFinancial Assets and Liabilities at Fair Value through Profit or LossRisk Contributions to VolatilitySIMULATION OF TWO DEPENDENT UNIFORM STANDARD VARIABLESThe Simulation AlgorithmSection 6. RegulationsEXTENSIONS OF THE MARKET VAR METHODOLOGYApplication: Finding the Factor Value Matching a Given Portfolio Loss PercentileSAMPLE COMPARISON BETWEEN BASEL I AND BASEL 2 CAPITAL FOR CORPORATE ASSET CLASS CREDIT RISKReplicating an Interest Rate SwapVOLATILITYCREDIT RATINGS AND LINKS BETWEEN COUNTERPARTIESSecuritization Economics and the Return on EquityCOVENANTSOTHER ARBITRAGE BETWEEN ECONOMIC PRICES AND RATING-BASED PRICESAmortized CostConditional Density of Normal BivariateThe Binomial Tree for Interest RateGeneral Calculation of Default Probability over Two PeriodsMain PrincipleINTEREST RATES AND TERM STRUCTURETypes of HedgesCREDIT RATINGSBANKING PORTFOLIO EXPOSURESLOSS DISTRIBUTIONSHistorical Volatility with Equally Weighted ObservationsDiscrete and Continuous ReturnsCOMMERCIAL SPREADS AND MATURITY SPREADSources of ConvexityPayoffs of the Option under Differed ExerciseTHE STANDARDIZED APPROACHHeld-to-maturity Financial AssetsFunds Transfer Pricing SystemsDeriving the Copula Density from Copula FunctionExposure and Expected LossCLASSICAL CONTAGION MECHANISMSPortfolio AnalysisAPPENDIX: MATRIX NOTATIONS AND FORMULASVanance-Covanance Matrices of Asset Returns and of FactorsSection 10. Market RiskThe Single-factor ModelBinomial Tree of Interest RatesDefinitionsExpectationsDistribution FunctionsCredit Components and Risk WeightsJoint Probability Density Functions with Two VariablesAnalysis of a Securitization Transaction (Case Study)Risk-Weighted Assets for Corporate, Sovereign, and Bank Exposures"Effectiveness" of HedgeTHE SAMPLE PORTFOLIO AND THE SIMULATIONSSPECIALIZED LENDINGCredit Risk MitigantsMANAGING GAPS: SETTING UP LIMITSThe Vanance-Covanance MatrixMIGRATIONS AND VAR UNDERTHE STRUCTURAL MODELCREDIT VAR AND MATRIX VALUATION: APPLICATIONSAMPLE CALCULATIONS OF EDF© AND OF THE PUT AND CALL VALUESBERNOULLI VARIABLEReplicating a Forward LoanThe Annualized All-in Cost of Financing through SecuritizationMODELING DEFAULT PROBABILITY AND CREDIT STANDING AT HORIZONInterest Rate Gap and Liquidity GapsExchanging Net Balances of Funds between UnitsDEFAULT STATISTICS
 
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