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«Risk management in banking»

Derivatives and Credit RiskEconomic Capital and Credit Risk VaRHedging Implicit Options to Renegotiate Fixed RatesModeling RecoveriesBOOK STRUCTURESCORING IN RETAIL BANKING: BEHAVIORAL VERSUS ORIGINATION MODELSBASIC POSTULATES OF THIS TEXTCalculation of RaRoC and SVALIQUIDITY CONTAGIONECONOMIC VALUE, DURATION AND CONVEXITYMigration RiskVALUATION OF AN OPTION UNDER RISK-NEUTRAL PROBABILITIESStandalone Loss Volatilities and Portfolio Loss VolatilityCONTAGION THROUGH RATING DOWNGRADESPortfolio Return VolatilityVOLATILITY AND DELTA-NORMAL VAR OF THE FORWARD VALUEEquity ExposuresSOVEREIGN RISK CREDIT DERIVATIVESEmbedded Options in Banking ProductsMark-to-market Value of an IRSRisk-Weighted Assets for Corporate, Sovereign, and Bank ExposuresSECURITIZATIONSPortfolio SimulationsThe Generalized Wiener ProcessRisk-neutral ProbabilityMAXIMUM LIKELIHOOD METHODOLOGYThree Basic Liquidity PositionsThe Current Value of the Prepayment OptionINDEPENDENT DEFAULT EVENTS:THE BINOMIAL DISTRIBUTIONECONOMICS OF SECURITIZATIONSCredit Portfolio View Conceptual FrameworkCredit Risk DataBASIC PROPERTIES OF RISK CONTRIBUTIONSFixed Assets and EquityRating Methodologies for Structured NotesRISK-BASED PERFORMANCE, PRICING AND CAPITAL ALLOCATIONCorrelations, Variances, and CovariancesREGULATORY ADD-ONS FOR DERIVATIVESEconomic Derivation of Minimum Over-collateralizationLines without MaturityCREDITRISK+AND ANALYTICAL DISTRIBUTIONSThe Sensitivity of Nil and Interest Rate GapModeling Potential Variations of ValueVALUATION OF CREDIT RISK GUARANTEES, INSURANCE OR CREDIT DERIVATIVESEnhancing the Bank's Return on Capital through SecuritizationMaterializationISSUES FOR DETERMINING THE LIQUIDITY GAP TIME PROFILELogit Model FamilyCREDIT SPREAD, IMPLIED DEFAULT INTENSITY AND RECOVERY RATEAllocating Income through the FTP SystemLOGNORMAL DISTRIBUTIONCompounding Discrete Returns over Multiple PeriodsRaise International Regulatory Standards and Improve International CooperationComparing Continuous and Discrete ReturnsMARKET LIQUIDITY RISKFrom Daily Volatility of the Position to Daily VaRExpected Return on Assets and Compensations to InvestorsDEFINITIONS OF RISK CONTRIBUTIONSRaRoC and Shareholders' Value Added PRICING CREDIT DERIVATIVESDependencies and Copula FunctionsDetermining the Percentile of the Final Asset ValueIMPLEMENTING THE EDF© MODELCREDIT RISK MITIGATIONSection 3. Financial ProductsA Simple Portfolio of Two Zero-coupon BondsSECURITY LENDING AND BORROWINGRisk Contributions to Portfolio Loss VolatilityThe Effect of DiversificationControlling Duration with DerivativesBASKET SWAPS, FIRST-TO-DEFAULT, N-TO-DEFAULTMatrix Notations Portfolio Total Risk and Two-factor ModelApplication: Finding the Factor Value Matching a Given Portfolio Loss PercentileFixed and Variable RatesEarnings Allocation and Fund Transfer Pricing (FTP) SystemHow to Solve Numerically a PDESPECIALIZED LENDINGFORWARD VALUATION AND EXCESS SPREADSMANAGEMENT PRACTICES DIFFER ACROSS AND WITHIN BUSINESS LINESKEY BENEFITS OF COPULA DEPENDENCYMODELING POTENTIAL VARIATIONS AND PERCENTILESRevenuesSIMULATIONSCREDIT VAR AND MATRIX VALUATION: APPLICATIONThe Normal Standard Copula Density and the Joint Density of Two VariablesBinomial Tree of Interest RatesRisk Oversight: Banks' ChallengesTRADING CREDIT RISKStatic Liquidity GapsThe Stock Price ProcessNIL AND EVREGULATIONSAmortized CostForeign Exchange SwapsTHE NEW BASEL ACCORDPayments under a Credit EventThe Hurdle Rate and the Cost of CapitalRECOVERY STATISTICSCREDIT SPREAD PRODUCTSSecuritizations: SyntheticDeriving the Copula Density from Copula FunctionATWO-ASSET PORTFOLIO WITH TWO-FACTOR MODELSTHE SUB-PRIME CRISISImplementing the Matrix ApproachPORTFOLIO RETURN RISK AND CORRELATIONRisk-based Pricing and Risk Contribution to CapitalOPERATIONAL RISKValuation in Discrete Time and the Rationale of DiscountingProbability of Default (DP) and Default EventDuration GapOptional Risk is Always Adverse to the BankSection 1. The Financial CrisisExposure at Default (EAD)Credit Event DependenciesHEDGING INTEREST RATE RISK BY CORPORATE BORROWER (CASE STUDY)THE THIRD EDITIONThe Securitization OrganizationForward Default IntensityPayoff of Interest Rate OptionsConditional Density of Normal BivariateRISK-ADJUSTED MEASURES OF PERFORMANCEUNCERTAINTY, RISK,AND EXPOSURETO RISKSection 10. Market RiskContinuous VariablesContingencies Given (Off-balance Sheet)SIMULATION OF TWO DEPENDENT TIMES TO DEFAULTFrom Sensitivity to VolatilityAccounting StandardsOptions as Volatility InstrumentsMAPPING SCORING MODELS TO A MASTER SCALE OF DEFAULT PROBABILITIESInstruments Traded in Active MarketsSupervisionSample Bank Balance SheetValue PercentileMONTE CARLO SIMULATIONS OF DEFAULT EVENTS BASED ON THE STRUCTURAL MODEL OF DEFAULTTHE RATIONALE FOR CREDIT PORTFOLIO MANAGEMENTThe "Notional" Funding of LoansTHE VALUE OF IMPLICIT OPTIONSTHE CONCEPTUAL FRAMEWORK OF DELTA-NORMAL VARTwo Random Normal VariablesIMPAIRMENT OF FINANCIAL ASSETSPORTFOLIO OF TWO OBLIGORSExchanging Net Balances of Funds between UnitsPORTFOLIO RISK WITH MULTIPLE-FACTOR MODELSTHE SIMPLE "BINOMIALTREE" TECHNIQUE APPLIED TO INTEREST RATESLoss StatisticsTHE ECONOMICS OF SCORING SYSTEMSAPPLICATIONS OF CREDIT DERIVATIVESSTANDALONE INDIVIDUAL LOSSESSection 2. Business Lines, Risks, and Risk ManagementAccounting StandardsRisk-adjusted Performance versus Risk-based PricingExpected LossJoint Probability Density Functions with Two VariablesLiquidity Crises and Stress Test ScenariosBasic Specifications of Reporting SystemsSIMULATION OF TWO DEPENDENT UNIFORM STANDARD VARIABLESINTEREST RATE PROCESSESBonds and LoansValuation and Pricing RiskFINANCIAL RISKSSovereign ExposuresFOREIGN EXCHANGE RATES AND FORWARD CONTRACTSMARGINAL RISK CONTRIBUTION AND SIZE OF AN EXISTING EXPOSUREIndirect Effects and Factor-push ScenariosLIQUIDITY RISK: FUNDINGSAMPLE CALCULATIONS OF EDF© AND OF THE PUT AND CALL VALUESPRINCIPAL COMPONENT ANALYSIS AND THE TERM STRUCTURE OF INTEREST RATESSPECIFICS OF STOCHASTIC PROCESSES AND ITO LEMMAInterest Rate Gap and Liquidity GapsThe Option Approach to Defaults and MigrationsPayment TermsDiscrete VariablesValue PreservationDealing with Different Default Probabilities and Discrepancies of ExposuresReplicating a Forward Exchange RateTHE VARIANCE-COVARIANCE MATRIXSimulating Increased Diversification with Loss IndependenceFOREIGN EXCHANGE RISKEquity ExposuresRecovery RiskCREDIT PORTFOLIO MODEL OVERVIEWThe Global Calibration of the Binomial TreeTHE VAR METHODOLOGY: MARKET RISKAsset-liability Management (ALM)COMPARISONS OF CLASSIFICATIONS: RISK REGULATIONS AND IFRSThe Simulation AlgorithmThe Pricing Paradox with Marginal Risk ContributionsFROM PORTFOLIO VALUE DISTRIBUTION TO CREDIT CAPITALTHE STUDENT DISTRIBUTIONSection 13. Capital AllocationRegulated RatesMismatch RiskA Single Obligor Dependent on the State of the EconomyMARKET RISKMARGINAL RISK CONTRIBUTIONS TO VOLATILITY VERSUS RISK CONTRIBUTIONSThe Two-factor Model Applied to a Two-asset PortfolioCOMPARISON OF THE DEPENDENT AND THE INDEPENDENT CASESCREDIT METRICSIRB ApproachesThe "Ex Ante" and the "Ex Post" ViewsRationales For SecuritizationsINVERSE FUNCTIONSRisks and Risk ManagementThe Waterfalls of Cash Flows and LossesStatistical and Scoring ModelsEconomie Value and NiL: General ExampleGeneration of Portfolio Value DistributionDEFAULT PROBABILITY OF A FIRM DEPENDENT ON THE STATE OF THE ECONOMYCONTAGION THROUGH SECURITIZATIONSNET INTEREST INCOME AND INTEREST RATE GAPSExample: Option ContractECONOMICS OF SECURITIZATION FORTHE BANKLines without MaturityRisk Management versus Risk InstrumentsInterest Rate GapsThe Valuation of American OptionsImplicit Options RiskIto LemmaHistorical VaR: Forward Contract ExampleCalculation of Joint Default and Conditional ProbabilitiesCredit Risk Mitigation: Collateral TreatmentCounterparty Risk of DerivativesOFF-BALANCE SHEET ITEMSLoss Distributions, Potential Losses and VaRALM SCOPE AND STRUCTURE OF THE SECTIONConditional and Joint ProbabilitiesEconomic Value and Convexity RiskFrom Portfolio Risk to Individual FacilitiesSTRESS TESTING, HYPOTHETICAL SCENARIOS AND SENSITIVITY ANALYSESPrinciplesMODELING DEFAULT PROBABILITY AND CREDIT STANDING AT HORIZONLOGIT MODELSCapital RequirementsCapitalINTEREST RATES AND FACTOR MODELSMarket Risk and Trading ActivitiesPORTFOLIO OVERVIEWThe Cost of Financing through SecuritizationNumerical ExampleMANAGING GAPS: SETTING UP LIMITSCustomizing Credit RiskInterpolation of Interest Rate from Selected Risk FactorsBivariate Normal Standard DensitySection 9. Dependencies and Portfolio RiskBasel 2 Treatment of Collateralized TransactionsTHE ORGANIZATION OF FTP SYSTEMSDuration Gap and Sensitivity of EVThe Cooke Ratio and Credit RiskCALCULATING INCOME WITHIN A FTP SYSTEMHeld-to-maturity Financial AssetsStochastic CalculusINTEREST RATE RISKCorporate Sample Rating GridBENCHMARKINGVolatility PreservationPRINCIPLES OF SAMPLE SIMULATIONSRisk Oversight: Regulators' ChallengesThe Annualized All-in Cost of Financing through SecuritizationSTRUCTURAL EXCESSES OF LIQUIDITYEV and Projected Interest Income at Risk-free RateTHE ACCORD FOR MARKET RISKCONDITIONAL PROBABILITY FROM THE COPULA DENSITYJoint Density of a Bivariate Normal Distribution and the Copula Density FunctionThe Limit DistributionCapital and Risk Allocation SystemOption PricingConstructing Attributes from Observed CharacteristicsINTEREST RATE RISKEvolution of Credit Risk ModelsPRICING FOR LENDINGHedging Over Multiple PeriodsLiquid AssetsTHE CAPITAL ALLOCATION MODEL AND RISK CONTRIBUTIONSExample of a One-factor ModelE-VaR or Expected ShortfallOptionsRisk Contributions to VolatilityScope and Goals of this TextCredit Risk Potential ExposureApplications for Credit Portfolio ManagementHedging Caps Sold to ClientsSection 12. Credit Portfolio RiskThe Financial CrisisRetail PortfolioDiscriminating VariablesSample Gap ReportsDependency and Joint Migration ProbabilitiesTranches are Subject to Correlation RiskMain PrincipleBANKS'FINANCIAL STATEMENTSCONTAGION AND PROCYCLICALITYTHROUGH FAIR VALUE RULESVAR AND ECONOMIC CAPITALAPPENDIX: CALCULATION OF STANDARD DEVIATION FROM TIME SERIESThe Firm ValueSingle Period Discrete ReturnCREDIT RATINGS AND LINKS BETWEEN COUNTERPARTIESSAMPLE COMPARISON BETWEEN BASEL I AND BASEL 2 CAPITAL FOR CORPORATE ASSET CLASS CREDIT RISKEQUALLY WEIGHTED HISTORICAL VOLATILITYCorrelations and CovariancesOff Balance Sheet ItemsFORWARD RATES: DEFINITIONSIncome-producing Real EstateRISK OVERSIGHT CHALLENGESPortfolio Concentration and Correlation RiskFACTOR MODELSRAROC CALCULATIONS AT PORTFOLIO AND FACILITY LEVELSDelta-normal VaRVariance and VolatilityAPPENDIX:THE GAMMA DISTRIBUTIONUsages of Forward Rate ContractsTRANSFERRING LIQUIDITY AND INTEREST RATE RISK TO ALM THROUGH THE FTP SYSTEMPORTFOLIO DELTA-NORMAL VARAPPENDIX: MATRIX DIAGONALIZATIONPortfolio OptimizationEXTENSIONS OF THE MARKET VAR METHODOLOGYALM APPLICATIONSTypes of HedgesDEFINITIONS OF CREDIT DERIVATIVESExceptional LossesThe Retail PortfolioRISK-BASED PRICINGAPPENDIX: CONDITIONING, EXPECTATION AND VARIANCEMOODY'S-KMV CREDIT MONITOR AND MOODY'S-KMV PORTFOLIO MANAGERMIGRATION MATRICESThe Payoff of Option ContractsThe "Basic" Linear Model DrawbacksTHE STANDARDIZED APPROACHLogarithmic ReturnsCalculating Marginal Default ProbabilitiesPAYOFF OF PREPAYMENTFROM GAPS TO SIMULATIONSVaR at Different HorizonsAPPENDIX I: SAMPLE PORTFOLIO INPUTSExpectationsThe One-factor ModelOther CostsVisual Representation of the Diversification EffectMARGINAL RISK CONTRIBUTIONS TO CAPITALOPTIONAL RISK AND OPTIONAL GAPSThe Accounting N11 of the BankThe Basic Mechanism of LimitsLIQUIDITY DEFINITIONSGENERAL PROPERTIES OF RISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONSPILLAR 2: SUPERVISORY REVIEW PROCESSThe Multiple SimulationsSUPPORTOTHER ARBITRAGE BETWEEN ECONOMIC PRICES AND RATING-BASED PRICESSIMULATION OF DEPENDENT VARIABLES WITH THE COPULA APPROACHUsages of Risk Contributions and of Marginal Risk ContributionsCONSTRUCTING A RISK-FREE PORTFOLIOSome Applications of Valuation TechniquesTHE "BASEL I ACCORD" FOR CREDIT RISKADDITIONAL PROPOSALSSTRUCTURING AND THE WATERFALL MECHANISMTHE VASICEK MODELConceptual FrameworkVariance Formula and Correlation MatrixStructuring Debt MaturitiesREGULATORY ISSUESSIMULATIONS OF TIMES TO DEFAULTIntermediate Flows and NIL CalculationsSection 8. Funds Transfer Pricing SystemsVALUATION RULESLending, Borrowing and the Term Structure of Interest RatesDirect Effects or "Factor-push" TechniquesThe Generic Form of Multiple-factor ModelsCredit Risk in the Trading PortfolioTraceability of Aggregated Measures and Risk ManagementHigh-volatility Commercial Real EstateSOLVENCY RISKApplication: The Stressed Default Probability under Basel 2MEASURES OF DEPENDENCIESTOTAL RETURN SWAPSExample of Portfolio Loss Distribution HEDGING BUSINESS RISK AND INTEREST RATE RISKBasel I DrawbacksAPPENDIX: RATING SCALES OF RATING AGENCIESALM GOALSTHE OPTION THEORETIC FRAMEWORK OF VALUATION OF EQUITY AND DEBTTHE FOREIGN EXCHANGE MARKET AND RATESRegulation and CompetitionCredit Risk and Lending ActivitiesSETTING-UP LIMITSMotivations for Risk OversightSOME IMPLICATIONSCREDIT RISK VARReverting to Better Risk Practices and Lessons of the CrisisCredit Components and Risk WeightsValuation of a BondTHE MOMENTS OF A DISTRIBUTIONCollateral: Haircut CalculationsSection 15. Credit Portfolio ManagementPORTFOLIO CREDIT RISK MANAGEMENT (CASE STUDY)BINOMIAL DISTRIBUTION OF SUM OF BERNOULLI VARIABLESConvexityRisk-based Capital and GrowthThe Single-factor ModelHEDGING THE VARIATIONS OF THE TERM STRUCTURE OF INTEREST RATES (CASE STUDY)ProvisioningOptional Risk and HedgingStandardizing the Single-factor ModelFORWARD DEFAULT AND SURVIVAL PROBABILITIESInstruments Traded in Inactive MarketsMEASURES OF POTENTIAL LOSSESBasic FormulasMAPPING RATINGS TO DEFAULT PROBABILITIESValuation and LeverageRating SystemsNature of Borrower or Low Value of Individual ExposuresCorrelation and Concentration RisksDerivation of the Normal Copula DensityVOLATILITYTrading Credit RiskExample: Stock Price DistributionOPERATIONAL RISKThe Costs of Funding On Balance Sheet and through SecuritizationPortfolio Systematic Risk: Two-factor ModelsTHE CONTRIBUTIONS OF VAR-BASED MEASURESThe Independence CaseVALUATION OF RISKY DEBT FROM CREDIT SPREADS AND RISK-NEUTRAL PROBABILITIESUsing PCA for Single AssetsThe Underlying AssetsCommercial SpreadsExpected LossCredit Risk Mitigation under Basel 2The Vanance-Covanance MatrixTHE EXPONENTIAL DISTRIBUTION AND TIME TO DEFAULTOptions Allow Hedging RisksSimulation of Time to Default for a Single ObligorBanks: Sample Rating GridTRANSACTION-SPECIFIC CREDIT RISKOn Balance SheetHypothetical Scenarios, Stress-tests and Extreme VaRAsset Swaps: GeneralizationEconomic and Commercial Transfer PricesRISK-ADJUSTED PERFORMANCE AND MISPRICING REPORTSDistribution FunctionsTHE BETA DISTRIBUTIONReplicating an Interest Rate SwapPreemptive Risk Control versus Risk InsuranceThe Variance-Covariance Matrix of Portfolio ReturnSPECIALIZED LENDINGThe Ito ProcessSecuritization and Capital ManagementThe Mean Reverting ProcessCOMMON SENSITIVITIESCredit EventsContinuous Returns and VarianceCollarCumulative Default RatesRegulatory Risk Weights for Corporates, Sovereigns and BanksDURATION PROPERTIESBank ExposuresThe Copula Density FunctionCredit Risk Valuation and Credit SpreadsTHE TWO-OBLIGOR PORTFOLIO AND CONDITIONAL PROBABILITIESECONOMIC TRANSFER PRICES FOR RESOURCESMarginal Risk ContributionsSIMULATION OF TWO DEPENDENT NORMAL STANDARD VARIABLESRisk ManagementExposure and Capital Allocation or Loss VolatilityECONOMIC VALUE AND NET INTEREST INCOME FOR A BANK WITHOUT CAPITALCOMMERCIAL SPREADS AND MATURITY SPREADRevaluation of Facilities at HorizonSources of ConvexityLIQUIDITY MANAGEMENTSIMULATION OF CORRELATED NORMAL VARIABLES WITH FACTOR MODELSDynamic Liquidity GapsStress Testing and What-if AnalysesJudgmental Ratings versus "Rating Models"Exposure and Expected LossOPTIONSRAROC CALCULATIONSEconomic Transfer PricesIMPLEMENTATION OF SCORING IN RETAIL BANKINGBANKING PORTFOLIO EXPOSURESUnderlying of OptionsSection 7. Asset Liability Management (ALM)Separating All-in Flows into Capital and Interest FlowsINDICATOR FUNCTIONOptionsAPPENDIX: MATRIX NOTATIONS AND FORMULASDEPENDENCIES MODELING ASA KEY BUILDING BLOCK FOR RISK MODELINGFORWARD CONTRACTS VERSUS OPTIONSStructuring of NotesMathematical SensitivitiesCONVEXITY GAPS AND OPTIONSMeasure of ConvexityGeneralization to Several VariablesModeling Defaults under the Structural ModelCLASSIFICATION OF LENDING PRODUCTS AND BASEL 2 CRITERIARisk Contributions, Portfolio Loss Volatility and CapitalPortfolio AnalysisSection 14. Risk-adjusted PerformanceSAMPLE CALCULATIONS OF RISK CONTRIBUTIONSASSETS AND POSITIONSHOW FIRMS DEFAULTDefinition of Interest Rate SwapLoss Given Default (LGD)The Uniform Granular PortfolioBERNOULLI DISTRIBUTIONDefault Intensity ModelsHEDGING: CLOSING INTEREST RATE GAPSExpected LossRATING GRIDSThe Default Probability Conditional on The State of the EconomyCONTAGION AND PROCYCLICALITY IN A LEVERAGED INDUSTRYBreaking Down the Bank Margin into Contributions of Business UnitsDependency StructureThe Cost of the Mirror DebtMapping and AllocationCredit DerivativesInterest Rate SwapsDefault Probability and Default IntensityAPPENDIX 2: SAMPLE PORTFOLIO OUTPUTSMODELING PREPAYMENTSThe Bivariate Normal CopulaALM and Hedging PoliciesSingle PeriodSECTION ORGANIZATIONDERIVATIVES: BASIC DEFINITIONS AND PRINCIPLESForms of the Gaussian CopulaCredit Risk Mitigation: Guarantees and Credit DerivativesThe Market Value of LoanRISK-BASED PRICING AND MARGINAL RISK CONTRIBUTIONSSOVEREIGN, BANK, AND EQUITY EXPOSURESLoans and ReceivablesProject FinanceVariance-Covariance Matrix and Correlation MatrixYield-to-Maturity and Zero-coupon RatesSection 5. Risk ModelingThe "Model Divide"Risk Factors and Dependence StructureIdentification of Potentially Significant AttributesBuying Protection for the Portfolio from Another BankSpecific CasesThe Standardized ApproachObject FinanceSection 6. RegulationsREMINDERS AND NOTATIONSEffective LGD for Collateral-based TransactionsVolatilityBivariate CopulaFrom Future Values to Current CapitalEconomic Value and Convexity GapsPILLAR 3: MARKET DISCIPLINERisk RegulationsCredit Events and Credit State at HorizonHISTORICAL SIMULATIONSThe Benefits from the Mirror DebtDISCRETE AND CONTINUOUS RETURNSAPPENDIX 3: PORTFOLIO ANALYSIS AND REPORTING ISSUESBUSINESS POLES IN THE BANKING INDUSTRYESTIMATING EWMA VOLATILITYA Simple Example of a Forward ContractAnalytical Loss DistributionsVariety of SecuritizationsCREDIT DEFAULT SWAPS (CDS)Revaluation of Facilities at HorizonRISK FOR A SINGLE ASSET AND TWO-FACTOR MODELSConditional ProbabilitiesSENSITIVITY DEFINITIONSPayoffs of the Option under Differed ExerciseProjected GapsBanking Regulations: The Basel 2 AccordThe Reference Capital for Risk ContributionsCOLLATERALIZED SECURITIES LENDING/BORROWINGFinancial Assets and Liabilities at Fair Value through Profit or LossTHE CALCULATION OF RAROC AND SVA FOR CREDIT RISKTHE WHITE PAPER FROM THE WHITE HOUSELoss Statistics and CapitalAbout the AuthorCALCULATIONS OF INTEREST RATE GAPSRISK-NEUTRAL VALUATION:THE CASE OF A STOCK PRICECAPITAL CALCULATIONInterpretation of Basel 2 Formulas for Risk WeightsCLASSICAL CONTAGION MECHANISMSValuation of a Forward Contract or FRAThe Simulation Algorithm for Standardized Normal Variables using Single-factor ModelsEssentials on Derivative ProductsThe Cost of Existing ResourcesDEFINITION OF COPULA FUNCTIONSAPPENDIX: CALCULATION OF ABSOLUTE RISK CONTRIBUTIONS FROM THE VARIANCE-COVARIANCE MATRIXSTOCHASTIC PROCESSESDetermination of the Default ProbabilityThe Asset Value and Default Probability Conditional on the State of the EconomyPORTFOLIO OF TWO INDEPENDENT OBLIGORSVALUATION UNDER UNCERTAINTYPORTFOLIO ANALYSIS AND REPORTING TECHNICAL CHALLENGESDefinitionsHedging and Speculating with Forward ContractsDerivatives and P & LOff Balance Sheet CommitmentsLoss DistributionTHE RISK PREMIUM EMBEDDED IN RISK-BASED PRICINGSimulation of Two Exponentially Distributed Dependent Times to DefaultStandardized ApproachFinancial ApplicationsTHE ALM FUNCTIONLIQUIDITY SCENARIOSLOSS DISTRIBUTIONSMapping Interest Rates to Selected Risk FactorsCREDIT RISK COMPONENTSENTERPRISE-WIDE RISK MANAGEMENT (ERM)How to Form Risk-free PortfoliosCOMMON STOCHASTIC PROCESSESAmortizing LoansDependency and Joint Default ProbabilityUnexpected Loss and VaRDefault RiskSIMULATION OF JOINT DEFAULTS AND MIGRATIONSThe Simulation AlgorithmOption-adjusted SpreadCompounding Continuous ReturnsStock Price Dynamics under Risk-neutral ProbabilitiesThe Cholesky Decomposition Method: Two VariablesAnalysis of a Securitization Transaction (Case Study)Economic Capital and Loss VolatilityPORTFOLIO LOSS DISTRIBUTIONINTEREST RATES AND TERM STRUCTURETHE DILEMMAS OF THE REGULATORLIQUIDITY GAP CALCULATIONSMAPPING AN INSTRUMENTTO RISK FACTORSBook Measures of Profitability versus Risk-adjusted MeasuresThe Portfolio Loss VolatilityThe Loss StatisticsForward Contracts and Interest Rate SwapsCredit Portfolio Models and SecuritizationsSimulations with Factor Models or the Copula ApproachBack Tests, Benchmarks and Stress Tests DISTRIBUTION OF RANDOM RECOVERIESAPPLICATION: STOCK VALUE DISTRIBUTIONNumber of Default Events over a Given HorizonCREDIT PORTFOLIO VIEW: ECONOMETRIC MODELSMethod of Determining Fair ValueMispricing ReportsDeriving SensitivitiesLIQUIDITY GAP TIME PROFILESBACK TESTINGACCURACY OF SCORING MODELS:THE "CAP"The Value-at-Risk MeasureCapital UtilizationsRisk Management Organization and Central FunctionsTwo-asset Portfolio and Two-factor Model: Specific RiskTHE SAMPLE PORTFOLIO AND THE SIMULATIONSTransaction Versus Client Revenues and PricingCORRELATIONS AND COVARIANCESSENSITIVITIES AND RISK CONTROLLINGHEDGING A CORPORATE LONG EXPOSURE IN FOREIGN CURRENCY (CASE STUDY)Asset Distribution and Default ProbabilityDiscrete and Continuous ReturnsGeneral Calculation of Default Probability over Two PeriodsCOUNTERPARTY CREDIT RISKMONTE CARLO SIMULATIONSHedging both Interest Rate and Business RisksINTEREST RATE RISK FOR BORROWERS AND LENDERSCREDIT RISK FOR DERIVATIVES: METHODOLOGYProprietary Models of Market Risk VaRUnivariate and Bivariate Normal DistributionsDemand DepositsFunds Transfer Pricing SystemsCUMULATIVE DEFAULT AND SURVIVAL PROBABILITIESAPPENDIX: COPULA FUNCTION AND COPULA DENSITYVarious Forms of Bivariate Copula FunctionsThe Pricing of Assets Sold to the SPEGenerator MatricesLIMITATIONS OF INTEREST RATE GAPSINTERNAL CREDIT RATINGS AND BUSINESS RULESSellers of OptionsStochastic ProcessesDEFAULT STATISTICSCredit Events and Credit State at HorizonAPPLICATION TO MARKET VARVaR and CapitalMISMATCH RISKRisk-based Capital RegulationsLiquidity Management and Liquidity GapsCredit Risk MitigantsASSESSING THE RISK OF ASSET-BACKED NOTESREPORTING ALTERNATE METRICS OF RISKSpot and Forward PricesEARNINGS-AT-RISK ("EAR")INTEREST RATE SIMULATIONS WITH PCAThe "Rare Event" ProcessJOINT MIGRATION MATRICESINTEREST RATE SWAPS (IRS)The Distribution of Firm ValueSENSITIVITY OF ECONOMIC VALUE AND DURATION GAPSBIVARIATE NORMAL STANDARD DISTRIBUTIONSTHE EXAMPLE OF A FORWARD FOREIGN EXCHANGE RATEThe Two-asset Portfolio ReturnSecuritization Economics and the Return on EquityRISK OF A TWO-STOCK PORTFOLIO WITH THE ONE-FACTOR MODELEstablish Comprehensive Supervision and Regulation of Financial MarketsRANDOM VARIABLES AND PROBABILITY DISTRIBUTION FUNCTIONSGARCH MODELSHistorical and Hypothetical SimulationsAsset Value and Market Required ReturnThe 2007-2008 Financial CrisisNORMATIVE CAPITAL ALLOCATIONS AND CAPITAL EFFECTIVE UTILIZATIONSCredit Conversion Factors (CCFs)REPORTING RISK AND RETURN VERSUS BUSINESS DIMENSIONSHedging Credit Risk"Effectiveness" of HedgeSCORINGCALCULATING THE PFE FOR AN INTEREST RATE SWAPSensitivityCapital AllocationDealing with Different Default Probabilities and Discrepancies of ExposuresTHE GENERIC FORM OF FACTOR MODELSCapital Under Full Migration ModeAnnual Default RatesExtension to any Number of VariablesBuying Protection for the Portfolio and Selling ProtectionMARKET INSTRUMENTS AND POTENTIAL FUTURE EXPOSURES (PFES)Large Number of ExposuresEffective Maturity (M)Matrix Methodology and The Risk-Return Profile of the Balance SheetTHE PRICE OF RISK AND ARBITRAGEIMPLEMENTING THE STRUCTURAL MODEL OF DEFAULTRETAIL PORTFOLIO IN BASEL 2CREDIT INTENSITY MODELSDealing with Multiple DimensionsCAPITAL ADEQUACYSimulations of Default DistributionsJOINT DEFAULT PROBABILITY USING DISCRETE VARIABLESEXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA) MODELThe Case of FloatersNon-linear Relationship between Selected Attributes and Credit StateRisk-based PricingCREDIT RISKMODELING JOINT MIGRATIONS AND DEFAULTS WITH THE STRUCTURAL MODELCorrelation and Volatility of a Sum of Random VariablesIDENTITY BETWEEN EV AND "ALL-IN" CASH FLOWS (CAPITAL AND INTEREST)Replicating a Forward LoanSecuritizations: TraditionalInteractive Implementation of Risk SystemsNormative Risk Allocations Versus Capital UtilizationsVARIATIONS ON THE MERTON'S MODELPortfolio Risk Return ProfileEconomic Income StatementsMAIN SPECIFICS AND KEYTERMSCREDIT VAR AND MATRIX VALUATIONThe Exercise Price and the Payoff of the OptionDeterministic CalculusASSET CLASSESBERNOULLI VARIABLEThe Matrices of Net Interest IncomeHEDGE ACCOUNTINGRisk Factors and Dependence StructureNORMAL DISTRIBUTIONCredit Portfolio ManagementMIGRATIONS AND VAR UNDERTHE STRUCTURAL MODELConditional Distributions and SimulationsExposure RiskSteps for Determining VaRBanking and Financial ProductsFitting and Back Testing Scoring ModelsMarginal Risk ContributionsDEPENDENT DEFAULT EVENTSDirect Calculation of Default Probability over Two PeriodsExpanded RaRoC FormulaVALIDATIONOPTIONAL RISKThe All-in Cost of Funds of the Mirror DebtThe Original LoanAPPENDIX:THE TAYLOR EXPANSION FORMULAMigration Matrices and Cumulative Default ProbabilitiesECONOMIC TRANSFER PRICES FOR LOANSDistribution Functions and PercentilesUNIFORM DISTRIBUTIONProjected Net Interest IncomeTHE "STANDARDIZED" STANDALONE STRUCTURAL MODELEconomic Value of the Balance SheetLoss PercentilesFull Monte Carlo SimulationsPortfolio DataTHE DISCOUNTED CASH FLOW MODELProtect Consumers and Investors from Financial AbuseAPPENDIX:THE CHOLESKY DECOMPOSITION METHODThe "Three Lines of Defense" PrincipleThe Binomial Tree for Interest RateApplication: Simulating Two Uniform Standard Variables with Conditional CopulaWHERE DO INTEREST RATES COME FROM?Conditional ProbabilitiesTHE POISSON DISTRIBUTIONECONOMIC VALUE (EV)Mark-to-market Valuation of Forward ContractsRISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONS TO PORTFOLIO LOSS VOLATILITY AND TO CAPITALSimulation of Interest RatesInterest Rate Risk and Interest. Rate DerivativesBanking Regulations: Basel I and Market RiskCONDITIONAL PROBABILITIES AND CORRELATIONRisk-based PerformanceHow to Derive the Pricing PDESection 11. Credit Risk: StandaloneThe Effective Return on Capital for the BankThe Cost of Credit Risk and the Risk PremiumPortfolio Systematic Risk Decomposition into Additive ItemsCommodities FinanceCREDIT RATINGSConditional Distributions and CopulaExample of Calculations of the Forward Yield CurvesSVA MEASURESTranspose MatrixRetail Portfolio: Further Differentiation for Capital TreatmentMultiple ScenariosFrom Discrete to Continuous ReturnsFOREIGN EXCHANGE OPTIONSTHEORETICAL VALUES OF THE OPTION TO DEFAULT ANDTHE EDF©Banking Business LinesGeneration of Portfolio Value DistributionCredit Events and Credit State at HorizonMark-ups and Mark-downs over Reference RatesProperties of Copula FunctionsDEFINITION OF INTEREST RATE GAPSApplication: The Square Root of Time Rule for the Simple Wiener ProcessMAPPING DEFAULT PROBABILITY TO THE STANDARDIZED NORMAL DISTANCE TO DEFAULTBANKING REGULATIONS AND ACCOUNTING STANDARDSThe Bivariate Copula Function: Expanded FormMODELING DEFAULTS IN A UNIFORM PORTFOLIO:THE LIMIT DISTRIBUTIONCredit Portfolio ModelsRISK MANAGEMENT PROCESSESPayoff of a Forward ContractSensitivityNumerical SensitivitiesFORWARD CONTRACTSThe Loss DistributionCOVENANTSExposures, Default Probability and Loss Given DefaultRisk-based Pricing and Marginal Risk Contribution to CapitalThe Dependent CaseTop-down and Bottom-up Risk Management Processes and SystemsCountry RiskTRANSITION MATRICESSECURITIZATIONSFrom Risk Contributions to Capital AllocationSimulation AlgorithmAPPLICATION TO LOSS DISTRIBUTIONS AND LOSS PERCENTILESVALUATION: END RESULTSGeneration of Portfolio Value DistributionVariance-Covariance Matrix of Portfolio ReturnsStocksLimits and "Nil at Risk"Continuous TimeSimulation of Credit Portfolio Loss DistributionsHow Gaps Change Through TimeTwo-asset Portfolio and Two Orthogonal FactorsStandalone Expected Loss and Portfolio Expected LossINTEREST RATE OPTIONS: CAPS AND FLOORSDEFINITION OF CONDITIONAL AND JOINT PROBABILITIESValuation of the Put Option to DefaultVanance-Covanance Matrices of Asset Returns and of FactorsINITIAL RECOGNITION OF FINANCIAL ASSETS AND LIABILITIESPOSITIONING OF THE TEXTMultiple Business and Interest Rate ScenariosRisk FactorsForeign Exchange Risk and Foreign Exchange DerivativesCapital Under Default ModeThe Wiener ProcessCapital Allocation and Risk ContributionsMARGINAL RISK CONTRIBUTIONS TO LOSS VOLATILITYConceptual FrameworkBUILDING BLOCKS OF THE INTERNAL CREDIT RATING SYSTEMRisk and Return of Option ContractsLimits and DelegationsSection 4. ValuationGrid SimulationsCREDIT RISK EXPOSURE FOR PORTFOLIOS OF DERIVATIVESApplication of Cholesky DecompositionImprove Tools for Managing Financial CrisesSTATIC VERSUS DYNAMIC GAPSINTERNAL RATINGS BASED FRAMEWORKTHE GAP MODELSpread RiskSIMULATIONS AND INVERSE FUNCTIONSORIGINATION AND POST-ORIGINATION FOLLOW UPSENSITIVITY AND RISK FACTORSTYPES OF RISKSLegal IssuesFactor ModelsDefinitionTime to DefaultForward and Spot Rates: No ArbitrageExchanging all Outstanding BalancesHORIZON FOR CREDIT CAPITALORTHOGONAL MULTIPLE FACTOR MODELS AND PCADecomposition of the Forward as a Linear Function of Elementary PositionsHistorical Volatility with Equally Weighted ObservationsThe All-in Cost of Funding through SecuritizationAvailable-for-sale Financial Assets
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