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A short course of lectures
«Risk management in banking»

Credit Portfolio Models and SecuritizationsLines without MaturityStandalone Expected Loss and Portfolio Expected LossRAROC CALCULATIONS AT PORTFOLIO AND FACILITY LEVELSThe Effect of DiversificationGeneralization to Several VariablesExpectationsThe Limit DistributionHedging Caps Sold to ClientsTHE POISSON DISTRIBUTIONALM and Hedging PoliciesThe Effective Return on Capital for the BankLoans and ReceivablesVALIDATIONTHE VARIANCE-COVARIANCE MATRIXCompounding Discrete Returns over Multiple PeriodsSteps for Determining VaRTHEORETICAL VALUES OF THE OPTION TO DEFAULT ANDTHE EDF©Standalone Loss Volatilities and Portfolio Loss VolatilityCALCULATIONS OF INTEREST RATE GAPSBanks: Sample Rating GridThe Cost of Financing through SecuritizationRISK-BASED PERFORMANCE, PRICING AND CAPITAL ALLOCATIONHEDGING: CLOSING INTEREST RATE GAPSBASIC PROPERTIES OF RISK CONTRIBUTIONSRisk RegulationsSecuritization and Capital ManagementDefault Probability and Default IntensityStress Testing and What-if AnalysesRISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONS TO PORTFOLIO LOSS VOLATILITY AND TO CAPITALThe Financial CrisisCOMPARISONS OF CLASSIFICATIONS: RISK REGULATIONS AND IFRSFull Monte Carlo SimulationsLOGIT MODELSCredit Portfolio ModelsOptional Risk is Always Adverse to the BankDirect Calculation of Default Probability over Two PeriodsSpread RiskBIVARIATE NORMAL STANDARD DISTRIBUTIONSRegulated RatesPORTFOLIO DELTA-NORMAL VARControlling Duration with DerivativesCapital RequirementsRISK-BASED PRICINGForeign Exchange SwapsValuation and Pricing RiskLiquid AssetsLIQUIDITY GAP CALCULATIONSThe Copula Density Function"Effectiveness" of HedgeDEFINITION OF COPULA FUNCTIONSThe Retail PortfolioSeparating All-in Flows into Capital and Interest FlowsRisk-Weighted Assets for Corporate, Sovereign, and Bank ExposuresThe Benefits from the Mirror DebtHEDGE ACCOUNTINGThe Cholesky Decomposition Method: Two VariablesEconomie Value and NiL: General ExampleFunds Transfer Pricing SystemsREPORTING RISK AND RETURN VERSUS BUSINESS DIMENSIONSTraceability of Aggregated Measures and Risk ManagementREMINDERS AND NOTATIONSInteractive Implementation of Risk SystemsIdentification of Potentially Significant AttributesComparing Continuous and Discrete ReturnsRisk Management versus Risk InstrumentsALM APPLICATIONSAPPLICATION: STOCK VALUE DISTRIBUTIONMark-to-market Value of an IRSBINOMIAL DISTRIBUTION OF SUM OF BERNOULLI VARIABLESCollateral: Haircut CalculationsTranches are Subject to Correlation RiskLines without MaturityDiscriminating VariablesCREDIT DEFAULT SWAPS (CDS)SIMULATION OF DEPENDENT VARIABLES WITH THE COPULA APPROACHApplication: The Stressed Default Probability under Basel 2ECONOMIC VALUE AND NET INTEREST INCOME FOR A BANK WITHOUT CAPITALConceptual FrameworkOption-adjusted SpreadThe Bivariate Normal CopulaA Simple Example of a Forward ContractThe Payoff of Option ContractsLiquidity Crises and Stress Test ScenariosAsset Swaps: GeneralizationPORTFOLIO OVERVIEWSection 2. Business Lines, Risks, and Risk ManagementRevaluation of Facilities at HorizonInstruments Traded in Inactive MarketsConditional Density of Normal BivariateEmbedded Options in Banking ProductsCOMMON STOCHASTIC PROCESSESDeriving the Copula Density from Copula FunctionVALUATION UNDER UNCERTAINTYSection 10. Market RiskCONDITIONAL PROBABILITIES AND CORRELATIONPRINCIPLES OF SAMPLE SIMULATIONSContinuous Returns and VarianceEarnings Allocation and Fund Transfer Pricing (FTP) SystemSection 12. Credit Portfolio RiskFORWARD CONTRACTS VERSUS OPTIONSEconomic and Commercial Transfer PricesRisk Oversight: Regulators' ChallengesBASKET SWAPS, FIRST-TO-DEFAULT, N-TO-DEFAULTSENSITIVITY OF ECONOMIC VALUE AND DURATION GAPSAsset Distribution and Default ProbabilityEffective LGD for Collateral-based TransactionsThe Single-factor ModelAPPENDIX I: SAMPLE PORTFOLIO INPUTSStatic Liquidity GapsAsset-liability Management (ALM)Section 3. Financial ProductsVarious Forms of Bivariate Copula FunctionsIMPLEMENTING THE STRUCTURAL MODEL OF DEFAULTSellers of OptionsSTOCHASTIC PROCESSESVolatility PreservationIRB ApproachesDetermination of the Default ProbabilityApplication: The Square Root of Time Rule for the Simple Wiener ProcessPORTFOLIO CREDIT RISK MANAGEMENT (CASE STUDY)SECURITIZATIONSSAMPLE COMPARISON BETWEEN BASEL I AND BASEL 2 CAPITAL FOR CORPORATE ASSET CLASS CREDIT RISKDecomposition of the Forward as a Linear Function of Elementary PositionsLimits and "Nil at Risk"IMPLEMENTING THE EDF© MODELIMPAIRMENT OF FINANCIAL ASSETSEvolution of Credit Risk ModelsThe Bivariate Copula Function: Expanded FormTHE EXPONENTIAL DISTRIBUTION AND TIME TO DEFAULTFINANCIAL RISKSTwo-asset Portfolio and Two-factor Model: Specific RiskThe Binomial Tree for Interest RateThe Market Value of LoanDeriving SensitivitiesCredit DerivativesPortfolio Systematic Risk Decomposition into Additive ItemsPortfolio OptimizationPreemptive Risk Control versus Risk InsuranceHedging Over Multiple PeriodsTHE ORGANIZATION OF FTP SYSTEMSBENCHMARKINGSAMPLE CALCULATIONS OF EDF© AND OF THE PUT AND CALL VALUESCREDIT RISK EXPOSURE FOR PORTFOLIOS OF DERIVATIVESMODELING POTENTIAL VARIATIONS AND PERCENTILESThe Waterfalls of Cash Flows and LossesUsages of Forward Rate ContractsExample: Stock Price DistributionMARKET INSTRUMENTS AND POTENTIAL FUTURE EXPOSURES (PFES)From Discrete to Continuous ReturnsAnalytical Loss DistributionsRisk Factors and Dependence StructureSIMULATION OF CORRELATED NORMAL VARIABLES WITH FACTOR MODELSImplicit Options RiskMatrix Methodology and The Risk-Return Profile of the Balance SheetRetail PortfolioA Simple Portfolio of Two Zero-coupon BondsStructuring of NotesApplications for Credit Portfolio ManagementUNIFORM DISTRIBUTIONSECURITY LENDING AND BORROWINGLIQUIDITY RISK: FUNDINGHOW FIRMS DEFAULTBuying Protection for the Portfolio from Another BankProprietary Models of Market Risk VaRConstructing Attributes from Observed CharacteristicsGrid SimulationsFactor ModelsAccounting StandardsSENSITIVITY AND RISK FACTORSThe 2007-2008 Financial CrisisAPPENDIX 2: SAMPLE PORTFOLIO OUTPUTSTHE STANDARDIZED APPROACHGARCH MODELSCORRELATIONS AND COVARIANCESVolatilitySETTING-UP LIMITSVariance Formula and Correlation MatrixCREDIT VAR AND MATRIX VALUATIONNumber of Default Events over a Given HorizonMODELING DEFAULT PROBABILITY AND CREDIT STANDING AT HORIZONNORMAL DISTRIBUTIONUsing PCA for Single AssetsRAROC CALCULATIONSRegulatory Risk Weights for Corporates, Sovereigns and BanksHistorical and Hypothetical SimulationsMEASURES OF DEPENDENCIESTHE CALCULATION OF RAROC AND SVA FOR CREDIT RISKLIQUIDITY GAP TIME PROFILESTHE ECONOMICS OF SCORING SYSTEMSThe Current Value of the Prepayment OptionPORTFOLIO LOSS DISTRIBUTIONSection 15. Credit Portfolio ManagementTRANSFERRING LIQUIDITY AND INTEREST RATE RISK TO ALM THROUGH THE FTP SYSTEMRisk-based PerformanceCALCULATING INCOME WITHIN A FTP SYSTEMFOREIGN EXCHANGE RATES AND FORWARD CONTRACTSPortfolio Risk Return ProfileHedging and Speculating with Forward ContractsOFF-BALANCE SHEET ITEMSOPTIONAL RISK AND OPTIONAL GAPSLending, Borrowing and the Term Structure of Interest RatesEV and Projected Interest Income at Risk-free RateCredit Portfolio ManagementEconomic Derivation of Minimum Over-collateralizationDISTRIBUTION OF RANDOM RECOVERIESThe Exercise Price and the Payoff of the OptionLarge Number of ExposuresContinuous VariablesIto LemmaTwo Random Normal VariablesTHE CONTRIBUTIONS OF VAR-BASED MEASURESEconomic Capital and Loss VolatilityDERIVATIVES: BASIC DEFINITIONS AND PRINCIPLESTHE CONCEPTUAL FRAMEWORK OF DELTA-NORMAL VARDiscrete VariablesSOVEREIGN, BANK, AND EQUITY EXPOSURESHEDGING INTEREST RATE RISK BY CORPORATE BORROWER (CASE STUDY)Risk Factors and Dependence StructureMODELING DEFAULTS IN A UNIFORM PORTFOLIO:THE LIMIT DISTRIBUTIONCredit Risk Mitigation under Basel 2Portfolio Return VolatilityRationales For SecuritizationsDefinitionSTRUCTURING AND THE WATERFALL MECHANISMDependency and Joint Default ProbabilityOption PricingStocksDefinitionsDealing with Multiple DimensionsDependencies and Copula FunctionsLoss Given Default (LGD)MONTE CARLO SIMULATIONSMARKET LIQUIDITY RISKBOOK STRUCTUREValue PreservationCredit Risk Mitigation: Guarantees and Credit DerivativesRisks and Risk ManagementDEFAULT STATISTICSDefinition of Interest Rate SwapProperties of Copula FunctionsTHE MOMENTS OF A DISTRIBUTIONVanance-Covanance Matrices of Asset Returns and of FactorsNumerical ExampleTranspose MatrixTHE GAP MODELEffective Maturity (M)Regulation and CompetitionRisk Management Organization and Central FunctionsCREDIT RATINGSDEFINITIONS OF RISK CONTRIBUTIONSMaterializationMODELING JOINT MIGRATIONS AND DEFAULTS WITH THE STRUCTURAL MODELDistribution Functions and PercentilesSimulations with Factor Models or the Copula ApproachHypothetical Scenarios, Stress-tests and Extreme VaRBANKS'FINANCIAL STATEMENTSFOREIGN EXCHANGE OPTIONSSimulation of Two Exponentially Distributed Dependent Times to DefaultFrom Portfolio Risk to Individual FacilitiesThe "Basic" Linear Model DrawbacksConditional ProbabilitiesBACK TESTINGRisk Contributions, Portfolio Loss Volatility and CapitalMAPPING SCORING MODELS TO A MASTER SCALE OF DEFAULT PROBABILITIESEconomic Income StatementsMAIN SPECIFICS AND KEYTERMSOptionsPortfolio Total Risk and Two-factor ModelRisk-based Pricing and Marginal Risk Contribution to CapitalEXTENSIONS OF THE MARKET VAR METHODOLOGYDEPENDENT DEFAULT EVENTSTHE ALM FUNCTIONPrinciplesFROM GAPS TO SIMULATIONSCorrelations and CovariancesSample Gap ReportsFrom Sensitivity to VolatilityProjected GapsTHE BETA DISTRIBUTIONDURATION PROPERTIESValuation in Discrete Time and the Rationale of DiscountingIMPLEMENTATION OF SCORING IN RETAIL BANKINGHEDGING A CORPORATE LONG EXPOSURE IN FOREIGN CURRENCY (CASE STUDY)FORWARD VALUATION AND EXCESS SPREADSAnalysis of a Securitization Transaction (Case Study)Generation of Portfolio Value DistributionCREDIT RISK MITIGATIONRisk-based Capital RegulationsCREDIT RISKRISK-ADJUSTED MEASURES OF PERFORMANCEThe "Model Divide"The Option Approach to Defaults and MigrationsRISK MANAGEMENT PROCESSESPORTFOLIO RETURN RISK AND CORRELATIONJOINT DEFAULT PROBABILITY USING DISCRETE VARIABLESMAPPING DEFAULT PROBABILITY TO THE STANDARDIZED NORMAL DISTANCE TO DEFAULTOPERATIONAL RISKCorrelation and Concentration RisksIncome-producing Real EstateLIQUIDITY CONTAGIONFrom Risk Contributions to Capital AllocationLogit Model FamilyCapital and Risk Allocation SystemSVA MEASURESPILLAR 2: SUPERVISORY REVIEW PROCESSPortfolio Systematic Risk: Two-factor ModelsReverting to Better Risk Practices and Lessons of the CrisisCredit Portfolio View Conceptual FrameworkDemand DepositsModeling RecoveriesSupervisionThe Mean Reverting ProcessRevenuesForward Contracts and Interest Rate SwapsVariety of SecuritizationsRisk-based PricingThe Ito ProcessMotivations for Risk OversightStructuring Debt MaturitiesPAYOFF OF PREPAYMENTVaR at Different HorizonsCapital UtilizationsDEFAULT PROBABILITY OF A FIRM DEPENDENT ON THE STATE OF THE ECONOMYSection 1. The Financial CrisisBanking Business LinesRisk-based Capital and GrowthCOVENANTSCapital Under Default ModeJudgmental Ratings versus "Rating Models"Asset Value and Market Required ReturnINTEREST RATES AND FACTOR MODELSThe Variance-Covariance Matrix of Portfolio ReturnMARGINAL RISK CONTRIBUTION AND SIZE OF AN EXISTING EXPOSUREREGULATORY ISSUESCumulative Default RatesVOLATILITY AND DELTA-NORMAL VAR OF THE FORWARD VALUECredit Risk and Lending ActivitiesAPPENDIX:THE CHOLESKY DECOMPOSITION METHODRisk-based Pricing and Risk Contribution to CapitalThe Stock Price ProcessSCORINGMEASURES OF POTENTIAL LOSSESECONOMIC TRANSFER PRICES FOR RESOURCESLIQUIDITY SCENARIOSOTHER ARBITRAGE BETWEEN ECONOMIC PRICES AND RATING-BASED PRICESFrom Daily Volatility of the Position to Daily VaRMarginal Risk ContributionsExpected LossTwo-asset Portfolio and Two Orthogonal FactorsHeld-to-maturity Financial AssetsCREDIT INTENSITY MODELSVAR AND ECONOMIC CAPITALMethod of Determining Fair ValueExample of Portfolio Loss Distribution Limits and DelegationsTHE PRICE OF RISK AND ARBITRAGEThe Wiener ProcessMARGINAL RISK CONTRIBUTIONS TO CAPITALTHE THIRD EDITIONCREDIT SPREAD, IMPLIED DEFAULT INTENSITY AND RECOVERY RATELOSS DISTRIBUTIONSSTATIC VERSUS DYNAMIC GAPSFACTOR MODELSEconomic Value of the Balance SheetCOMMON SENSITIVITIESCREDIT PORTFOLIO MODEL OVERVIEWGeneral Calculation of Default Probability over Two PeriodsThe Loss StatisticsBUILDING BLOCKS OF THE INTERNAL CREDIT RATING SYSTEMCREDIT RISK VAREquity ExposuresSOME IMPLICATIONSIntermediate Flows and NIL CalculationsREGULATIONSSPECIALIZED LENDINGAPPENDIX: CALCULATION OF STANDARD DEVIATION FROM TIME SERIESThe Cost of Credit Risk and the Risk PremiumInterest Rate Gap and Liquidity GapsCredit Risk Mitigation: Collateral TreatmentESTIMATING EWMA VOLATILITYJoint Probability Density Functions with Two VariablesSPECIFICS OF STOCHASTIC PROCESSES AND ITO LEMMASection 5. Risk ModelingKEY BENEFITS OF COPULA DEPENDENCYCredit Components and Risk WeightsSection 7. Asset Liability Management (ALM)CLASSIFICATION OF LENDING PRODUCTS AND BASEL 2 CRITERIAALM GOALSCONDITIONAL PROBABILITY FROM THE COPULA DENSITYThe Simulation AlgorithmReplicating a Forward LoanJoint Density of a Bivariate Normal Distribution and the Copula Density FunctionSECTION ORGANIZATIONValuation of a BondEstablish Comprehensive Supervision and Regulation of Financial MarketsPRINCIPAL COMPONENT ANALYSIS AND THE TERM STRUCTURE OF INTEREST RATESINTEREST RATE SIMULATIONS WITH PCAThe Portfolio Loss VolatilityCOUNTERPARTY CREDIT RISKForms of the Gaussian CopulaValuation of the Put Option to DefaultADDITIONAL PROPOSALSFORWARD CONTRACTSSovereign ExposuresHedging Implicit Options to Renegotiate Fixed RatesFixed Assets and EquityThe Cooke Ratio and Credit RiskCREDIT RISK COMPONENTSOPTIONAL RISKOptions Allow Hedging RisksSIMULATIONS OF TIMES TO DEFAULTRISK OF A TWO-STOCK PORTFOLIO WITH THE ONE-FACTOR MODELExchanging Net Balances of Funds between UnitsOff Balance Sheet ItemsThe Two-factor Model Applied to a Two-asset PortfolioSimulations of Default DistributionsApplication: Finding the Factor Value Matching a Given Portfolio Loss PercentileTHE SAMPLE PORTFOLIO AND THE SIMULATIONSRATING GRIDSALM SCOPE AND STRUCTURE OF THE SECTIONEQUALLY WEIGHTED HISTORICAL VOLATILITYFinancial ApplicationsThe Accounting N11 of the BankBasic Specifications of Reporting SystemsCollarRISK-ADJUSTED PERFORMANCE AND MISPRICING REPORTSConceptual FrameworkTHE RATIONALE FOR CREDIT PORTFOLIO MANAGEMENTVALUATION OF CREDIT RISK GUARANTEES, INSURANCE OR CREDIT DERIVATIVESExposure and Capital Allocation or Loss VolatilityTHE DILEMMAS OF THE REGULATORFitting and Back Testing Scoring ModelsDEPENDENCIES MODELING ASA KEY BUILDING BLOCK FOR RISK MODELINGAPPENDIX: RATING SCALES OF RATING AGENCIESVariance-Covariance Matrix of Portfolio ReturnsAPPLICATIONS OF CREDIT DERIVATIVESSingle PeriodThe Case of FloatersEconomic Transfer PricesInterpretation of Basel 2 Formulas for Risk WeightsINTEREST RATE PROCESSESPayments under a Credit EventAvailable-for-sale Financial AssetsRISK-BASED PRICING AND MARGINAL RISK CONTRIBUTIONSContinuous TimeDistribution FunctionsCREDIT VAR AND MATRIX VALUATION: APPLICATIONRisk-neutral ProbabilityGENERAL PROPERTIES OF RISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONSOff Balance Sheet CommitmentsThe Costs of Funding On Balance Sheet and through SecuritizationTRANSACTION-SPECIFIC CREDIT RISKOPERATIONAL RISKINDEPENDENT DEFAULT EVENTS:THE BINOMIAL DISTRIBUTIONLoss Statistics and CapitalThe "Ex Ante" and the "Ex Post" ViewsPORTFOLIO RISK WITH MULTIPLE-FACTOR MODELSEnhancing the Bank's Return on Capital through SecuritizationFOREIGN EXCHANGE RISKBack Tests, Benchmarks and Stress Tests The Global Calibration of the Binomial TreeFixed and Variable RatesINDICATOR FUNCTIONRecovery RiskConditional and Joint ProbabilitiesTYPES OF RISKSExample: Option ContractSecuritizations: TraditionalThe "Notional" Funding of LoansHORIZON FOR CREDIT CAPITALJOINT MIGRATION MATRICESORTHOGONAL MULTIPLE FACTOR MODELS AND PCAValuation and LeverageLogarithmic ReturnsTHE ACCORD FOR MARKET RISKBreaking Down the Bank Margin into Contributions of Business UnitsATWO-ASSET PORTFOLIO WITH TWO-FACTOR MODELSBanking and Financial ProductsPOSITIONING OF THE TEXTVALUATION OF RISKY DEBT FROM CREDIT SPREADS AND RISK-NEUTRAL PROBABILITIESBANKING REGULATIONS AND ACCOUNTING STANDARDSRisk Contributions to VolatilityRECOVERY STATISTICSLoss PercentilesTHE VALUE OF IMPLICIT OPTIONSSpecific CasesBonds and LoansThe All-in Cost of Funds of the Mirror DebtRating Methodologies for Structured NotesNIL AND EVDerivatives and Credit RiskPortfolio AnalysisREPORTING ALTERNATE METRICS OF RISKCREDIT SPREAD PRODUCTSASSESSING THE RISK OF ASSET-BACKED NOTESVARIATIONS ON THE MERTON'S MODELTHE WHITE PAPER FROM THE WHITE HOUSEApplication: Simulating Two Uniform Standard Variables with Conditional CopulaFORWARD RATES: DEFINITIONSSimulating Increased Diversification with Loss IndependenceThe Generalized Wiener ProcessCredit Conversion Factors (CCFs)APPENDIX: CONDITIONING, EXPECTATION AND VARIANCEThe Dependent CaseLiquidity Management and Liquidity GapsSensitivityCalculation of Joint Default and Conditional ProbabilitiesOptions as Volatility InstrumentsINTEREST RATE RISKAPPENDIX:THE GAMMA DISTRIBUTIONThe "Rare Event" ProcessSimulation of Time to Default for a Single ObligorTHE TWO-OBLIGOR PORTFOLIO AND CONDITIONAL PROBABILITIESThe Hurdle Rate and the Cost of CapitalMigration RiskDerivation of the Normal Copula DensityBivariate CopulaPILLAR 3: MARKET DISCIPLINEInterest Rate SwapsVALUATION RULESThe "Three Lines of Defense" PrincipleNumerical SensitivitiesGeneration of Portfolio Value DistributionTHE RISK PREMIUM EMBEDDED IN RISK-BASED PRICINGInterpolation of Interest Rate from Selected Risk FactorsAmortizing LoansCredit Risk in the Trading PortfolioCommercial SpreadsDependency StructureMAPPING RATINGS TO DEFAULT PROBABILITIESCapital Under Full Migration ModeAPPENDIX: COPULA FUNCTION AND COPULA DENSITYStandardizing the Single-factor ModelThe All-in Cost of Funding through SecuritizationCONTAGION AND PROCYCLICALITY IN A LEVERAGED INDUSTRYORIGINATION AND POST-ORIGINATION FOLLOW UPAPPENDIX:THE TAYLOR EXPANSION FORMULARaise International Regulatory Standards and Improve International CooperationTransaction Versus Client Revenues and PricingFORWARD DEFAULT AND SURVIVAL PROBABILITIESLegal IssuesRETAIL PORTFOLIO IN BASEL 2COLLATERALIZED SECURITIES LENDING/BORROWINGSection 13. Capital AllocationVariance-Covariance Matrix and Correlation MatrixSensitivityBanking Regulations: The Basel 2 AccordBinomial Tree of Interest RatesTHE "BASEL I ACCORD" FOR CREDIT RISKRisk Oversight: Banks' ChallengesCAPITAL CALCULATIONDEFINITION OF INTEREST RATE GAPSRisk ManagementBook Measures of Profitability versus Risk-adjusted MeasuresDeterministic CalculusBanking Regulations: Basel I and Market RiskAccounting StandardsHistorical Volatility with Equally Weighted ObservationsINVERSE FUNCTIONSINTEREST RATE OPTIONS: CAPS AND FLOORSSample Bank Balance SheetSIMULATION OF JOINT DEFAULTS AND MIGRATIONSHow to Solve Numerically a PDECAPITAL ADEQUACYCREDITRISK+AND ANALYTICAL DISTRIBUTIONSECONOMICS OF SECURITIZATIONSMARGINAL RISK CONTRIBUTIONS TO LOSS VOLATILITYDefault Intensity ModelsTRADING CREDIT RISKThe Original LoanMarket Risk and Trading ActivitiesTHE CAPITAL ALLOCATION MODEL AND RISK CONTRIBUTIONSSOVEREIGN RISK CREDIT DERIVATIVESBANKING PORTFOLIO EXPOSURESStandardized ApproachRetail Portfolio: Further Differentiation for Capital TreatmentApplication of Cholesky DecompositionThe Value-at-Risk MeasureSimulation of Interest RatesThe Independence CaseScope and Goals of this TextNORMATIVE CAPITAL ALLOCATIONS AND CAPITAL EFFECTIVE UTILIZATIONSBERNOULLI DISTRIBUTIONContingencies Given (Off-balance Sheet)SCORING IN RETAIL BANKING: BEHAVIORAL VERSUS ORIGINATION MODELSMARGINAL RISK CONTRIBUTIONS TO VOLATILITY VERSUS RISK CONTRIBUTIONSForward and Spot Rates: No ArbitrageMatrix Notations MIGRATIONS AND VAR UNDERTHE STRUCTURAL MODELSENSITIVITIES AND RISK CONTROLLINGImprove Tools for Managing Financial CrisesRANDOM VARIABLES AND PROBABILITY DISTRIBUTION FUNCTIONSEconomic Value and Convexity RiskINTERNAL CREDIT RATINGS AND BUSINESS RULESThe Simulation Algorithm for Standardized Normal Variables using Single-factor ModelsBuying Protection for the Portfolio and Selling ProtectionConditional Distributions and CopulaThe Two-asset Portfolio ReturnPayoffs of the Option under Differed ExerciseForeign Exchange Risk and Foreign Exchange DerivativesThe Standardized ApproachFrom Future Values to Current CapitalTHE SIMPLE "BINOMIALTREE" TECHNIQUE APPLIED TO INTEREST RATESBank ExposuresUNCERTAINTY, RISK,AND EXPOSURETO RISKEquity ExposuresMapping and AllocationForward Default IntensityThe Firm ValueCALCULATING THE PFE FOR AN INTEREST RATE SWAPGeneration of Portfolio Value DistributionMAXIMUM LIKELIHOOD METHODOLOGYDEFINITION OF CONDITIONAL AND JOINT PROBABILITIESCustomizing Credit RiskVaR and CapitalMismatch RiskBERNOULLI VARIABLETHE GENERIC FORM OF FACTOR MODELSDependency and Joint Migration ProbabilitiesExpected LossThe Pricing of Assets Sold to the SPEExample of a One-factor ModelRISK-NEUTRAL VALUATION:THE CASE OF A STOCK PRICEHow to Form Risk-free PortfoliosHigh-volatility Commercial Real EstatePortfolio SimulationsExpected LossECONOMIC VALUE, DURATION AND CONVEXITYEXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA) MODELNET INTEREST INCOME AND INTEREST RATE GAPSCredit Risk Valuation and Credit SpreadsLoss StatisticsExposure RiskHow Gaps Change Through TimeExample of Calculations of the Forward Yield CurvesSection 11. Credit Risk: StandaloneCOMMERCIAL SPREADS AND MATURITY SPREADTHE EXAMPLE OF A FORWARD FOREIGN EXCHANGE RATECredit Risk Potential ExposureNormative Risk Allocations Versus Capital UtilizationsThe Simulation AlgorithmTOTAL RETURN SWAPSACCURACY OF SCORING MODELS:THE "CAP"Basel 2 Treatment of Collateralized TransactionsMIGRATION MATRICESThe Matrices of Net Interest IncomeThe Pricing Paradox with Marginal Risk ContributionsMain PrincipleCredit Risk MitigantsMONTE CARLO SIMULATIONS OF DEFAULT EVENTS BASED ON THE STRUCTURAL MODEL OF DEFAULTTHE "STANDARDIZED" STANDALONE STRUCTURAL MODELUsages of Risk Contributions and of Marginal Risk ContributionsCalculation of RaRoC and SVASingle Period Discrete ReturnConvexityProtect Consumers and Investors from Financial AbuseCredit Event DependenciesTop-down and Bottom-up Risk Management Processes and SystemsSecuritizations: SyntheticCONTAGION AND PROCYCLICALITYTHROUGH FAIR VALUE RULESLIQUIDITY MANAGEMENTAbout the AuthorINTEREST RATE RISK FOR BORROWERS AND LENDERSOther CostsDelta-normal VaRStochastic ProcessesLoss Distributions, Potential Losses and VaRPRICING FOR LENDINGDuration GapSome Applications of Valuation TechniquesBUSINESS POLES IN THE BANKING INDUSTRYTHE SUB-PRIME CRISISPayoff of a Forward ContractTHE VAR METHODOLOGY: MARKET RISKSources of ConvexityThe Default Probability Conditional on The State of the EconomyTypes of HedgesExposure at Default (EAD)Bivariate Normal Standard DensityConditional Distributions and SimulationsDynamic Liquidity GapsSIMULATIONS AND INVERSE FUNCTIONSSection 9. Dependencies and Portfolio RiskTrading Credit RiskPortfolio DataThe Basic Mechanism of LimitsModeling Defaults under the Structural ModelPORTFOLIO OF TWO OBLIGORSMultiple Business and Interest Rate ScenariosASSETS AND POSITIONSIndirect Effects and Factor-push ScenariosProbability of Default (DP) and Default EventSimulation of Credit Portfolio Loss DistributionsRating SystemsThe One-factor ModelInterest Rate Risk and Interest. Rate DerivativesThe Cost of the Mirror DebtMARKET RISKCREDIT METRICSEconomic Value and Convexity GapsPayoff of Interest Rate OptionsVisual Representation of the Diversification EffectRisk-adjusted Performance versus Risk-based PricingMigration Matrices and Cumulative Default ProbabilitiesStatistical and Scoring ModelsPRICING CREDIT DERIVATIVESINTEREST RATE RISKThe Vanance-Covanance MatrixBasic FormulasPORTFOLIO OF TWO INDEPENDENT OBLIGORSNature of Borrower or Low Value of Individual ExposuresStock Price Dynamics under Risk-neutral ProbabilitiesExpected Return on Assets and Compensations to InvestorsProject FinanceTHE OPTION THEORETIC FRAMEWORK OF VALUATION OF EQUITY AND DEBTOn Balance SheetThe Asset Value and Default Probability Conditional on the State of the EconomyWHERE DO INTEREST RATES COME FROM?CREDIT PORTFOLIO VIEW: ECONOMETRIC MODELSINTEREST RATES AND TERM STRUCTUREAPPENDIX 3: PORTFOLIO ANALYSIS AND REPORTING ISSUESThe Uniform Granular PortfolioRISK FOR A SINGLE ASSET AND TWO-FACTOR MODELSBASIC POSTULATES OF THIS TEXTVariance and VolatilityExtension to any Number of VariablesEconomic Capital and Credit Risk VaRCONTAGION THROUGH RATING DOWNGRADESCUMULATIVE DEFAULT AND SURVIVAL PROBABILITIESA Single Obligor Dependent on the State of the EconomyDiscrete and Continuous ReturnsTHE DISCOUNTED CASH FLOW MODELE-VaR or Expected ShortfallValuation of a Forward Contract or FRASTRUCTURAL EXCESSES OF LIQUIDITYDerivatives and P & LRisk Contributions to Portfolio Loss VolatilityLIQUIDITY DEFINITIONSExchanging all Outstanding BalancesMispricing ReportsThe Securitization OrganizationCredit Events and Credit State at HorizonSECURITIZATIONSCONSTRUCTING A RISK-FREE PORTFOLIOEssentials on Derivative ProductsUnivariate and Bivariate Normal DistributionsSpot and Forward PricesNon-linear Relationship between Selected Attributes and Credit StateSection 4. ValuationAnnual Default RatesThree Basic Liquidity PositionsMOODY'S-KMV CREDIT MONITOR AND MOODY'S-KMV PORTFOLIO MANAGERFROM PORTFOLIO VALUE DISTRIBUTION TO CREDIT CAPITALDefault RiskProjected Net Interest IncomeThe Underlying AssetsHistorical VaR: Forward Contract ExampleThe Valuation of American OptionsSTRESS TESTING, HYPOTHETICAL SCENARIOS AND SENSITIVITY ANALYSESThe Reference Capital for Risk ContributionsReplicating a Forward Exchange RateENTERPRISE-WIDE RISK MANAGEMENT (ERM)APPLICATION TO MARKET VARAPPENDIX: MATRIX NOTATIONS AND FORMULASTime to DefaultCLASSICAL CONTAGION MECHANISMSProvisioningSTANDALONE INDIVIDUAL LOSSESThe Normal Standard Copula Density and the Joint Density of Two VariablesCorrelations, Variances, and CovariancesPayment TermsLIMITATIONS OF INTEREST RATE GAPSCREDIT RISK FOR DERIVATIVES: METHODOLOGYSimulation AlgorithmReplicating an Interest Rate SwapVALUATION OF AN OPTION UNDER RISK-NEUTRAL PROBABILITIESHEDGING THE VARIATIONS OF THE TERM STRUCTURE OF INTEREST RATES (CASE STUDY)The Distribution of Firm ValueINTERNAL RATINGS BASED FRAMEWORKDISCRETE AND CONTINUOUS RETURNSMANAGEMENT PRACTICES DIFFER ACROSS AND WITHIN BUSINESS LINESThe Annualized All-in Cost of Financing through SecuritizationMapping Interest Rates to Selected Risk FactorsThe Cost of Existing ResourcesExpanded RaRoC FormulaRisk FactorsCapitalRisk and Return of Option ContractsASSET CLASSESSIMULATION OF TWO DEPENDENT TIMES TO DEFAULTSUPPORTMeasure of ConvexityPortfolio Concentration and Correlation RiskCredit Risk DataSOLVENCY RISKMark-to-market Valuation of Forward ContractsUnexpected Loss and VaRECONOMICS OF SECURITIZATION FORTHE BANKOptional Risk and HedgingAPPLICATION TO LOSS DISTRIBUTIONS AND LOSS PERCENTILESDirect Effects or "Factor-push" TechniquesMANAGING GAPS: SETTING UP LIMITSEARNINGS-AT-RISK ("EAR")SIMULATIONSLOGNORMAL DISTRIBUTIONREGULATORY ADD-ONS FOR DERIVATIVESDealing with Different Default Probabilities and Discrepancies of ExposuresVALUATION: END RESULTSVOLATILITYMarginal Risk ContributionsTRANSITION MATRICESThe Sensitivity of Nil and Interest Rate GapUnderlying of OptionsDuration Gap and Sensitivity of EVPORTFOLIO ANALYSIS AND REPORTING TECHNICAL CHALLENGESINTEREST RATE SWAPS (IRS)Conditional ProbabilitiesHISTORICAL SIMULATIONSSENSITIVITY DEFINITIONSOptionsImplementing the Matrix ApproachSPECIALIZED LENDINGMODELING PREPAYMENTSMISMATCH RISKISSUES FOR DETERMINING THE LIQUIDITY GAP TIME PROFILECommodities FinanceSIMULATION OF TWO DEPENDENT UNIFORM STANDARD VARIABLESHedging Credit RiskTHE STUDENT DISTRIBUTIONCONTAGION THROUGH SECURITIZATIONSDealing with Different Default Probabilities and Discrepancies of ExposuresTHE FOREIGN EXCHANGE MARKET AND RATESTHE VASICEK MODELECONOMIC VALUE (EV)MAPPING AN INSTRUMENTTO RISK FACTORSAPPENDIX: CALCULATION OF ABSOLUTE RISK CONTRIBUTIONS FROM THE VARIANCE-COVARIANCE MATRIXECONOMIC TRANSFER PRICES FOR LOANSCapital AllocationSection 8. Funds Transfer Pricing SystemsThe Loss DistributionCOMPARISON OF THE DEPENDENT AND THE INDEPENDENT CASESCompounding Continuous ReturnsModeling Potential Variations of ValueSecuritization Economics and the Return on EquitySection 14. Risk-adjusted PerformanceHEDGING BUSINESS RISK AND INTEREST RATE RISKRevaluation of Facilities at HorizonAPPENDIX: MATRIX DIAGONALIZATIONYield-to-Maturity and Zero-coupon RatesCredit EventsBasel I DrawbacksInterest Rate GapsMathematical SensitivitiesAmortized CostInstruments Traded in Active MarketsExceptional LossesCapital Allocation and Risk ContributionsSIMULATION OF TWO DEPENDENT NORMAL STANDARD VARIABLESHow to Derive the Pricing PDECountry RiskCalculating Marginal Default ProbabilitiesFinancial Assets and Liabilities at Fair Value through Profit or LossIDENTITY BETWEEN EV AND "ALL-IN" CASH FLOWS (CAPITAL AND INTEREST)THE NEW BASEL ACCORDExposures, Default Probability and Loss Given DefaultDetermining the Percentile of the Final Asset ValueMultiple ScenariosCorporate Sample Rating GridObject FinanceSection 6. RegulationsCorrelation and Volatility of a Sum of Random VariablesCredit Events and Credit State at HorizonValue PercentileThe Multiple SimulationsOPTIONSDEFINITIONS OF CREDIT DERIVATIVESStochastic CalculusCREDIT RATINGS AND LINKS BETWEEN COUNTERPARTIESHedging both Interest Rate and Business RisksLoss DistributionAllocating Income through the FTP SystemExposure and Expected LossCounterparty Risk of DerivativesINITIAL RECOGNITION OF FINANCIAL ASSETS AND LIABILITIESCONVEXITY GAPS AND OPTIONSGenerator MatricesRISK OVERSIGHT CHALLENGESCredit Events and Credit State at HorizonRaRoC and Shareholders' Value Added SAMPLE CALCULATIONS OF RISK CONTRIBUTIONSThe Generic Form of Multiple-factor ModelsMark-ups and Mark-downs over Reference Rates
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