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A short course of lectures
«Risk management in banking»





THE CONCEPTUAL FRAMEWORK OF DELTA-NORMAL VARASSET CLASSESEQUALLY WEIGHTED HISTORICAL VOLATILITYReplicating an Interest Rate SwapPILLAR 3: MARKET DISCIPLINERisk-based Capital and GrowthAPPLICATION TO MARKET VARSimulations of Default DistributionsLIQUIDITY MANAGEMENTUsages of Forward Rate ContractsTHE FOREIGN EXCHANGE MARKET AND RATESCLASSICAL CONTAGION MECHANISMSFactor ModelsSENSITIVITY AND RISK FACTORSFixed Assets and EquityCapital Under Full Migration ModeAPPENDIX: COPULA FUNCTION AND COPULA DENSITYGeneration of Portfolio Value DistributionInterest Rate Risk and Interest. Rate DerivativesSVA MEASURESThe "Ex Ante" and the "Ex Post" ViewsMEASURES OF DEPENDENCIESPORTFOLIO ANALYSIS AND REPORTING TECHNICAL CHALLENGESMotivations for Risk OversightOptional Risk is Always Adverse to the BankHEDGE ACCOUNTINGTHE "STANDARDIZED" STANDALONE STRUCTURAL MODELBook Measures of Profitability versus Risk-adjusted MeasuresExample of Portfolio Loss Distribution General Calculation of Default Probability over Two PeriodsHow to Solve Numerically a PDECounterparty Risk of DerivativesTHE RISK PREMIUM EMBEDDED IN RISK-BASED PRICINGVolatilityDirect Calculation of Default Probability over Two PeriodsCOVENANTSFACTOR MODELSProtect Consumers and Investors from Financial AbuseRationales For SecuritizationsTHE "BASEL I ACCORD" FOR CREDIT RISKLegal IssuesIdentification of Potentially Significant AttributesHow Gaps Change Through TimeGARCH MODELSSupervisionLoss PercentilesRevenuesApplication: The Stressed Default Probability under Basel 2THE CALCULATION OF RAROC AND SVA FOR CREDIT RISKCALCULATIONS OF INTEREST RATE GAPSThe Cooke Ratio and Credit RiskThe Single-factor ModelConditional Density of Normal BivariateCredit Risk Mitigation: Guarantees and Credit DerivativesOPERATIONAL RISKRISK MANAGEMENT PROCESSESRisk Contributions to VolatilityEstablish Comprehensive Supervision and Regulation of Financial MarketsFROM GAPS TO SIMULATIONSMAPPING DEFAULT PROBABILITY TO THE STANDARDIZED NORMAL DISTANCE TO DEFAULTPORTFOLIO CREDIT RISK MANAGEMENT (CASE STUDY)E-VaR or Expected ShortfallREPORTING RISK AND RETURN VERSUS BUSINESS DIMENSIONSINTEREST RATE PROCESSESSection 15. Credit Portfolio ManagementDependency and Joint Default ProbabilityRISK-BASED PRICING AND MARGINAL RISK CONTRIBUTIONSLines without MaturityThe Value-at-Risk MeasureConditional Distributions and SimulationsThe Default Probability Conditional on The State of the EconomyConvexityREGULATORY ADD-ONS FOR DERIVATIVESInteractive Implementation of Risk SystemsSecuritization Economics and the Return on EquityNIL AND EVLIQUIDITY RISK: FUNDINGHedging Caps Sold to ClientsTYPES OF RISKSCalculation of RaRoC and SVAINTEREST RATES AND FACTOR MODELSThe Loss StatisticsCollateral: Haircut CalculationsBivariate Normal Standard DensityValuation of a BondThe Mean Reverting ProcessREPORTING ALTERNATE METRICS OF RISKLogit Model FamilyThree Basic Liquidity PositionsVALUATION OF CREDIT RISK GUARANTEES, INSURANCE OR CREDIT DERIVATIVESMODELING JOINT MIGRATIONS AND DEFAULTS WITH THE STRUCTURAL MODELBANKING PORTFOLIO EXPOSURESTHE TWO-OBLIGOR PORTFOLIO AND CONDITIONAL PROBABILITIESImplicit Options RiskVALUATION: END RESULTSRegulated RatesStandardizing the Single-factor ModelEconomic Transfer PricesThe Ito ProcessCredit Risk MitigantsSimulation of Credit Portfolio Loss DistributionsDISTRIBUTION OF RANDOM RECOVERIESESTIMATING EWMA VOLATILITYMain PrincipleInstruments Traded in Active MarketsEXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA) MODELAPPENDIX I: SAMPLE PORTFOLIO INPUTSThe Exercise Price and the Payoff of the OptionDuration Gap and Sensitivity of EVALM and Hedging PoliciesThe Simulation AlgorithmCREDIT RISK MITIGATIONTHE BETA DISTRIBUTIONBuying Protection for the Portfolio from Another BankThe Financial CrisisRegulation and CompetitionCumulative Default RatesTHE CAPITAL ALLOCATION MODEL AND RISK CONTRIBUTIONSValuation and Pricing RiskRisk Factors and Dependence StructureMarginal Risk ContributionsTHE WHITE PAPER FROM THE WHITE HOUSECollarSTATIC VERSUS DYNAMIC GAPSRisk FactorsSTRESS TESTING, HYPOTHETICAL SCENARIOS AND SENSITIVITY ANALYSESFitting and Back Testing Scoring ModelsEV and Projected Interest Income at Risk-free RateTHE GENERIC FORM OF FACTOR MODELSSovereign ExposuresThe Dependent CaseDEFINITIONS OF CREDIT DERIVATIVESCREDIT RISKBasel 2 Treatment of Collateralized TransactionsExample: Stock Price DistributionDERIVATIVES: BASIC DEFINITIONS AND PRINCIPLESDealing with Different Default Probabilities and Discrepancies of ExposuresJOINT MIGRATION MATRICESBasic FormulasNumerical ExamplePRICING FOR LENDINGHedging Over Multiple PeriodsHigh-volatility Commercial Real EstateStructuring Debt MaturitiesRaRoC and Shareholders' Value Added CONVEXITY GAPS AND OPTIONSThe Costs of Funding On Balance Sheet and through SecuritizationAPPENDIX:THE CHOLESKY DECOMPOSITION METHODValuation of the Put Option to DefaultSAMPLE CALCULATIONS OF EDF© AND OF THE PUT AND CALL VALUESOptionsMark-to-market Valuation of Forward ContractsGrid SimulationsDemand DepositsLIMITATIONS OF INTEREST RATE GAPSModeling Defaults under the Structural ModelPrinciplesDURATION PROPERTIESSection 13. Capital AllocationCREDIT RATINGSRisk ManagementMark-to-market Value of an IRSHow to Derive the Pricing PDETranspose MatrixAmortized CostCLASSIFICATION OF LENDING PRODUCTS AND BASEL 2 CRITERIAExpected LossYield-to-Maturity and Zero-coupon RatesTHE DILEMMAS OF THE REGULATORSection 4. ValuationBERNOULLI DISTRIBUTIONBASIC PROPERTIES OF RISK CONTRIBUTIONSDuration GapDerivatives and P & LDEPENDENT DEFAULT EVENTSThe Effective Return on Capital for the BankPRICING CREDIT DERIVATIVESThe Cost of Existing ResourcesJoint Density of a Bivariate Normal Distribution and the Copula Density FunctionDEFAULT STATISTICSTOTAL RETURN SWAPSCapital Allocation and Risk ContributionsSection 11. Credit Risk: StandaloneApplication: The Square Root of Time Rule for the Simple Wiener ProcessRisk-based Pricing and Risk Contribution to CapitalACCURACY OF SCORING MODELS:THE "CAP"CREDIT VAR AND MATRIX VALUATION: APPLICATIONEconomic Capital and Loss VolatilityCredit Risk Potential ExposureSection 3. Financial ProductsSIMULATION OF TWO DEPENDENT UNIFORM STANDARD VARIABLESExample of a One-factor ModelThe Vanance-Covanance MatrixINTERNAL RATINGS BASED FRAMEWORKVaR and CapitalThe Simulation Algorithm for Standardized Normal Variables using Single-factor ModelsGenerator MatricesSPECIALIZED LENDINGSome Applications of Valuation TechniquesHow to Form Risk-free PortfoliosThe Firm ValueTHE SAMPLE PORTFOLIO AND THE SIMULATIONSUNIFORM DISTRIBUTIONCREDIT INTENSITY MODELSDEFINITION OF CONDITIONAL AND JOINT PROBABILITIESEconomic Derivation of Minimum Over-collateralizationMONTE CARLO SIMULATIONS OF DEFAULT EVENTS BASED ON THE STRUCTURAL MODEL OF DEFAULTMAPPING AN INSTRUMENTTO RISK FACTORSCALCULATING THE PFE FOR AN INTEREST RATE SWAPSpread RiskMARGINAL RISK CONTRIBUTIONS TO LOSS VOLATILITYCredit Events and Credit State at HorizonBanking Business LinesBinomial Tree of Interest RatesCREDIT DEFAULT SWAPS (CDS)Equity ExposuresCredit Risk DataLIQUIDITY DEFINITIONSBasic Specifications of Reporting SystemsTRANSACTION-SPECIFIC CREDIT RISKDiscrete and Continuous ReturnsInstruments Traded in Inactive MarketsAsset-liability Management (ALM)APPENDIX 2: SAMPLE PORTFOLIO OUTPUTSECONOMIC VALUE (EV)SOVEREIGN, BANK, AND EQUITY EXPOSURESVariety of SecuritizationsForward Default IntensityThe All-in Cost of Funds of the Mirror DebtTHEORETICAL VALUES OF THE OPTION TO DEFAULT ANDTHE EDF©Mispricing ReportsCONDITIONAL PROBABILITIES AND CORRELATIONFORWARD CONTRACTSLoss Statistics and CapitalSTRUCTURING AND THE WATERFALL MECHANISMDefault RiskVariance and VolatilitySENSITIVITY OF ECONOMIC VALUE AND DURATION GAPSDiscriminating VariablesNET INTEREST INCOME AND INTEREST RATE GAPSAccounting StandardsTime to DefaultLIQUIDITY GAP CALCULATIONSDynamic Liquidity GapsSection 10. Market RiskINDEPENDENT DEFAULT EVENTS:THE BINOMIAL DISTRIBUTIONCUMULATIVE DEFAULT AND SURVIVAL PROBABILITIESBENCHMARKINGThe Cost of the Mirror DebtSimulating Increased Diversification with Loss IndependenceSection 14. Risk-adjusted PerformanceAnalytical Loss DistributionsOther CostsValue PercentileThe Wiener ProcessASSETS AND POSITIONSCompounding Discrete Returns over Multiple PeriodsDeterministic CalculusINTEREST RATE RISK FOR BORROWERS AND LENDERSBivariate CopulaDependency StructureMultiple ScenariosFrom Sensitivity to VolatilityAPPENDIX:THE GAMMA DISTRIBUTIONCONDITIONAL PROBABILITY FROM THE COPULA DENSITYMOODY'S-KMV CREDIT MONITOR AND MOODY'S-KMV PORTFOLIO MANAGERMODELING POTENTIAL VARIATIONS AND PERCENTILESRATING GRIDSOFF-BALANCE SHEET ITEMSLOGNORMAL DISTRIBUTIONRisk-Weighted Assets for Corporate, Sovereign, and Bank ExposuresUnivariate and Bivariate Normal DistributionsSTANDALONE INDIVIDUAL LOSSESStatic Liquidity GapsCREDIT RISK EXPOSURE FOR PORTFOLIOS OF DERIVATIVESExposure and Expected LossA Simple Portfolio of Two Zero-coupon BondsDeriving SensitivitiesRAROC CALCULATIONS AT PORTFOLIO AND FACILITY LEVELSPAYOFF OF PREPAYMENTCREDIT SPREAD PRODUCTSDefault Intensity ModelsCorrelations, Variances, and CovariancesDependencies and Copula FunctionsDistribution Functions and PercentilesCredit Components and Risk WeightsSCORING IN RETAIL BANKING: BEHAVIORAL VERSUS ORIGINATION MODELSTHE MOMENTS OF A DISTRIBUTIONRisk Factors and Dependence StructureIMPLEMENTATION OF SCORING IN RETAIL BANKINGSETTING-UP LIMITSRISK-BASED PRICINGSECURITY LENDING AND BORROWINGCREDIT RISK VARBanks: Sample Rating GridATWO-ASSET PORTFOLIO WITH TWO-FACTOR MODELSSimulation of Two Exponentially Distributed Dependent Times to DefaultCommodities FinanceSensitivityPORTFOLIO RETURN RISK AND CORRELATIONEquity ExposuresCAPITAL CALCULATIONCalculating Marginal Default ProbabilitiesBASKET SWAPS, FIRST-TO-DEFAULT, N-TO-DEFAULTORTHOGONAL MULTIPLE FACTOR MODELS AND PCAINTERNAL CREDIT RATINGS AND BUSINESS RULESThe Cholesky Decomposition Method: Two VariablesCOUNTERPARTY CREDIT RISKAsset Distribution and Default ProbabilityCorrelation and Concentration RisksOptionsTypes of HedgesLoss Distributions, Potential Losses and VaRSIMULATIONSFinancial Assets and Liabilities at Fair Value through Profit or LossMARGINAL RISK CONTRIBUTION AND SIZE OF AN EXISTING EXPOSUREThe Limit DistributionRevaluation of Facilities at HorizonJudgmental Ratings versus "Rating Models"The Generalized Wiener ProcessTHE VAR METHODOLOGY: MARKET RISKINTEREST RATES AND TERM STRUCTUREAPPENDIX:THE TAYLOR EXPANSION FORMULARISK-ADJUSTED PERFORMANCE AND MISPRICING REPORTSMAPPING SCORING MODELS TO A MASTER SCALE OF DEFAULT PROBABILITIESHedging Implicit Options to Renegotiate Fixed RatesRISK-BASED PERFORMANCE, PRICING AND CAPITAL ALLOCATIONPortfolio SimulationsFINANCIAL RISKSCredit Portfolio ManagementHistorical VaR: Forward Contract ExampleTHE CONTRIBUTIONS OF VAR-BASED MEASURESBACK TESTINGLimits and "Nil at Risk"Section 6. RegulationsCREDIT VAR AND MATRIX VALUATIONPORTFOLIO DELTA-NORMAL VARPortfolio Concentration and Correlation RiskProject FinanceMANAGING GAPS: SETTING UP LIMITSA Simple Example of a Forward ContractHedging Credit RiskReplicating a Forward LoanMISMATCH RISKPortfolio Systematic Risk: Two-factor ModelsSensitivityPayoff of Interest Rate OptionsProvisioningAPPENDIX: MATRIX NOTATIONS AND FORMULASLines without MaturityASSESSING THE RISK OF ASSET-BACKED NOTESRANDOM VARIABLES AND PROBABILITY DISTRIBUTION FUNCTIONSSPECIALIZED LENDINGValuation in Discrete Time and the Rationale of DiscountingMARKET RISKBASIC POSTULATES OF THIS TEXTTHE THIRD EDITIONORIGINATION AND POST-ORIGINATION FOLLOW UPIncome-producing Real EstateThe Asset Value and Default Probability Conditional on the State of the EconomyOPTIONAL RISK AND OPTIONAL GAPSLiquidity Crises and Stress Test ScenariosPRINCIPLES OF SAMPLE SIMULATIONSRisks and Risk ManagementIntermediate Flows and NIL CalculationsConditional ProbabilitiesBUILDING BLOCKS OF THE INTERNAL CREDIT RATING SYSTEMMark-ups and Mark-downs over Reference RatesThe Securitization OrganizationAllocating Income through the FTP SystemEconomic Value of the Balance SheetRisk Management Organization and Central FunctionsDEFINITION OF COPULA FUNCTIONSBonds and LoansDirect Effects or "Factor-push" TechniquesDealing with Different Default Probabilities and Discrepancies of ExposuresVariance-Covariance Matrix and Correlation MatrixPRINCIPAL COMPONENT ANALYSIS AND THE TERM STRUCTURE OF INTEREST RATESBanking Regulations: The Basel 2 AccordSecuritization and Capital ManagementInterest Rate SwapsINTEREST RATE SIMULATIONS WITH PCAExpanded RaRoC FormulaSIMULATION OF JOINT DEFAULTS AND MIGRATIONSPayoffs of the Option under Differed ExerciseThe Retail PortfolioExample: Option ContractCredit Portfolio View Conceptual FrameworkCONSTRUCTING A RISK-FREE PORTFOLIOOPTIONSVariance Formula and Correlation MatrixFrom Portfolio Risk to Individual FacilitiesFrom Discrete to Continuous ReturnsAPPENDIX: CONDITIONING, EXPECTATION AND VARIANCEContinuous VariablesNORMATIVE CAPITAL ALLOCATIONS AND CAPITAL EFFECTIVE UTILIZATIONSECONOMICS OF SECURITIZATION FORTHE BANKFOREIGN EXCHANGE RATES AND FORWARD CONTRACTSVALUATION OF AN OPTION UNDER RISK-NEUTRAL PROBABILITIESMarginal Risk ContributionsMatrix Notations Hypothetical Scenarios, Stress-tests and Extreme VaRRating SystemsOption-adjusted SpreadBOOK STRUCTUREINDICATOR FUNCTIONLoss DistributionProjected Net Interest IncomeJOINT DEFAULT PROBABILITY USING DISCRETE VARIABLESThe Payoff of Option ContractsMaterializationIMPLEMENTING THE EDF© MODELThe Current Value of the Prepayment OptionExpected Return on Assets and Compensations to InvestorsVarious Forms of Bivariate Copula FunctionsConditional ProbabilitiesSecuritizations: TraditionalCOMMERCIAL SPREADS AND MATURITY SPREADREMINDERS AND NOTATIONSALM SCOPE AND STRUCTURE OF THE SECTIONCOMPARISONS OF CLASSIFICATIONS: RISK REGULATIONS AND IFRSContinuous Returns and VarianceSOVEREIGN RISK CREDIT DERIVATIVESBreaking Down the Bank Margin into Contributions of Business UnitsINITIAL RECOGNITION OF FINANCIAL ASSETS AND LIABILITIESVALIDATIONBanking and Financial ProductsPortfolio OptimizationEXTENSIONS OF THE MARKET VAR METHODOLOGYOptional Risk and HedgingIRB ApproachesThe "Three Lines of Defense" PrincipleExceptional LossesGENERAL PROPERTIES OF RISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONSInterest Rate Gap and Liquidity GapsExtension to any Number of VariablesRisk Contributions to Portfolio Loss VolatilityOff Balance Sheet ItemsSIMULATIONS OF TIMES TO DEFAULTTHE VARIANCE-COVARIANCE MATRIXForward and Spot Rates: No ArbitrageMODELING DEFAULTS IN A UNIFORM PORTFOLIO:THE LIMIT DISTRIBUTIONUNCERTAINTY, RISK,AND EXPOSURETO RISKOption PricingPayments under a Credit EventECONOMIC VALUE, DURATION AND CONVEXITYSIMULATIONS AND INVERSE FUNCTIONSLogarithmic ReturnsPILLAR 2: SUPERVISORY REVIEW PROCESSTHE VALUE OF IMPLICIT OPTIONSIto LemmaEconomic Income StatementsDEFINITION OF INTEREST RATE GAPSAnalysis of a Securitization Transaction (Case Study)CapitalThe Valuation of American OptionsCREDIT PORTFOLIO VIEW: ECONOMETRIC MODELSTHE PRICE OF RISK AND ARBITRAGESteps for Determining VaRRisk-based PerformanceCredit EventsMismatch RiskSAMPLE CALCULATIONS OF RISK CONTRIBUTIONSPORTFOLIO LOSS DISTRIBUTIONVolatility PreservationTwo-asset Portfolio and Two Orthogonal FactorsStructuring of NotesAmortizing LoansThe Copula Density FunctionLiquidity Management and Liquidity GapsSection 9. Dependencies and Portfolio RiskMapping and AllocationCOLLATERALIZED SECURITIES LENDING/BORROWINGGeneralization to Several VariablesDelta-normal VaRDEFAULT PROBABILITY OF A FIRM DEPENDENT ON THE STATE OF THE ECONOMYINTEREST RATE OPTIONS: CAPS AND FLOORSTHE EXAMPLE OF A FORWARD FOREIGN EXCHANGE RATEAPPLICATIONS OF CREDIT DERIVATIVESINTEREST RATE RISKINTEREST RATE RISKSecuritizations: SyntheticTHE VASICEK MODELSection 8. Funds Transfer Pricing SystemsTwo Random Normal VariablesTHE EXPONENTIAL DISTRIBUTION AND TIME TO DEFAULTNon-linear Relationship between Selected Attributes and Credit StateAPPLICATION TO LOSS DISTRIBUTIONS AND LOSS PERCENTILESFunds Transfer Pricing SystemsAsset Value and Market Required ReturnThe "Model Divide"The Global Calibration of the Binomial TreeExposure at Default (EAD)Buying Protection for the Portfolio and Selling ProtectionAPPENDIX: RATING SCALES OF RATING AGENCIESRISK OF A TWO-STOCK PORTFOLIO WITH THE ONE-FACTOR MODELThe Sensitivity of Nil and Interest Rate GapSample Bank Balance SheetCredit Portfolio ModelsDetermining the Percentile of the Final Asset ValueHistorical and Hypothetical SimulationsExchanging Net Balances of Funds between UnitsExposure RiskTHE ACCORD FOR MARKET RISKIDENTITY BETWEEN EV AND "ALL-IN" CASH FLOWS (CAPITAL AND INTEREST)Specific CasesThe Generic Form of Multiple-factor ModelsMIGRATIONS AND VAR UNDERTHE STRUCTURAL MODELPORTFOLIO OF TWO OBLIGORSThe Basic Mechanism of LimitsSpot and Forward PricesEssentials on Derivative ProductsDependency and Joint Migration ProbabilitiesRisk Oversight: Banks' ChallengesRetail Portfolio: Further Differentiation for Capital TreatmentINVERSE FUNCTIONSCREDIT RISK FOR DERIVATIVES: METHODOLOGYVALUATION UNDER UNCERTAINTYStandalone Expected Loss and Portfolio Expected LossIMPLEMENTING THE STRUCTURAL MODEL OF DEFAULTECONOMIC VALUE AND NET INTEREST INCOME FOR A BANK WITHOUT CAPITALA Single Obligor Dependent on the State of the EconomyDetermination of the Default ProbabilityHedging and Speculating with Forward ContractsStochastic ProcessesConditional Distributions and CopulaLoans and ReceivablesTRADING CREDIT RISKSIMULATION OF TWO DEPENDENT NORMAL STANDARD VARIABLESFrom Future Values to Current CapitalTHE POISSON DISTRIBUTIONInterest Rate GapsFull Monte Carlo SimulationsCapital RequirementsRetail PortfolioDeriving the Copula Density from Copula FunctionHEDGING A CORPORATE LONG EXPOSURE IN FOREIGN CURRENCY (CASE STUDY)DEFINITIONS OF RISK CONTRIBUTIONSSection 5. Risk ModelingHOW FIRMS DEFAULTFORWARD RATES: DEFINITIONSTHE RATIONALE FOR CREDIT PORTFOLIO MANAGEMENTRisk RegulationsHEDGING INTEREST RATE RISK BY CORPORATE BORROWER (CASE STUDY)STRUCTURAL EXCESSES OF LIQUIDITYEconomie Value and NiL: General ExampleDerivation of the Normal Copula DensityStochastic CalculusSECURITIZATIONSHistorical Volatility with Equally Weighted ObservationsPayoff of a Forward ContractTHE ALM FUNCTIONCREDIT RISK COMPONENTSCALCULATING INCOME WITHIN A FTP SYSTEMFROM PORTFOLIO VALUE DISTRIBUTION TO CREDIT CAPITALReverting to Better Risk Practices and Lessons of the CrisisEnhancing the Bank's Return on Capital through SecuritizationMigration Matrices and Cumulative Default ProbabilitiesEconomic Capital and Credit Risk VaRGeneration of Portfolio Value DistributionPortfolio Return VolatilityBack Tests, Benchmarks and Stress Tests Market Risk and Trading ActivitiesValue PreservationPayment TermsCOMMON STOCHASTIC PROCESSESThe Cost of Credit Risk and the Risk PremiumNature of Borrower or Low Value of Individual ExposuresSection 1. The Financial CrisisThe Case of FloatersRISK OVERSIGHT CHALLENGESConceptual FrameworkVaR at Different HorizonsDecomposition of the Forward as a Linear Function of Elementary PositionsValuation and LeverageOff Balance Sheet CommitmentsDefinition of Interest Rate SwapAccounting StandardsExample of Calculations of the Forward Yield CurvesSimulation AlgorithmThe Normal Standard Copula Density and the Joint Density of Two VariablesStock Price Dynamics under Risk-neutral ProbabilitiesIndirect Effects and Factor-push ScenariosEffective Maturity (M)Compounding Continuous ReturnsCREDIT RATINGS AND LINKS BETWEEN COUNTERPARTIESMARKET INSTRUMENTS AND POTENTIAL FUTURE EXPOSURES (PFES)PORTFOLIO OF TWO INDEPENDENT OBLIGORSThe Two-asset Portfolio ReturnFORWARD VALUATION AND EXCESS SPREADSThe Variance-Covariance Matrix of Portfolio ReturnThe Loss DistributionCredit Event DependenciesThe "Notional" Funding of LoansScope and Goals of this TextThe Uniform Granular PortfolioCredit Risk Valuation and Credit SpreadsProbability of Default (DP) and Default EventSection 2. Business Lines, Risks, and Risk ManagementLOGIT MODELSApplication: Simulating Two Uniform Standard Variables with Conditional CopulaRISK FOR A SINGLE ASSET AND TWO-FACTOR MODELSSources of ConvexityOptions Allow Hedging RisksBUSINESS POLES IN THE BANKING INDUSTRYTHE ECONOMICS OF SCORING SYSTEMSFORWARD DEFAULT AND SURVIVAL PROBABILITIESCredit Events and Credit State at HorizonSingle PeriodPORTFOLIO RISK WITH MULTIPLE-FACTOR MODELSSimulation of Time to Default for a Single ObligorFrom Daily Volatility of the Position to Daily VaRGeneration of Portfolio Value DistributionLending, Borrowing and the Term Structure of Interest RatesCapital Under Default ModeTRANSFERRING LIQUIDITY AND INTEREST RATE RISK TO ALM THROUGH THE FTP SYSTEMMAPPING RATINGS TO DEFAULT PROBABILITIESTransaction Versus Client Revenues and PricingVisual Representation of the Diversification EffectPortfolio Total Risk and Two-factor ModelOTHER ARBITRAGE BETWEEN ECONOMIC PRICES AND RATING-BASED PRICESMANAGEMENT PRACTICES DIFFER ACROSS AND WITHIN BUSINESS LINESLIQUIDITY CONTAGIONExpected LossAPPENDIX: MATRIX DIAGONALIZATIONCapital UtilizationsCOMPARISON OF THE DEPENDENT AND THE INDEPENDENT CASESAPPENDIX: CALCULATION OF STANDARD DEVIATION FROM TIME SERIESProjected GapsRisk Contributions, Portfolio Loss Volatility and CapitalSPECIFICS OF STOCHASTIC PROCESSES AND ITO LEMMAThe Benefits from the Mirror DebtVanance-Covanance Matrices of Asset Returns and of FactorsTHE SUB-PRIME CRISISThe Effect of DiversificationThe One-factor ModelCredit Risk in the Trading PortfolioDistribution FunctionsVALUATION OF RISKY DEBT FROM CREDIT SPREADS AND RISK-NEUTRAL PROBABILITIESThe Underlying AssetsThe Independence CaseCorrelations and CovariancesInterpolation of Interest Rate from Selected Risk FactorsAPPLICATION: STOCK VALUE DISTRIBUTIONValuation of a Forward Contract or FRAThe Two-factor Model Applied to a Two-asset PortfolioThe Option Approach to Defaults and MigrationsFixed and Variable RatesCountry RiskSECTION ORGANIZATIONThe Pricing Paradox with Marginal Risk ContributionsDefinitionOPTIONAL RISKIMPAIRMENT OF FINANCIAL ASSETSRisk-neutral ProbabilityFORWARD CONTRACTS VERSUS OPTIONSCorporate Sample Rating GridDealing with Multiple DimensionsConstructing Attributes from Observed CharacteristicsNumerical SensitivitiesAPPENDIX 3: PORTFOLIO ANALYSIS AND REPORTING ISSUESThe "Rare Event" ProcessThe Original LoanPOSITIONING OF THE TEXTMODELING DEFAULT PROBABILITY AND CREDIT STANDING AT HORIZONApplications for Credit Portfolio ManagementRegulatory Risk Weights for Corporates, Sovereigns and BanksSIMULATION OF TWO DEPENDENT TIMES TO DEFAULTBANKS'FINANCIAL STATEMENTSThe Market Value of LoanVOLATILITYCredit Risk Mitigation: Collateral TreatmentSample Gap ReportsENTERPRISE-WIDE RISK MANAGEMENT (ERM)StocksRisk Management versus Risk InstrumentsConditional and Joint ProbabilitiesTHE STUDENT DISTRIBUTIONThe Reference Capital for Risk ContributionsSIMULATION OF CORRELATED NORMAL VARIABLES WITH FACTOR MODELSRETAIL PORTFOLIO IN BASEL 2STOCHASTIC PROCESSESTHE OPTION THEORETIC FRAMEWORK OF VALUATION OF EQUITY AND DEBTStandardized ApproachHEDGING BUSINESS RISK AND INTEREST RATE RISKNormative Risk Allocations Versus Capital UtilizationsFOREIGN EXCHANGE OPTIONSMARKET LIQUIDITY RISKHeld-to-maturity Financial AssetsThe Accounting N11 of the BankFinancial ApplicationsCREDIT METRICSRisk-adjusted Performance versus Risk-based PricingBIVARIATE NORMAL STANDARD DISTRIBUTIONSThe Portfolio Loss VolatilityPortfolio DataThe Waterfalls of Cash Flows and LossesVOLATILITY AND DELTA-NORMAL VAR OF THE FORWARD VALUESection 7. Asset Liability Management (ALM)CONTAGION THROUGH RATING DOWNGRADESRisk-based PricingPortfolio Risk Return ProfileLarge Number of ExposuresMapping Interest Rates to Selected Risk FactorsVAR AND ECONOMIC CAPITALRisk Oversight: Regulators' ChallengesExchanging all Outstanding BalancesMIGRATION MATRICESUnderlying of OptionsEarnings Allocation and Fund Transfer Pricing (FTP) SystemRisk-based Pricing and Marginal Risk Contribution to CapitalDEPENDENCIES MODELING ASA KEY BUILDING BLOCK FOR RISK MODELINGTwo-asset Portfolio and Two-factor Model: Specific RiskLIQUIDITY GAP TIME PROFILESComparing Continuous and Discrete ReturnsLiquid AssetsECONOMICS OF SECURITIZATIONSImprove Tools for Managing Financial CrisesSimulation of Interest RatesSOLVENCY RISKRISK-NEUTRAL VALUATION:THE CASE OF A STOCK PRICEISSUES FOR DETERMINING THE LIQUIDITY GAP TIME PROFILERECOVERY STATISTICSExpectationsRisk-based Capital RegulationsDefinitionsCORRELATIONS AND COVARIANCESThe Distribution of Firm ValueApplication of Cholesky DecompositionExposures, Default Probability and Loss Given DefaultModeling RecoveriesHEDGING THE VARIATIONS OF THE TERM STRUCTURE OF INTEREST RATES (CASE STUDY)Default Probability and Default IntensitySOME IMPLICATIONSForeign Exchange Swaps"Effectiveness" of HedgeHORIZON FOR CREDIT CAPITALHedging both Interest Rate and Business RisksRecovery RiskTHE GAP MODELBasel I DrawbacksLoss Given Default (LGD)PORTFOLIO OVERVIEWDiscrete VariablesCommercial SpreadsUsages of Risk Contributions and of Marginal Risk ContributionsUsing PCA for Single AssetsCREDIT SPREAD, IMPLIED DEFAULT INTENSITY AND RECOVERY RATETHE DISCOUNTED CASH FLOW MODELModeling Potential Variations of ValueNumber of Default Events over a Given HorizonLimits and DelegationsCapital AllocationBank ExposuresMeasure of ConvexityCONTAGION AND PROCYCLICALITYTHROUGH FAIR VALUE RULESCREDITRISK+AND ANALYTICAL DISTRIBUTIONSADDITIONAL PROPOSALSAvailable-for-sale Financial AssetsThe Hurdle Rate and the Cost of CapitalUnexpected Loss and VaRSUPPORTVariance-Covariance Matrix of Portfolio ReturnsTranches are Subject to Correlation RiskRISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONS TO PORTFOLIO LOSS VOLATILITY AND TO CAPITALTHE NEW BASEL ACCORDSAMPLE COMPARISON BETWEEN BASEL I AND BASEL 2 CAPITAL FOR CORPORATE ASSET CLASS CREDIT RISKExposure and Capital Allocation or Loss VolatilityAPPENDIX: CALCULATION OF ABSOLUTE RISK CONTRIBUTIONS FROM THE VARIANCE-COVARIANCE MATRIXPortfolio Systematic Risk Decomposition into Additive ItemsCredit Risk Mitigation under Basel 2Options as Volatility InstrumentsSection 12. Credit Portfolio RiskThe Bivariate Normal CopulaThe Binomial Tree for Interest RateECONOMIC TRANSFER PRICES FOR RESOURCESRaise International Regulatory Standards and Improve International CooperationThe Standardized ApproachForms of the Gaussian CopulaReplicating a Forward Exchange RateBINOMIAL DISTRIBUTION OF SUM OF BERNOULLI VARIABLESRisk and Return of Option ContractsMatrix Methodology and The Risk-Return Profile of the Balance SheetThe Annualized All-in Cost of Financing through SecuritizationObject FinanceAsset Swaps: GeneralizationMARGINAL RISK CONTRIBUTIONS TO VOLATILITY VERSUS RISK CONTRIBUTIONSAnnual Default RatesCredit Risk and Lending ActivitiesEconomic Value and Convexity RiskCorrelation and Volatility of a Sum of Random VariablesThe Simulation AlgorithmThe "Basic" Linear Model DrawbacksThe Stock Price ProcessCONTAGION THROUGH SECURITIZATIONSJoint Probability Density Functions with Two VariablesNORMAL DISTRIBUTIONALM APPLICATIONSMEASURES OF POTENTIAL LOSSESRISK-ADJUSTED MEASURES OF PERFORMANCEStatistical and Scoring ModelsALM GOALSKEY BENEFITS OF COPULA DEPENDENCYMAXIMUM LIKELIHOOD METHODOLOGYDISCRETE AND CONTINUOUS RETURNSWHERE DO INTEREST RATES COME FROM?Rating Methodologies for Structured NotesSENSITIVITIES AND RISK CONTROLLINGINTEREST RATE SWAPS (IRS)THE ORGANIZATION OF FTP SYSTEMSTraceability of Aggregated Measures and Risk ManagementTrading Credit RiskCONTAGION AND PROCYCLICALITY IN A LEVERAGED INDUSTRYPortfolio AnalysisThe Matrices of Net Interest IncomeDerivatives and Credit RiskTop-down and Bottom-up Risk Management Processes and SystemsOPERATIONAL RISKCredit DerivativesForeign Exchange Risk and Foreign Exchange DerivativesSCORINGProprietary Models of Market Risk VaRCredit Events and Credit State at HorizonSECURITIZATIONSMigration RiskForward Contracts and Interest Rate SwapsTHE STANDARDIZED APPROACHSingle Period Discrete ReturnRAROC CALCULATIONSThe Cost of Financing through SecuritizationCredit Conversion Factors (CCFs)Multiple Business and Interest Rate ScenariosBERNOULLI VARIABLEMODELING PREPAYMENTSMethod of Determining Fair ValueStandalone Loss Volatilities and Portfolio Loss VolatilityThe 2007-2008 Financial CrisisCustomizing Credit RiskProperties of Copula FunctionsREGULATIONSEconomic Value and Convexity GapsPreemptive Risk Control versus Risk InsuranceSimulations with Factor Models or the Copula ApproachEvolution of Credit Risk ModelsSENSITIVITY DEFINITIONSLIQUIDITY SCENARIOSMAIN SPECIFICS AND KEYTERMSFrom Risk Contributions to Capital AllocationCredit Portfolio Models and SecuritizationsCalculation of Joint Default and Conditional ProbabilitiesThe Pricing of Assets Sold to the SPESIMULATION OF DEPENDENT VARIABLES WITH THE COPULA APPROACHLOSS DISTRIBUTIONSThe Bivariate Copula Function: Expanded FormVARIATIONS ON THE MERTON'S MODELLoss StatisticsEARNINGS-AT-RISK ("EAR")HEDGING: CLOSING INTEREST RATE GAPSRevaluation of Facilities at HorizonControlling Duration with DerivativesTRANSITION MATRICESConceptual FrameworkCapital and Risk Allocation SystemCOMMON SENSITIVITIESTHE SIMPLE "BINOMIALTREE" TECHNIQUE APPLIED TO INTEREST RATESBANKING REGULATIONS AND ACCOUNTING STANDARDSCAPITAL ADEQUACYThe All-in Cost of Funding through SecuritizationCREDIT PORTFOLIO MODEL OVERVIEWExpected LossVALUATION RULESThe Multiple SimulationsFOREIGN EXCHANGE RISKContinuous TimeECONOMIC TRANSFER PRICES FOR LOANSInterpretation of Basel 2 Formulas for Risk WeightsSellers of OptionsEffective LGD for Collateral-based TransactionsMathematical SensitivitiesMONTE CARLO SIMULATIONSEconomic and Commercial Transfer PricesHISTORICAL SIMULATIONSMARGINAL RISK CONTRIBUTIONS TO CAPITALSeparating All-in Flows into Capital and Interest FlowsBanking Regulations: Basel I and Market RiskREGULATORY ISSUESStress Testing and What-if AnalysesApplication: Finding the Factor Value Matching a Given Portfolio Loss PercentileOn Balance SheetAbout the AuthorEmbedded Options in Banking ProductsImplementing the Matrix ApproachContingencies Given (Off-balance Sheet)
 
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