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Risk management in banking

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About the Author BASIC POSTULATES OF THIS TEXT The Financial Crisis Scope and Goals of this Text POSITIONING OF THE TEXT The "Model Divide"Risk Management versus Risk Instruments Reverting to Better Risk Practices and Lessons of the Crisis BOOK STRUCTURE THE THIRD EDITION Section 1. The Financial Crisis The 2007-2008 Financial Crisis THE SUB-PRIME CRISIS CLASSICAL CONTAGION MECHANISMS FINANCIAL RISKS REGULATIONS Risk Regulations Accounting Standards CONTAGION THROUGH SECURITIZATIONS LIQUIDITY CONTAGION CONTAGION AND PROCYCLICALITYTHROUGH FAIR VALUE RULES CONTAGION THROUGH RATING DOWNGRADES CONTAGION AND PROCYCLICALITY IN A LEVERAGED INDUSTRY SOME IMPLICATIONS Section 2. Business Lines, Risks, and Risk Management Banking Business Lines BUSINESS POLES IN THE BANKING INDUSTRY MANAGEMENT PRACTICES DIFFER ACROSS AND WITHIN BUSINESS LINES BANKING REGULATIONS AND ACCOUNTING STANDARDS Risks and Risk Management UNCERTAINTY, RISK,AND EXPOSURETO RISK TYPES OF RISKS CREDIT RISK Default Risk Migration Risk Exposure Risk Counterparty Risk of Derivatives Recovery Risk Correlation and Concentration Risks Credit Risk in the Trading Portfolio Spread Risk Country Risk LIQUIDITY RISK: FUNDING INTEREST RATE RISK MISMATCH RISK MARKET LIQUIDITY RISK MARKET RISK FOREIGN EXCHANGE RISK SOLVENCY RISK OPERATIONAL RISK Risk Management RISK OVERSIGHT CHALLENGES Motivations for Risk Oversight Risk Oversight: Banks' Challenges Risk Oversight: Regulators' Challenges RISK MANAGEMENT PROCESSES The "Three Lines of Defense" Principle Risk Management Organization and Central Functions Limits and Delegations SETTING-UP LIMITS Credit Risk and Lending Activities Market Risk and Trading Activities Asset-liability Management (ALM)ENTERPRISE-WIDE RISK MANAGEMENT (ERM)Top-down and Bottom-up Risk Management Processes and Systems Earnings Allocation and Fund Transfer Pricing (FTP) System Capital and Risk Allocation System Section 3. Financial Products Banking and Financial Products CLASSIFICATION OF LENDING PRODUCTS AND BASEL 2 CRITERIA SOVEREIGN, BANK, AND EQUITY EXPOSURES Bank Exposures Sovereign Exposures Equity Exposures RETAIL PORTFOLIO IN BASEL 2 Nature of Borrower or Low Value of Individual Exposures Large Number of Exposures Retail Portfolio: Further Differentiation for Capital Treatment TRANSACTION-SPECIFIC CREDIT RISK Credit Risk Mitigants Credit Risk Mitigation under Basel 2 SECURITY LENDING AND BORROWING SPECIALIZED LENDING Project Finance Object Finance Commodities Finance Income-producing Real Estate High-volatility Commercial Real Estate SECURITIZATIONS Securitizations: Traditional Securitizations: Synthetic OFF-BALANCE SHEET ITEMS Essentials on Derivative Products ASSETS AND POSITIONS DERIVATIVES: BASIC DEFINITIONS AND PRINCIPLES FORWARD CONTRACTS A Simple Example of a Forward Contract Spot and Forward Prices Hedging and Speculating with Forward Contracts Payoff of a Forward Contract FORWARD CONTRACTS VERSUS OPTIONS OPTIONS Options Allow Hedging Risks The Payoff of Option Contracts Sellers of Options Risk and Return of Option Contracts Option Pricing Underlying of Options Interest Rate Risk and Interest. Rate Derivatives INTEREST RATE RISK FOR BORROWERS AND LENDERS INTEREST RATES AND TERM STRUCTURE Lending, Borrowing and the Term Structure of Interest Rates Fixed and Variable Rates FORWARD RATES: DEFINITIONS Replicating a Forward Loan Forward and Spot Rates: No Arbitrage Example of Calculations of the Forward Yield Curves Usages of Forward Rate Contracts Valuation of a Forward Contract or FRA INTEREST RATE SWAPS (IRS)Definition of Interest Rate Swap Replicating an Interest Rate Swap Asset Swaps: Generalization Mark-to-market Value of an IRS Derivatives and P & L INTEREST RATE OPTIONS: CAPS AND FLOORS Payoff of Interest Rate Options Collar Options as Volatility Instruments HEDGING INTEREST RATE RISK BY CORPORATE BORROWER (CASE STUDY)WHERE DO INTEREST RATES COME FROM?Foreign Exchange Risk and Foreign Exchange Derivatives FOREIGN EXCHANGE RATES AND FORWARD CONTRACTS Replicating a Forward Exchange Rate Mark-to-market Valuation of Forward Contracts FOREIGN EXCHANGE OPTIONS HEDGING A CORPORATE LONG EXPOSURE IN FOREIGN CURRENCY (CASE STUDY)THE FOREIGN EXCHANGE MARKET AND RATES Credit Derivatives DEFINITIONS OF CREDIT DERIVATIVES CREDIT DEFAULT SWAPS (CDS)TOTAL RETURN SWAPS CREDIT SPREAD PRODUCTS BASKET SWAPS, FIRST-TO-DEFAULT, N-TO-DEFAULT SOVEREIGN RISK CREDIT DERIVATIVES MAIN SPECIFICS AND KEYTERMS The Underlying Assets Payment Terms Legal Issues Payments under a Credit Event Credit Events Materialization PRICING CREDIT DERIVATIVES Section 4. Valuation Distribution Functions RANDOM VARIABLES AND PROBABILITY DISTRIBUTION FUNCTIONS Discrete Variables Continuous Variables INVERSE FUNCTIONS THE MOMENTS OF A DISTRIBUTION Expectations Variance and Volatility UNIFORM DISTRIBUTION APPLICATION TO LOSS DISTRIBUTIONS AND LOSS PERCENTILES BERNOULLI VARIABLE INDICATOR FUNCTION BERNOULLI DISTRIBUTION BINOMIAL DISTRIBUTION OF SUM OF BERNOULLI VARIABLES NORMAL DISTRIBUTION LOGNORMAL DISTRIBUTION THE POISSON DISTRIBUTION Definition Financial Applications Number of Default Events over a Given Horizon THE EXPONENTIAL DISTRIBUTION AND TIME TO DEFAULT THE BETA DISTRIBUTION THE STUDENT DISTRIBUTION A SUMMARY APPENDIX: CALCULATION OF STANDARD DEVIATION FROM TIME SERIES Discrete and Continuous Returns DISCRETE AND CONTINUOUS RETURNS Single Period Discrete Return Compounding Discrete Returns over Multiple Periods From Discrete to Continuous Returns Logarithmic Returns Compounding Continuous Returns Comparing Continuous and Discrete Returns THE DISCOUNTED CASH FLOW MODEL Valuation in Discrete Time and the Rationale of Discounting The Case of Floaters Continuous Time Asset Value and Market Required Return Yield-to-Maturity and Zero-coupon Rates VALUATION UNDER UNCERTAINTY APPENDIX:THE TAYLOR EXPANSION FORMULA Stochastic Processes STOCHASTIC PROCESSES COMMON STOCHASTIC PROCESSES The Wiener Process Application: The Square Root of Time Rule for the Simple Wiener Process The Generalized Wiener Process The Ito Process The Stock Price Process The Mean Reverting Process The "Rare Event" Process APPLICATION: STOCK VALUE DISTRIBUTION INTEREST RATE PROCESSES SPECIFICS OF STOCHASTIC PROCESSES AND ITO LEMMA Deterministic Calculus Stochastic Calculus Ito Lemma Example: Stock Price Distribution Valuation and Pricing Risk CONSTRUCTING A RISK-FREE PORTFOLIO How to Form Risk-free Portfolios How to Derive the Pricing PDE How to Solve Numerically a PDE RISK-NEUTRAL VALUATION:THE CASE OF A STOCK PRICE Risk-neutral Probability Stock Price Dynamics under Risk-neutral Probabilities VALUATION: END RESULTS Some Applications of Valuation Techniques VALUATION OF RISKY DEBT FROM CREDIT SPREADS AND RISK-NEUTRAL PROBABILITIES VALUATION OF AN OPTION UNDER RISK-NEUTRAL PROBABILITIES THE VASICEK MODEL Section 5. Risk Modeling Sensitivity SENSITIVITY DEFINITIONS COMMON SENSITIVITIES Stocks Bonds and Loans Options Forward Contracts and Interest Rate Swaps SENSITIVITY AND RISK FACTORS SENSITIVITIES AND RISK CONTROLLING Volatility VOLATILITY EQUALLY WEIGHTED HISTORICAL VOLATILITY Continuous Returns and Variance Historical Volatility with Equally Weighted Observations EXPONENTIALLY WEIGHTED MOVING AVERAGE (EWMA) MODEL GARCH MODELS MAXIMUM LIKELIHOOD METHODOLOGY ESTIMATING EWMA VOLATILITY The Value-at-Risk Measure MODELING POTENTIAL VARIATIONS AND PERCENTILES Modeling Potential Variations of Value Value Percentile THE VAR METHODOLOGY: MARKET RISK Sensitivity From Sensitivity to Volatility From Daily Volatility of the Position to Daily VaR VaR at Different Horizons Summary and Extensions CREDIT RISK VAR The Firm Value The Distribution of Firm Value VaR and Capital THE CONTRIBUTIONS OF VAR-BASED MEASURES LOSS DISTRIBUTIONS MEASURES OF POTENTIAL LOSSES Expected Loss Loss Percentiles Unexpected Loss and VaR Exceptional Losses Loss Distributions, Potential Losses and VaR VAR AND ECONOMIC CAPITAL EARNINGS-AT-RISK ("EAR")Section 6. Regulations Banking Regulations: Basel I and Market Risk REGULATORY ISSUES THE DILEMMAS OF THE REGULATOR Regulation and Competition Preemptive Risk Control versus Risk Insurance CAPITAL ADEQUACY Risk-based Capital Regulations Capital Requirements Risk-based Capital and Growth THE "BASEL I ACCORD" FOR CREDIT RISK The Cooke Ratio and Credit Risk Derivatives and Credit Risk Basel I Drawbacks THE ACCORD FOR MARKET RISK The Standardized Approach Proprietary Models of Market Risk VaR Banking Regulations: The Basel 2 Accord THE NEW BASEL ACCORD ASSET CLASSES CREDIT RISK COMPONENTS Probability of Default (DP) and Default Event Exposure at Default (EAD)Loss Given Default (LGD)Credit Conversion Factors (CCFs)Credit Components and Risk Weights THE STANDARDIZED APPROACH Regulatory Risk Weights for Corporates, Sovereigns and Banks The Retail Portfolio Effective Maturity (M)Off Balance Sheet Items INTERNAL RATINGS BASED FRAMEWORK CREDIT RISK MITIGATION Credit Risk Mitigation: Guarantees and Credit Derivatives Credit Risk Mitigation: Collateral Treatment Collateral: Haircut Calculations Effective LGD for Collateral-based Transactions COUNTERPARTY CREDIT RISK CAPITAL CALCULATION Risk-Weighted Assets for Corporate, Sovereign, and Bank Exposures Interpretation of Basel 2 Formulas for Risk Weights Retail Portfolio Equity Exposures SAMPLE COMPARISON BETWEEN BASEL I AND BASEL 2 CAPITAL FOR CORPORATE ASSET CLASS CREDIT RISK SPECIALIZED LENDING SECURITIZATIONS Standardized Approach IRB Approaches INTEREST RATE RISK OPERATIONAL RISK PILLAR 2: SUPERVISORY REVIEW PROCESS PILLAR 3: MARKET DISCIPLINE ADDITIONAL PROPOSALS Accounting Standards BANKS'FINANCIAL STATEMENTS INITIAL RECOGNITION OF FINANCIAL ASSETS AND LIABILITIES Financial Assets and Liabilities at Fair Value through Profit or Loss Loans and Receivables Held-to-maturity Financial Assets Available-for-sale Financial Assets VALUATION RULES Amortized Cost Method of Determining Fair Value Instruments Traded in Active Markets Instruments Traded in Inactive Markets IMPAIRMENT OF FINANCIAL ASSETS HEDGE ACCOUNTING Types of Hedges "Effectiveness" of Hedge COMPARISONS OF CLASSIFICATIONS: RISK REGULATIONS AND IFRS Section 7. Asset Liability Management (ALM)ALM GOALS ALM SCOPE AND STRUCTURE OF THE SECTION THE ALM FUNCTION Liquidity Management and Liquidity Gaps LIQUIDITY DEFINITIONS LIQUIDITY GAP TIME PROFILES Three Basic Liquidity Positions Mismatch Risk LIQUIDITY GAP CALCULATIONS Static Liquidity Gaps Dynamic Liquidity Gaps How Gaps Change Through Time Fixed Assets and Equity LIQUIDITY MANAGEMENT Structuring Debt Maturities Numerical Example STRUCTURAL EXCESSES OF LIQUIDITY ISSUES FOR DETERMINING THE LIQUIDITY GAP TIME PROFILE Lines without Maturity Demand Deposits Contingencies Given (Off-balance Sheet)Amortizing Loans Multiple Scenarios LIQUIDITY SCENARIOS Liquid Assets Liquidity Crises and Stress Test Scenarios Interest Rate Gaps DEFINITION OF INTEREST RATE GAPS CALCULATIONS OF INTEREST RATE GAPS Interest Rate Gap and Liquidity Gaps Sample Gap Reports THE GAP MODEL NET INTEREST INCOME AND INTEREST RATE GAPS Projected Gaps Projected Net Interest Income Commercial Spreads The Sensitivity of Nil and Interest Rate Gap STATIC VERSUS DYNAMIC GAPS LIMITATIONS OF INTEREST RATE GAPS Embedded Options in Banking Products Lines without Maturity Mapping Interest Rates to Selected Risk Factors Regulated Rates Mark-ups and Mark-downs over Reference Rates Intermediate Flows and NIL Calculations FROM GAPS TO SIMULATIONS ALM and Hedging Policies MANAGING GAPS: SETTING UP LIMITS The Basic Mechanism of Limits Limits and "Nil at Risk"HEDGING: CLOSING INTEREST RATE GAPS Single Period Hedging Over Multiple Periods HEDGING THE VARIATIONS OF THE TERM STRUCTURE OF INTEREST RATES (CASE STUDY)HEDGING BUSINESS RISK AND INTEREST RATE RISK Multiple Business and Interest Rate Scenarios Matrix Methodology and The Risk-Return Profile of the Balance Sheet Implementing the Matrix Approach Hedging both Interest Rate and Business Risks The Matrices of Net Interest Income Implicit Options Risk OPTIONAL RISK Optional Risk is Always Adverse to the Bank Optional Risk and Hedging MODELING PREPAYMENTS PAYOFF OF PREPAYMENT THE VALUE OF IMPLICIT OPTIONS THE SIMPLE "BINOMIALTREE" TECHNIQUE APPLIED TO INTEREST RATES The Binomial Tree for Interest Rate Valuation of a Bond The Global Calibration of the Binomial Tree The Valuation of American Options The Current Value of the Prepayment Option The Original Loan Binomial Tree of Interest Rates The Market Value of Loan The Exercise Price and the Payoff of the Option Payoffs of the Option under Differed Exercise Option-adjusted Spread Economic Value of the Balance Sheet ECONOMIC VALUE (EV)ECONOMIC VALUE AND NET INTEREST INCOME FOR A BANK WITHOUT CAPITAL Sample Bank Balance Sheet EV and Projected Interest Income at Risk-free Rate NIL AND EV IDENTITY BETWEEN EV AND "ALL-IN" CASH FLOWS (CAPITAL AND INTEREST)Separating All-in Flows into Capital and Interest Flows Economie Value and NiL: General Example Economic Value and Convexity Risk DURATION PROPERTIES SENSITIVITY OF ECONOMIC VALUE AND DURATION GAPS Duration Gap Controlling Duration with Derivatives Duration Gap and Sensitivity of EV ECONOMIC VALUE, DURATION AND CONVEXITY Convexity Sources of Convexity Measure of Convexity Economic Value and Convexity Gaps CONVEXITY GAPS AND OPTIONS OPTIONAL RISK AND OPTIONAL GAPS Hedging Caps Sold to Clients Hedging Implicit Options to Renegotiate Fixed Rates Section 8. Funds Transfer Pricing Systems Funds Transfer Pricing Systems THE ORGANIZATION OF FTP SYSTEMS Exchanging Net Balances of Funds between Units Exchanging all Outstanding Balances CALCULATING INCOME WITHIN A FTP SYSTEM Allocating Income through the FTP System The Accounting N11 of the Bank Breaking Down the Bank Margin into Contributions of Business Units Economic Transfer Prices COMMERCIAL SPREADS AND MATURITY SPREAD ECONOMIC TRANSFER PRICES FOR LOANS The Cost of Existing Resources The "Notional" Funding of Loans The Cost of the Mirror Debt The Benefits from the Mirror Debt ECONOMIC TRANSFER PRICES FOR RESOURCES TRANSFERRING LIQUIDITY AND INTEREST RATE RISK TO ALM THROUGH THE FTP SYSTEM PRICING FOR LENDING The All-in Cost of Funds of the Mirror Debt The Cost of Credit Risk and the Risk Premium Transaction Versus Client Revenues and Pricing Economic and Commercial Transfer Prices Section 9. Dependencies and Portfolio Risk DEPENDENCIES MODELING ASA KEY BUILDING BLOCK FOR RISK MODELING MEASURES OF DEPENDENCIES SIMULATIONS SECTION ORGANIZATION Correlations and Covariances CORRELATIONS AND COVARIANCES Correlations, Variances, and Covariances Correlation and Volatility of a Sum of Random Variables Visual Representation of the Diversification Effect Extension to any Number of Variables THE VARIANCE-COVARIANCE MATRIX Matrix Notations Variance-Covariance Matrix of Portfolio Returns The Variance-Covariance Matrix of Portfolio Return Portfolio Return Volatility PORTFOLIO RETURN RISK AND CORRELATION APPENDIX: MATRIX NOTATIONS AND FORMULAS Transpose Matrix Variance-Covariance Matrix and Correlation Matrix Variance Formula and Correlation Matrix Conditional Probabilities DEFINITION OF CONDITIONAL AND JOINT PROBABILITIES Conditional Probabilities Conditional and Joint Probabilities DEFAULT PROBABILITY OF A FIRM DEPENDENT ON THE STATE OF THE ECONOMY THE TWO-OBLIGOR PORTFOLIO AND CONDITIONAL PROBABILITIES The Independence Case The Dependent Case APPENDIX: CONDITIONING, EXPECTATION AND VARIANCE Factor Models FACTOR MODELS THE GENERIC FORM OF FACTOR MODELS Example of a One-factor Model The Single-factor Model The Generic Form of Multiple-factor Models RISK OF A TWO-STOCK PORTFOLIO WITH THE ONE-FACTOR MODEL The One-factor Model The Vanance-Covanance Matrix Vanance-Covanance Matrices of Asset Returns and of Factors PORTFOLIO RISK WITH MULTIPLE-FACTOR MODELS RISK FOR A SINGLE ASSET AND TWO-FACTOR MODELS ATWO-ASSET PORTFOLIO WITH TWO-FACTOR MODELS The Two-factor Model Applied to a Two-asset Portfolio The Two-asset Portfolio Return Portfolio Systematic Risk: Two-factor Models Portfolio Systematic Risk Decomposition into Additive Items Two-asset Portfolio and Two-factor Model: Specific Risk Portfolio Total Risk and Two-factor Model ORTHOGONAL MULTIPLE FACTOR MODELS AND PCA Using PCA for Single Assets Two-asset Portfolio and Two Orthogonal Factors PORTFOLIO RISK: SUMMARY OF MATRIX FORMAT CALCULATIONS APPENDIX I:THE CONCEPTUAL FOUNDATIONS OF PCA APPENDIX 2: PORTFOLIO GENERAL RISK, ORTHOGONAL FACTORS Dependencies and Copula Functions KEY BENEFITS OF COPULA DEPENDENCY REMINDERS AND NOTATIONS DEFINITION OF COPULA FUNCTIONS Bivariate Copula Properties of Copula Functions Distribution Functions and Percentiles Various Forms of Bivariate Copula Functions The Bivariate Copula Function: Expanded Form The Copula Density Function Generalization to Several Variables BIVARIATE NORMAL STANDARD DISTRIBUTIONS Univariate and Bivariate Normal Distributions Bivariate Normal Standard Density The Bivariate Normal Copula Forms of the Gaussian Copula The Normal Standard Copula Density and the Joint Density of Two Variables CONDITIONAL PROBABILITY FROM THE COPULA DENSITY Conditional Density of Normal Bivariate Conditional Distributions and Simulations Application: Simulating Two Uniform Standard Variables with Conditional Copula APPENDIX: COPULA FUNCTION AND COPULA DENSITY Deriving the Copula Density from Copula Function Joint Probability Density Functions with Two Variables Derivation of the Normal Copula Density Joint Density of a Bivariate Normal Distribution and the Copula Density Function Conditional Distributions and Copula Simulations with Factor Models or the Copula Approach SIMULATIONS AND INVERSE FUNCTIONS SIMULATION OF CORRELATED NORMAL VARIABLES WITH FACTOR MODELS Standardizing the Single-factor Model The Simulation Algorithm for Standardized Normal Variables using Single-factor Models The Cholesky Decomposition Method: Two Variables Two Random Normal Variables Application of Cholesky Decomposition Classical Methodology: Summary SIMULATION OF DEPENDENT VARIABLES WITH THE COPULA APPROACH Main Principle Simulation Algorithm SIMULATION OF TWO DEPENDENT UNIFORM STANDARD VARIABLES SIMULATION OF TWO DEPENDENT NORMAL STANDARD VARIABLES SIMULATION OF TWO DEPENDENT TIMES TO DEFAULT Simulation of Time to Default for a Single Obligor Simulation of Two Exponentially Distributed Dependent Times to Default APPENDIX:THE CHOLESKY DECOMPOSITION METHOD Section 10. Market Risk Delta-normal VaR PORTFOLIO DELTA-NORMAL VAR Steps for Determining VaR A Simple Portfolio of Two Zero-coupon Bonds MAPPING AN INSTRUMENTTO RISK FACTORS Interpolation of Interest Rate from Selected Risk Factors Value Preservation Volatility Preservation Mapping and Allocation THE EXAMPLE OF A FORWARD FOREIGN EXCHANGE RATE THE CONCEPTUAL FRAMEWORK OF DELTA-NORMAL VAR Deriving Sensitivities Mathematical Sensitivities Numerical Sensitivities Decomposition of the Forward as a Linear Function of Elementary Positions VOLATILITY AND DELTA-NORMAL VAR OF THE FORWARD VALUE THE DELTA-VAR OF THE FORWARD CONTRACT: SUMMARY Historical and Hypothetical Simulations HISTORICAL SIMULATIONS Principles Historical VaR: Forward Contract Example MONTE CARLO SIMULATIONS Grid Simulations Full Monte Carlo Simulations Example: Option Contract EXTENSIONS OF THE MARKET VAR METHODOLOGY E-VaR or Expected Shortfall Hypothetical Scenarios, Stress-tests and Extreme VaR Simulation of Interest Rates INTEREST RATES AND FACTOR MODELS PRINCIPAL COMPONENT ANALYSIS AND THE TERM STRUCTURE OF INTEREST RATES INTEREST RATE SIMULATIONS WITH PCA APPLICATION TO MARKET VAR ALM APPLICATIONS Back Tests, Benchmarks and Stress Tests BACK TESTING BENCHMARKING STRESS TESTING, HYPOTHETICAL SCENARIOS AND SENSITIVITY ANALYSES Direct Effects or "Factor-push" Techniques Indirect Effects and Factor-push Scenarios VALIDATION Section 11. Credit Risk: Standalone Credit Risk Data DEFAULT STATISTICS Annual Default Rates Cumulative Default Rates RECOVERY STATISTICS TRANSITION MATRICES Rating Systems CREDIT RATINGS CREDIT RATINGS AND LINKS BETWEEN COUNTERPARTIES INTERNAL CREDIT RATINGS AND BUSINESS RULES BUILDING BLOCKS OF THE INTERNAL CREDIT RATING SYSTEM RATING GRIDS Judgmental Ratings versus "Rating Models"Corporate Sample Rating Grid Banks: Sample Rating Grid MAPPING RATINGS TO DEFAULT PROBABILITIES APPENDIX: RATING SCALES OF RATING AGENCIES Statistical and Scoring Models SCORING THE ECONOMICS OF SCORING SYSTEMS LOGIT MODELS The "Basic" Linear Model Drawbacks Logit Model Family SCORING IN RETAIL BANKING: BEHAVIORAL VERSUS ORIGINATION MODELS IMPLEMENTATION OF SCORING IN RETAIL BANKING Discriminating Variables Identification of Potentially Significant Attributes Non-linear Relationship between Selected Attributes and Credit State Constructing Attributes from Observed Characteristics Fitting and Back Testing Scoring Models ACCURACY OF SCORING MODELS:THE "CAP"MAPPING SCORING MODELS TO A MASTER SCALE OF DEFAULT PROBABILITIES The Option Approach to Defaults and Migrations HOW FIRMS DEFAULT THE OPTION THEORETIC FRAMEWORK OF VALUATION OF EQUITY AND DEBT IMPLEMENTING THE STRUCTURAL MODEL OF DEFAULT MODELING DEFAULT PROBABILITY AND CREDIT STANDING AT HORIZON IMPLEMENTING THE EDF© MODEL THEORETICAL VALUES OF THE OPTION TO DEFAULT ANDTHE EDF©Valuation of the Put Option to Default Determination of the Default Probability Determining the Percentile of the Final Asset Value SAMPLE CALCULATIONS OF EDF© AND OF THE PUT AND CALL VALUES VARIATIONS ON THE MERTON'S MODEL MAPPING DEFAULT PROBABILITY TO THE STANDARDIZED NORMAL DISTANCE TO DEFAULT Default Probability and Default Intensity CUMULATIVE DEFAULT AND SURVIVAL PROBABILITIES FORWARD DEFAULT AND SURVIVAL PROBABILITIES Basic Formulas Calculating Marginal Default Probabilities MIGRATION MATRICES Migration Matrices and Cumulative Default Probabilities Direct Calculation of Default Probability over Two Periods General Calculation of Default Probability over Two Periods Generator Matrices CREDIT INTENSITY MODELS Default Intensity Models Forward Default Intensity Time to Default APPENDIX: MATRIX DIAGONALIZATION Credit Risk Potential Exposure BANKING PORTFOLIO EXPOSURES On Balance Sheet Off Balance Sheet Commitments MARKET INSTRUMENTS AND POTENTIAL FUTURE EXPOSURES (PFES)Interest Rate Swaps Foreign Exchange Swaps Options REGULATORY ADD-ONS FOR DERIVATIVES CREDIT RISK FOR DERIVATIVES: METHODOLOGY CALCULATING THE PFE FOR AN INTEREST RATE SWAP CREDIT RISK EXPOSURE FOR PORTFOLIOS OF DERIVATIVES Modeling Recoveries COLLATERALIZED SECURITIES LENDING/BORROWING Economic Derivation of Minimum Over-collateralization Basel 2 Treatment of Collateralized Transactions VALUATION OF CREDIT RISK GUARANTEES, INSURANCE OR CREDIT DERIVATIVES SUPPORT DISTRIBUTION OF RANDOM RECOVERIES COVENANTS Credit Risk Valuation and Credit Spreads CREDIT SPREAD, IMPLIED DEFAULT INTENSITY AND RECOVERY RATE CREDIT VAR AND MATRIX VALUATION CREDIT VAR AND MATRIX VALUATION: APPLICATION MIGRATIONS AND VAR UNDERTHE STRUCTURAL MODEL FORWARD VALUATION AND EXCESS SPREADS Section 12. Credit Portfolio Risk Credit Event Dependencies MODELING JOINT MIGRATIONS AND DEFAULTS WITH THE STRUCTURAL MODEL Dependency and Joint Default Probability Dependency and Joint Migration Probabilities JOINT DEFAULT PROBABILITY USING DISCRETE VARIABLES CONDITIONAL PROBABILITIES AND CORRELATION JOINT MIGRATION MATRICES SIMULATION OF JOINT DEFAULTS AND MIGRATIONS Example of Portfolio Loss Distribution PORTFOLIO OF TWO OBLIGORS PORTFOLIO OF TWO INDEPENDENT OBLIGORS The Loss Distribution The Loss Statistics DEPENDENT DEFAULT EVENTS Calculation of Joint Default and Conditional Probabilities Loss Distribution Loss Statistics COMPARISON OF THE DEPENDENT AND THE INDEPENDENT CASES Analytical Loss Distributions INDEPENDENT DEFAULT EVENTS:THE BINOMIAL DISTRIBUTION Simulating Increased Diversification with Loss Independence The Effect of Diversification THE "STANDARDIZED" STANDALONE STRUCTURAL MODEL A Single Obligor Dependent on the State of the Economy The Asset Value and Default Probability Conditional on the State of the Economy The Default Probability Conditional on The State of the Economy Application: The Stressed Default Probability under Basel 2 MODELING DEFAULTS IN A UNIFORM PORTFOLIO:THE LIMIT DISTRIBUTION The Uniform Granular Portfolio Modeling Defaults under the Structural Model The Limit Distribution Application: Finding the Factor Value Matching a Given Portfolio Loss Percentile Simulation of Credit Portfolio Loss Distributions PRINCIPLES OF SAMPLE SIMULATIONS MONTE CARLO SIMULATIONS OF DEFAULT EVENTS BASED ON THE STRUCTURAL MODEL OF DEFAULT Asset Distribution and Default Probability The Multiple Simulations The Simulation Algorithm Simulations of Default Distributions Dealing with Different Default Probabilities and Discrepancies of Exposures SIMULATIONS OF TIMES TO DEFAULT The Simulation Algorithm Dealing with Different Default Probabilities and Discrepancies of Exposures Credit Portfolio Models CREDIT PORTFOLIO MODEL OVERVIEW MOODY'S-KMV CREDIT MONITOR AND MOODY'S-KMV PORTFOLIO MANAGER Conceptual Framework Credit Events and Credit State at Horizon Risk Factors and Dependence Structure Revaluation of Facilities at Horizon Generation of Portfolio Value Distribution Portfolio Optimization CREDIT METRICS CREDIT PORTFOLIO VIEW: ECONOMETRIC MODELS Credit Portfolio View Conceptual Framework Credit Events and Credit State at Horizon Risk Factors and Dependence Structure Revaluation of Facilities at Horizon Generation of Portfolio Value Distribution CREDITRISK+AND ANALYTICAL DISTRIBUTIONS Conceptual Framework Credit Events and Credit State at Horizon Risk Factors Dependency Structure Generation of Portfolio Value Distribution APPENDIX:THE GAMMA DISTRIBUTION Section 13. Capital Allocation Economic Capital and Credit Risk VaR HORIZON FOR CREDIT CAPITAL FROM PORTFOLIO VALUE DISTRIBUTION TO CREDIT CAPITAL Capital Under Default Mode Capital Under Full Migration Mode Expected Loss Economic Capital and Loss Volatility From Future Values to Current Capital RAROC CALCULATIONS AT PORTFOLIO AND FACILITY LEVELS Capital Allocation and Risk Contributions NORMATIVE CAPITAL ALLOCATIONS AND CAPITAL EFFECTIVE UTILIZATIONS Normative Risk Allocations Versus Capital Utilizations Capital Utilizations DEFINITIONS OF RISK CONTRIBUTIONS STANDALONE INDIVIDUAL LOSSES RISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONS TO PORTFOLIO LOSS VOLATILITY AND TO CAPITAL Risk Contributions, Portfolio Loss Volatility and Capital Marginal Risk Contributions Usages of Risk Contributions and of Marginal Risk Contributions BASIC PROPERTIES OF RISK CONTRIBUTIONS THE CAPITAL ALLOCATION MODEL AND RISK CONTRIBUTIONS Risk Contributions to Portfolio Loss Volatility Specific Cases From Risk Contributions to Capital Allocation SAMPLE CALCULATIONS OF RISK CONTRIBUTIONS Standalone Expected Loss and Portfolio Expected Loss Standalone Loss Volatilities and Portfolio Loss Volatility The Portfolio Loss Volatility Risk Contributions to Volatility Capital Allocation APPENDIX: CALCULATION OF ABSOLUTE RISK CONTRIBUTIONS FROM THE VARIANCE-COVARIANCE MATRIX Marginal Risk Contributions MARGINAL RISK CONTRIBUTIONS TO LOSS VOLATILITY MARGINAL RISK CONTRIBUTIONS TO CAPITAL GENERAL PROPERTIES OF RISK CONTRIBUTIONS AND MARGINAL RISK CONTRIBUTIONS MARGINAL RISK CONTRIBUTIONS TO VOLATILITY VERSUS RISK CONTRIBUTIONS MARGINAL RISK CONTRIBUTION AND SIZE OF AN EXISTING EXPOSURE Section 14. Risk-adjusted Performance RaRoC and Shareholders' Value Added RISK-ADJUSTED MEASURES OF PERFORMANCE Definitions The Hurdle Rate and the Cost of Capital The "Ex Ante" and the "Ex Post" Views The Reference Capital for Risk Contributions RISK-BASED PRICING AND MARGINAL RISK CONTRIBUTIONS Risk-based Pricing and Marginal Risk Contribution to Capital Risk-based Pricing and Risk Contribution to Capital The Pricing Paradox with Marginal Risk Contributions Risk-adjusted Performance versus Risk-based Pricing RAROC CALCULATIONS Revenues Expected Loss Other Costs Expanded RaRoC Formula THE RISK PREMIUM EMBEDDED IN RISK-BASED PRICING SVA MEASURES THE PRICE OF RISK AND ARBITRAGE Economic Income Statements THE CALCULATION OF RAROC AND SVA FOR CREDIT RISK Calculation of RaRoC and SVA RISK-BASED PRICING RISK-BASED PERFORMANCE, PRICING AND CAPITAL ALLOCATION Risk-based Pricing Risk-based Performance ORIGINATION AND POST-ORIGINATION FOLLOW UP Section 15. Credit Portfolio Management Portfolio Analysis THE SAMPLE PORTFOLIO AND THE SIMULATIONS Portfolio Data Portfolio Simulations PORTFOLIO LOSS DISTRIBUTION PORTFOLIO OVERVIEW Loss Statistics and Capital Portfolio Risk Return Profile Portfolio Concentration and Correlation Risk From Portfolio Risk to Individual Facilities REPORTING ALTERNATE METRICS OF RISK Exposures, Default Probability and Loss Given Default Exposure and Expected Loss Exposure and Capital Allocation or Loss Volatility RISK-ADJUSTED PERFORMANCE AND MISPRICING REPORTS Book Measures of Profitability versus Risk-adjusted Measures Mispricing Reports REPORTING RISK AND RETURN VERSUS BUSINESS DIMENSIONS APPENDIX I: SAMPLE PORTFOLIO INPUTS APPENDIX 2: SAMPLE PORTFOLIO OUTPUTS APPENDIX 3: PORTFOLIO ANALYSIS AND REPORTING ISSUES Traceability of Aggregated Measures and Risk Management Dealing with Multiple Dimensions PORTFOLIO ANALYSIS AND REPORTING TECHNICAL CHALLENGES Basic Specifications of Reporting Systems Stress Testing and What-if Analyses Interactive Implementation of Risk Systems Securitization and Capital Management ECONOMICS OF SECURITIZATIONS Expected Return on Assets and Compensations to Investors Variety of Securitizations Rationales For Securitizations The Securitization Organization STRUCTURING AND THE WATERFALL MECHANISM Structuring of Notes The Waterfalls of Cash Flows and Losses ECONOMICS OF SECURITIZATION FORTHE BANK Analysis of a Securitization Transaction (Case Study)The Costs of Funding On Balance Sheet and through Securitization The Effective Return on Capital for the Bank The Cost of Financing through Securitization The Annualized All-in Cost of Financing through Securitization The Pricing of Assets Sold to the SPE The All-in Cost of Funding through Securitization Securitization Economics and the Return on Equity Enhancing the Bank's Return on Capital through Securitization ASSESSING THE RISK OF ASSET-BACKED NOTES Rating Methodologies for Structured Notes Credit Portfolio Models and Securitizations Tranches are Subject to Correlation Risk Credit Portfolio Management THE RATIONALE FOR CREDIT PORTFOLIO MANAGEMENT TRADING CREDIT RISK APPLICATIONS OF CREDIT DERIVATIVES Hedging Credit Risk Trading Credit Risk Customizing Credit Risk Applications for Credit Portfolio Management Evolution of Credit Risk Models PORTFOLIO CREDIT RISK MANAGEMENT (CASE STUDY)Buying Protection for the Portfolio from Another Bank Buying Protection for the Portfolio and Selling Protection OTHER ARBITRAGE BETWEEN ECONOMIC PRICES AND RATING-BASED PRICES The Financial System and Reforms THE FINANCIAL STABILITY FORUM RECOMMENDATIONS Capital Provisioning Valuation and Leverage THE WHITE PAPER FROM THE WHITE HOUSE Supervision Establish Comprehensive Supervision and Regulation of Financial Markets Protect Consumers and Investors from Financial Abuse Improve Tools for Managing Financial Crises Raise International Regulatory Standards and Improve International Cooperation AREAS UNDER SCRUTINY BY FINANCIAL AUTHORITIES: SUMMARY

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