Modelling Economic Capital: Practical Credit-Risk Methodologies, Applications, and Implementation Details

Foreword
Preface
	An Analyst's Objectives
	Analytic Axioms
		#1: Multiplicity of Perspective
		#2: Many Eyes
		#3: Pictures and Words
		#4: The Three Little Pigs
		#5: The Best for Last
	Why This Book?
Acknowledgements
	References
Testimonials
Contents
1 Introducing Economic Capital
	1.1 Presenting the Nordic Investment Bank
	1.2 Defining Capital
		1.2.1 The Risk Perspective
		1.2.2 Capital Supply and Demand
	1.3 An Enormous Simplification
	1.4 Categorizing Risk
	1.5 Risk Fundamentals
		1.5.1 Two Silly Games
		1.5.2 A Fundamental Characterization
		1.5.3 Introducing Concentration
		1.5.4 Modelling 101
	1.6 Managing Models
	1.7 NIB's Portfolio
	1.8 Looking Forward
	1.9 Wrapping Up
	References
Part I Modelling Credit-Risk Economic Capital
	2 Constructing a Practical Model
		2.1 A Naive, but Informative, Start
		2.2 Mixture and Threshold Models
			2.2.1 The Mixture Model
			2.2.2 The Threshold Model
		2.3 Asset-Return Dynamics
			2.3.1 Time Discretization
			2.3.2 Normalization
			2.3.3 A Matrix Formulation
			2.3.4 Orthogonalization
		2.4 The Legacy Model
			2.4.1 Introducing Default
			2.4.2 Stochastic Recovery
			2.4.3 Risk Metrics
		2.5 Extending the Legacy Model
			2.5.1 Changing the Copula
			2.5.2 Constructing the t Copula
			2.5.3 Default Correlation
			2.5.4 Modelling Credit Migration
			2.5.5 The Nuts and Bolts of Credit Migration
		2.6 Risk Attribution
			2.6.1 The Simplest Case
			2.6.2 An Important Relationship
			2.6.3 The Computational Path
			2.6.4 A Clever Trick
		2.7 Wrapping Up
		References
	3 Finding Model Parameters
		3.1 Credit States
			3.1.1 Defining Credit Ratings
			3.1.2 Transition Matrices
			3.1.3 Default Probabilities
		3.2 Systemic Factors
			3.2.1 Factor Choice
			3.2.2 Systemic-Factor Correlations
				Which Matrix?
				Which Correlation Measure?
				What Time Period?
			3.2.3 Distinguishing Systemic Weights and Factor Loadings
			3.2.4 Systemic-Factor Loadings
				Some Key Principles
				A Loading Estimation Approach
				A Simplifying Assumption
				Normalization
			3.2.5 Systemic Weights
				A Systemic-Weight Dataset
				Estimating Correlations
				Imposing Strict Monotonicity
				A Final Look
		3.3 A Portfolio Perspective
			3.3.1 Systemic Proportions
			3.3.2 Factor-, Asset-, and Default-Correlation
			3.3.3 Tail Dependence
		3.4 Recovery Rates
		3.5 Credit Migration
			3.5.1 Spread Duration
			3.5.2 Credit Spreads
				The Theory
				Pricing Credit Risky Instruments
				The Credit-Spread Model
				Credit-Spread Estimation
		3.6 Wrapping Up
		References
	4 Implementing the Model
		4.1 Managing Expectations
		4.2 A System Architecture
		4.3 The Data Layer
			4.3.1 Key Data Inputs
				Peculiarities of Loan Exposures
		4.4 The Application Layer
			4.4.1 Purchase or Build Application Software?
			4.4.2 Which Programming Environment?
			4.4.3 The Application Environment
			4.4.4 A High-Level Code Overview
			4.4.5 Book-Keeping and Parameter Assignment
			4.4.6 The Simulation Engine
		4.5 Convergence
			4.5.1 Constructing Confidence Bands
			4.5.2 Portfolio-Level Convergence
			4.5.3 Obligor-Level Convergence
			4.5.4 Computational Expense
			4.5.5 Choosing M
		4.6 Wrapping Up
		References
Part II Loan Pricing
	5 Approximating Economic Capital
		5.1 Framing the Problem
		5.2 Approximating Default Economic Capital
			5.2.1 Exploiting Existing Knowledge
			5.2.2 Borrowing from Regulatory Guidance
			5.2.3 A First Default Approximation Model
			5.2.4 Incorporating Concentration
			5.2.5 The Full Default Model
		5.3 Approximating Migration Economic Capital
			5.3.1 Conditional Migration Loss
			5.3.2 A First Migration Model
			5.3.3 The Full Migration Model
		5.4 Approximation Model Due Diligence
		5.5 The Full Picture
			5.5.1 A Word on Implementation
			5.5.2 An Immediate Application
		5.6 Wrapping Up
		References
	6 Loan Pricing
		6.1 Some Fundamentals
		6.2 A Holistic Perspective
			6.2.1 The Balance-Sheet Perspective
			6.2.2 Building the Foundation
		6.3 Estimating Marginal Asset Income
			6.3.1 Weighting Financing Sources
			6.3.2 Other Income and Expenses
		6.4 Risk-Adjusted Returns
		6.5 The Hurdle Rate
		6.6 Allocating Economic Capital
		6.7 Getting More Practical
			6.7.1 Immediate Disbursement
			6.7.2 Payment Frequency
			6.7.3 The Lending Margin
			6.7.4 Existing Loan Exposure
			6.7.5 Forward-Starting Disbursements
			6.7.6 Selecting Commitment Fees
		6.8 Wrapping Up
		References
Part III Modelling Expected Credit Loss
	7 Default-Probability Fundamentals
		7.1 The Basics
			7.1.1 The Limiting Case
			7.1.2 An Extended Aside
		7.2 A Thorny Problem
			7.2.1 Set-Up
			7.2.2 Some Theory
			7.2.3 Regularization
			7.2.4 Going to the Data
		7.3 Building Default-Probability Surfaces
			7.3.1 A Low-Dimensional Markov Chain
			7.3.2 A Borrowed Model
			7.3.3 Time Homogeneity
			7.3.4 A Final Decisive Factor
		7.4 Mapping to One's Master Scale
			7.4.1 Building an Internal Default Probability Surface
			7.4.2 Building an Internal Transition Matrix
		7.5 Wrapping Up
		References
	8 Building Stress Scenarios
		8.1 Our Response Variables
			8.1.1 Simplifying Matters
			8.1.2 Introducing the Default Curve
			8.1.3 Fitting Default Curves
		8.2 Our Explanatory Variables
			8.2.1 Data Issues
		8.3 An Empirically Motivated Approach
			8.3.1 A Linear Model
			8.3.2 An Indirect Approach
			8.3.3 An Alternative Formulation
			8.3.4 A Short Aside
			8.3.5 Building a Point-in-Time Transition Matrix
				The Role of P
				Upgrades and Downgrades
				Building h
		8.4 A Theoretically Motivated Approach
			8.4.1 Familiar Terrain
			8.4.2 Yang:2017's Contribution
			8.4.3 Adding Time
			8.4.4 Parameter Estimation
				Preparation
				The First Step
			8.4.5 The Second Step
			8.4.6 To a Point-in-Time Transition Matrix
		8.5 Constructing Default-Stress Scenarios
		8.6 Wrapping Up
		References
	9 Computing Loan Impairments
		9.1 The Calculation
			9.1.1 Defining Credit Loss
			9.1.2 Selecting a Probability Measure
			9.1.3 Managing the Time Horizon
				Time-Frequency, Interpolation and Bootstrapping
			9.1.4 The Simplest Example
			9.1.5 A More Realistic Example
			9.1.6 Coupon and Discount Rates
			9.1.7 Impact of Credit Rating
			9.1.8 Adding Macro-Financial Uncertainty
			9.1.9 Tying It All Together
		9.2 Introducing Stages
			9.2.1 Stage-Allocation Consequences
			9.2.2 Stage-Allocation Logic
		9.3 Managing Portfolio Composition
			9.3.1 Motivating Our Adjustment
			9.3.2 Building an Adjustment
			9.3.3 Retiring Our Concrete Example
		9.4 Wrapping Up
		References
Part IV Other Practical Topics
	10 Measuring Derivative Exposure
		10.1 The Big Picture
		10.2 Some Important Definitions
		10.3 An Important Choice
		10.4 A General, But Simplified Structure
			10.4.1 Expected Exposure
			10.4.2 Expected Positive Exposure
			10.4.3 Potential Future Exposure
		10.5 The Regulatory Approach
			10.5.1 Replacement Cost
			10.5.2 The Add-On
			10.5.3 The Trade Level
			10.5.4 The Multiplier
			10.5.5 Bringing It All Together
		10.6 The Asset-Class Perspective
			10.6.1 Interest Rates
			10.6.2 Currencies
		10.7 A Pair of Practical Applications
			10.7.1 Normalized Derivative Exposures
			10.7.2 Defining and Measuring Leverage
		10.8 Wrapping Up
		References
	11 Seeking External Comparison
		11.1 Pillar I
			11.1.1 The Standardized Regulatory Approach
			11.1.2 The Internal Ratings-Based Approach
			11.1.3 S&P's Approach to Risk-Weighting
			11.1.4 Risk-Weighted Assets
		11.2 Pillar II
			11.2.1 Geographic and Industrial Diversification
				Fisher's z-Transformation
			11.2.2 Preferred-Creditor Treatment
			11.2.3 Single-Name Concentration
				A First Try
				A Complicated Add-On
				The CreditRisk+ Case
			11.2.4 Working with Partial Information
			11.2.5 A Multi-Factor Adjustment
				A Generic Multi-Factor Model
				Introducing a One-Factor Model
				Calibrating the Multi- and Single-Factor Worlds
				Granularity Adjustment Revisited
				The Big Reveal
				The Drudgery
			11.2.6 Practical Granularity-Adjustment Results
		11.3 Wrapping Up
		References
	12 Thoughts on Stress Testing
		12.1 Organizing Stress-Testing
			12.1.1 The Main Risk Pathway
			12.1.2 Competing Approaches
			12.1.3 Managing Time
			12.1.4 Remaining Gameplan
		12.2 The Top-Down, or Macro, Approach
			12.2.1 Introducing the Vector Auto-Regressive Model
			12.2.2 The Basic Idea
			12.2.3 An Important Link
			12.2.4 The Impulse-Response Function
			12.2.5 A Base Sample Portfolio
			12.2.6 From Macro Shock to Our Portfolio
			12.2.7 The Portfolio Consequences
		12.3 The Bottom-Up, or Micro, Approach
			12.3.1 The Limits of Brute Force
			12.3.2 The Extreme Cases
			12.3.3 Traditional Bottom-Up Cases
			12.3.4 Randomization
			12.3.5 Collecting Our Bottom-Up Alternatives
		12.4 Wrapping Up
		References
Index
Author Index