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