Credit Risk Analytics E-Book

Bart Baesens

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: SAS Institute Inc
• Sprache: Englisch

Seitenzahl: 646

Veröffentlichungsjahr: 2016

Beschreibung

The long-awaited, comprehensive guide to practical credit risk modeling Credit Risk Analytics provides a targeted training guide for risk managers looking to efficiently build or validate in-house models for credit risk management. Combining theory with practice, this book walks you through the fundamentals of credit risk management and shows you how to implement these concepts using the SAS credit risk management program, with helpful code provided. Coverage includes data analysis and preprocessing, credit scoring; PD and LGD estimation and forecasting, low default portfolios, correlation modeling and estimation, validation, implementation of prudential regulation, stress testing of existing modeling concepts, and more, to provide a one-stop tutorial and reference for credit risk analytics. The companion website offers examples of both real and simulated credit portfolio data to help you more easily implement the concepts discussed, and the expert author team provides practical insight on this real-world intersection of finance, statistics, and analytics. SAS is the preferred software for credit risk modeling due to its functionality and ability to process large amounts of data. This book shows you how to exploit the capabilities of this high-powered package to create clean, accurate credit risk management models. * Understand the general concepts of credit risk management * Validate and stress-test existing models * Access working examples based on both real and simulated data * Learn useful code for implementing and validating models in SAS Despite the high demand for in-house models, there is little comprehensive training available; practitioners are left to comb through piece-meal resources, executive training courses, and consultancies to cobble together the information they need. This book ends the search by providing a comprehensive, focused resource backed by expert guidance. Credit Risk Analytics is the reference every risk manager needs to streamline the modeling process.

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Table of Contents

Title Page

Copyright

Dedication

Acknowledgments

About the Authors

Chapter 1: Introduction to Credit Risk Analytics

Why This Book Is Timely

The Current Regulatory Regime: Basel Regulations

Introduction to Our Data Sets

Housekeeping

Chapter 2: Introduction to SAS Software

SAS versus Open Source Software

Base SAS

SAS/STAT

Macros in Base SAS

SAS Output Delivery System (ODS)

SAS/IML

SAS Studio

SAS Enterprise Miner

Other SAS Solutions for Credit Risk Management

Reference

Chapter 3: Exploratory Data Analysis

Introduction

One-Dimensional Analysis

Two-Dimensional Analysis

Highlights of Inductive Statistics

Reference

Chapter 4: Data Preprocessing for Credit Risk Modeling

Types of Data Sources

Merging Data Sources

Sampling

Types of Data Elements

Visual Data Exploration and Exploratory Statistical Analysis

Descriptive Statistics

Missing Values

Outlier Detection and Treatment

Standardizing Data

Categorization

Weights of Evidence Coding

Variable Selection

Segmentation

Default Definition

Practice Questions

Notes

References

Chapter 5: Credit Scoring

Basic Concepts

Judgmental versus Statistical Scoring

Advantages of Statistical Credit Scoring

Techniques to Build Scorecards

Credit Scoring for Retail Exposures

Reject Inference

Credit Scoring for Nonretail Exposures

Big Data for Credit Scoring

Overrides

Evaluating Scorecard Performance

Business Applications of Credit Scoring

Limitations

Practice Questions

References

Chapter 6: Probabilities of Default (PD): Discrete-Time Hazard Models

Introduction

Discrete-Time Hazard Models

Which Model Should I Choose?

Fitting and Forecasting

Formation of Rating Classes

Practice Questions

References

Chapter 7: Probabilities of Default: Continuous-Time Hazard Models

Introduction

Censoring

Life Tables

Cox Proportional Hazards Models

Accelerated Failure Time Models

Extension: Mixture Cure Modeling

Discrete-Time Hazard versus Continuous-Time Hazard Models

Practice Questions

References

Chapter 8: Low Default Portfolios

Introduction

Basic Concepts

Developing Predictive Models for Skewed Data Sets

Mapping to an External Rating Agency

Confidence Level Based Approach

Other Methods

LGD and EAD for Low Default Portfolios

Practice Questions

References

Chapter 9: Default Correlations and Credit Portfolio Risk

Introduction

Modeling Loss Distributions with Correlated Defaults

Estimating Correlations

Extensions

Practice Questions

References

Chapter 10: Loss Given Default (LGD) and Recovery Rates

Introduction

Marginal LGD Models

PD-LGD Models

Extensions

Practice Questions

References

Chapter 11: Exposure at Default (EAD) and Adverse Selection

Introduction

Regulatory Perspective on EAD

EAD Modeling

Practice Questions

References

Chapter 12: Bayesian Methods for Credit Risk Modeling

Introduction

The Bayesian Approach to Statistics

PD Estimation with Bayesian Statistics

Correlation Estimation with Bayesian Statistics

PD Estimation for Low Default Portfolios

Practice Questions

Notes

References

Chapter 13: Model Validation

Introduction

Regulatory Perspective

Basic Concepts of Validation

Quantitative Validation

Qualitative Validation

Practice Questions

References

Chapter 14: Stress Testing

Introduction

Integration with the Basel Risk Model

Stress Testing Applications in SAS

Practice Questions

References

Chapter 15: Concluding Remarks

Other Credit Risk Exposures

Limitations of Credit Risk Analytics

Guiding Principles for Building Good Credit Risk Models

References

Index

End User License Agreement

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Guide

Table of Contents

Begin Reading

List of Exhibits

Chapter 1: Introduction to Credit Risk Analytics

Exhibit 1.1 Pillars of the Basel II/III Regulation

Exhibit 1.2 Basel III: Capital Requirements

Exhibit 1.3 Basel Foundation and Advanced IRB Approach

Exhibit 1.4 Data Set Usage in This Book

Chapter 2: Introduction to SAS Software

Exhibit 2.1 Start Screen of Base SAS 9.4

Exhibit 2.2 Output PROC MEAN

Exhibit 2.3 Output PROC REG

Exhibit 2.4 Examples Macro 1

Exhibit 2.5 Examples Macro 2

Exhibit 2.6 Examples Macro 3

Exhibit 2.7 Output PROC IML

Exhibit 2.8 Log on Screen of SAS Enterprise Miner

Exhibit 2.9 Welcome Screen of SAS Enterprise Miner

Exhibit 2.10 Creating a New Project in SAS Enterprise Miner

Exhibit 2.11 Start Screen of SAS Enterprise Miner

Exhibit 2.12 Creating a SAS Library in SAS Enterprise Miner

Exhibit 2.13 Selecting the HMEQ Data Set from the Mydata Library

Exhibit 2.14 Specifying the Measurement Level and Measurement Role for the Variables

Exhibit 2.15 Creating a New Diagram

Exhibit 2.16 Adding the HMEQ Data to the Diagram Workspace

Exhibit 2.17 Adding a Multiplot Node to the Diagram Workspace

Chapter 3: Exploratory Data Analysis

Exhibit 3.1 Absolute and Relative Frequencies

Exhibit 3.2 Histograms and CDF Plots

Exhibit 3.3 Location Measures

Exhibit 3.4 Q-Q Plot versus Normal Distribution

Exhibit 3.5 Dispersion Measures

Exhibit 3.6 Skewness and Kurtosis Measures

Exhibit 3.7 Two-Dimensional Contingency Table

Exhibit 3.8 Box Plot of FICO Grouped by Default

Exhibit 3.9 Box Plot of LTV Grouped by Default

Exhibit 3.10 Chi-Square-Related Measures of Association

Exhibit 3.11 Correlation Measures

Exhibit 3.12 Scatter Plot of FICO versus LTV (Sample)

Exhibit 3.13 Basic Confidence Intervals

Exhibit 3.14 Test for Location

Chapter 4: Data Preprocessing for Credit Risk Modeling

Exhibit 4.1 Aggregating Normalized Data Tables into a Non-normalized Data Table

Exhibit 4.2 The Reject Inference Problem in Credit Scoring

Exhibit 4.3 The FREQ Procedure

Exhibit 4.4 The FREQ Procedure

Exhibit 4.5 Sampling in SAS Enterprise Miner

Exhibit 4.6 Setting the Measurement Level of Variables in SAS Enterprise Miner

Exhibit 4.7 Plots in Base SAS

Exhibit 4.8 The Multiplot Node in SAS Enterprise Miner

Exhibit 4.9 Histogram of Job Status versus Good/Bad Status

Exhibit 4.10 Results of PROC Univariate

Exhibit 4.11 The StatExplore Node in SAS Enterprise Miner

Exhibit 4.12 Descriptive Statistics for the HMEQ Data Set

Exhibit 4.13 Class Conditional Descriptive Statistics for the HMEQ Data Set

Exhibit 4.14 Dealing with Missing Values

Exhibit 4.15 The Impute Node in SAS Enterprise Miner

Exhibit 4.16 Multivariate Outliers

Exhibit 4.17 Histogram for Outlier Detection

Exhibit 4.18 z-Scores for Outlier Detection

Exhibit 4.19 Using the z-Scores for Truncation

Exhibit 4.20 The Filter Node in SAS Enterprise Miner

Exhibit 4.21 The Replacement Node in SAS Enterprise Miner

Exhibit 4.22 The Transform Variables Node in SAS Enterprise Miner

Exhibit 4.23 Default Risk versus Age

Exhibit 4.24 Coarse Classifying the Purpose of Loan Variable

Exhibit 4.25 Pivot Table for Coarse Classifying the Purpose of Loan Variable

Exhibit 4.26 Coarse Classifying the Residential Status Variable

Exhibit 4.27 Empirical Frequencies Option 1 for Coarse Classifying Residential Status

Exhibit 4.28 Independence Frequencies Option 1 for Coarse Classifying Residential Status

Exhibit 4.29 Output for Categorization Option 1

Exhibit 4.30 Output for Categorization Option 2

Exhibit 4.31 Calculating Weights of Evidence (WOE)

Exhibit 4.32 The Interactive Grouping Node in SAS Enterprise Miner

Exhibit 4.33 Results of the Interactive Grouping Node in SAS Enterprise Miner

Exhibit 4.34 Results of the Interactive Grouping Node and Groupings Tab in SAS Enterprise Miner

Exhibit 4.35 Filters for Variable Selection

Exhibit 4.36 Calculating the Information Value Filter Measure

Exhibit 4.37 Contingency Table for Employment Status versus Good/Bad Customer

Exhibit 4.38 Roll-Rate Analysis

Chapter 5: Credit Scoring

Exhibit 5.1 Example Credit Scoring Data Set

Exhibit 5.2 Bounding Function for Logistic Regression

Exhibit 5.3 Linear Decision Boundary of Logistic Regression

Exhibit 5.4 Reference Values for Variable Significance

Exhibit 5.5 Variable Subsets for Four Variables,

V

1

,

V

2

,

V

3

, and

V

4

Exhibit 5.6 Output of PROC LOGISTIC

Exhibit 5.7 Logistic Regression in SAS Enterprise Miner

Exhibit 5.8 Example Credit Scorecard

Exhibit 5.9 The Scorecard Node in SAS Enterprise Miner

Exhibit 5.10 Output of the Scorecard Node in SAS Enterprise Miner

Exhibit 5.11 Credit Scorecard for HMEQ Data Set

Exhibit 5.12 Example Decision Tree for Credit Scoring

Exhibit 5.13 Example Data Sets for Calculating Impurity

Exhibit 5.14 Entropy versus Gini

Exhibit 5.15 Calculating the Entropy for Age Split

Exhibit 5.16 Using a Validation Set to Stop Growing a Decision Tree

Exhibit 5.17 Example Decision Tree.

Exhibit 5.18 Decision Boundary of a Decision Tree

Exhibit 5.19 Decision Tree Node in SAS Enterprise Miner

Exhibit 5.20 Output of the Decision Tree Node

Exhibit 5.21 Decision Tree for HMEQ Data Set

Exhibit 5.22 Example Application Scorecard

Exhibit 5.23 Application Scoring: Snapshot to Snapshot

Exhibit 5.24 Behavioral Scoring: Video Clip to Snapshot

Exhibit 5.25 Dynamic Scoring: Video Clip to Video Clip

Exhibit 5.26 Hard Cutoff Augmentation

Exhibit 5.27 Parceling

Exhibit 5.28 Fuzzy Augmentation

Exhibit 5.29 Expert-Based Scorecard (Ozdemir and Miu 2009)

Exhibit 5.30 Credit Ratings by Moody's, S&P, and Fitch (Van Gestel and Baesens 2009)

Exhibit 5.31 Example Data Set for the Shadow Rating Approach

Exhibit 5.32 Example Shadow Rating Model

Exhibit 5.33 Example Override Report for an Application Scorecard with Cutoff Equal to 500

Exhibit 5.34 Key Characteristics of Successful Scorecards

Chapter 6: Probabilities of Default (PD): Discrete-Time Hazard Models

Exhibit 6.1 Conditionality of Default Events

Exhibit 6.2 Merton Model

Exhibit 6.3 Panel Data

Exhibit 6.4 Linear Model

Exhibit 6.5 Nonlinear Link Functions

Exhibit 6.6 Probit Model

Exhibit 6.7 Probit Model (cont.)

Exhibit 6.8 Probit Model (cont.)

Exhibit 6.9 Probit Model (cont.)

Exhibit 6.10 Calibration of Probit Models: Comparison of Default Indicators and Estimated Default Probabilities

Exhibit 6.11 Logit Model

Exhibit 6.12 Cloglog Model

Exhibit 6.13 Probit Model with Categorical Covariates

Exhibit 6.14 Real-fit diagram for the TTC Probit Model and the PIT Probit Model

Exhibit 6.15 Rating Migration Matrix Based on Observed Migration Frequencies

Exhibit 6.16 Cumulative Probit Model for Rating Migration Probabilities

Exhibit 6.17 Rating Migration Matrix

Exhibit 6.18 Cumulative Probit Model for Rating Migration Probabilities with Time-Varying Covariates

Exhibit 6.19 T-test for FICO_orig_time by default_time

Exhibit 6.20 Weights-of-Evidence and Information Value for FICO_orig_time with Regard to default_time

Exhibit 6.21 Data Sampling Strategies

Exhibit 6.22 Real-Fit Diagram for In-Sample

Exhibit 6.23 Real-Fit Diagram for Out-of-Sample

Exhibit 6.24 Relative Frequencies of Observations per Rating Class

Exhibit 6.25 Default Rate per Rating Class

Chapter 7: Probabilities of Default: Continuous-Time Hazard Models

Exhibit 7.1 Observation Credit Outcomes: Default or Censoring

Exhibit 7.2 Example for Kaplan-Meier Analysis

Exhibit 7.3 Example for Kaplan-Meier Analysis (cont.)

Exhibit 7.4 Cross-Sectional Data

Exhibit 7.5 Life Table Model

Exhibit 7.6 PDF plot

Exhibit 7.7 Survival Function Plot

Exhibit 7.8 Hazard Rate Plot

Exhibit 7.9 Survival Plot

Exhibit 7.10 PROC LIFETEST: Test of Equality over Groups

Exhibit 7.11 Calibration of Life Tables: Comparison of Default Indicators and Estimated Default Probabilities

Exhibit 7.12 Proportional Hazards

Exhibit 7.13 CPH Model

Exhibit 7.14 Survival Plot

Exhibit 7.15 CPH Model

Exhibit 7.16 Counting Process Data

Exhibit 7.17 CPH Model

Exhibit 7.18 Survival Plot

Exhibit 7.19 Calibration of CPH Models: Comparison of Default Indicators and Estimated Default Probabilities

Exhibit 7.20 Graphical Procedures: Negative Log of Estimated Survivor Functions versus Time

Exhibit 7.21 Graphical Procedures: Log of Negative Log of Estimated Survivor Functions versus the Log of Time

Exhibit 7.22 Degrees of Freedom for Likelihood Ratio Test

Exhibit 7.23 LIFEREG Model

Exhibit 7.24 Calibration of AFT Models: Comparison of Default Indicators and Estimated Default Probabilities

Exhibit 7.25 Mixture Cure Modeling

Chapter 8: Low Default Portfolios

Exhibit 8.1 Varying the Time Window to Deal with Skewed Data Sets

Exhibit 8.2 Oversampling the Defaulters

Exhibit 8.3 Undersampling the Nondefaulters

Exhibit 8.4 Creating a balanced sample using PROC FREQ

Exhibit 8.5 Creating a Tailored Sample in SAS Enterprise Miner

Exhibit 8.6 Creating a Tailored Sample in SAS Enterprise Miner: Results

Exhibit 8.7 Synthetic Minority Oversampling Technique (SMOTE)

Exhibit 8.8 Adjusting the Posterior Probability

Exhibit 8.9 Adjusting the Posterior Probability in Base SAS

Exhibit 8.10 Misclassification Costs

Exhibit 8.11 Rating Probability Distribution (Van Gestel et al. 2007)

Exhibit 8.12 Maximum Likelihood Estimates from PROC LOGISTIC

Exhibit 8.13 Association Statistics from PROC LOGISTIC

Exhibit 8.14 Notch Difference Graph for the Ratings Data Set

Exhibit 8.15 Values for

PD

A

for a Data Set with No Defaulters

Exhibit 8.16 Values for

PD

B

for a Data Set with No Defaulters

Exhibit 8.17 Values for

PD

C

for a Data Set with No Defaulters

Exhibit 8.18 Example of Confidence Level Based Approach in Base SAS

Exhibit 8.19 Values for

PD

A

,

PD

B

, and

PD

C

for a Data Set with Defaulters

Chapter 9: Default Correlations and Credit Portfolio Risk

Exhibit 9.1 Stylized Loss Distribution

Exhibit 9.2 Analytical Loss Distributions

Exhibit 9.3 Numerically Computed Loss Distribution

Exhibit 9.4 Monte Carlo Simulation

Exhibit 9.5 Simulated Loss Distribution

Exhibit 9.6 Parameter Estimates

Exhibit 9.7 ASRF Maximum Likelihood Method

Exhibit 9.8 Probit-Linear Regression

Exhibit 9.9 Probit-Linear Regression

Exhibit 9.10 Probit-Linear Regression

Exhibit 9.11 Probit-Linear Regression with Lagged Default Rate

Exhibit 9.12 Probit-Linear Regression with Macroeconomic Variable

Exhibit 9.13 Probit-Linear Regression with Macroeconomic Variable

Exhibit 9.14 AR Model with Macroeconomic Variable

Exhibit 9.15 AR Model with Macroeconomic Variable

Exhibit 9.16 Comparison of Loss Distributions

Chapter 10: Loss Given Default (LGD) and Recovery Rates

Exhibit 10.1 Conditionality of LGDs

Exhibit 10.2 Workout LGDs

Exhibit 10.3 Cash Flow Example

Exhibit 10.4 Workout Costs

Exhibit 10.5 LGD Models in This Chapter

Exhibit 10.6 Descriptive Statistics

Exhibit 10.7 Descriptive Statistics

Exhibit 10.8 Descriptive Statistics

Exhibit 10.9 Descriptive Statistics

Exhibit 10.10 Descriptive Statistics

Exhibit 10.11 Descriptive Statistics

Exhibit 10.12 Descriptive Statistics

Exhibit 10.13 Descriptive Statistics

Exhibit 10.14 Descriptive Statistics

Exhibit 10.15 Descriptive Statistics

Exhibit 10.16 Linear Regression

Exhibit 10.17 Linear Regression

Exhibit 10.18 Logistic-Linear Regression

Exhibit 10.19 Logistic-Linear Regression

Exhibit 10.20 Probit-Linear Regression

Exhibit 10.21 Probit-Linear Regression

Exhibit 10.22 Nonlinear Regression

Exhibit 10.23 Fractional Logit Regression

Exhibit 10.24 Beta Regression

Exhibit 10.25 Real-Fit Plot of Beta Regression

Exhibit 10.26 Real-Fit Regression of Beta Regression

Exhibit 10.27 Tobit Regression with NL Mixed

Exhibit 10.28 Tobit Regression with QLIM

Exhibit 10.29 Tobit Regression with QLIM

Exhibit 10.30 Real-Fit Plot of Tobit Regression

Exhibit 10.31 Real-Fit Regression of Tobit Regression

Exhibit 10.32 Heckman Regression with QLIM

Exhibit 10.33 Beta Regression with Censoring and Selection

Chapter 11: Exposure at Default (EAD) and Adverse Selection

Exhibit 11.1 Conversion of Limits and Drawn Amounts to EAD for Off-Balance-Sheet Exposures

Exhibit 11.2 Panel Data

Exhibit 11.3 Definitions, Boundaries, and Transformations for Credit Conversion Measures

Exhibit 11.4 Percentiles for Conversion Measures

Exhibit 11.5 Percentiles for Conversion Measures

Exhibit 11.6 Histogram Credit Conversion Factor (CCF)

Exhibit 11.7 Histogram Credit Equivalent (CEQ)

Exhibit 11.8 Histogram Limit Conversion Factor (LCF)

Exhibit 11.9 Histogram Used Amount Conversion Factor (UACF)

Exhibit 11.10 Histogram Transformed Credit Conversion Factor (CCF_t)

Exhibit 11.11 Histogram Transformed Credit Equivalent (CEQ_t)

Exhibit 11.12 Histogram Transformed Limit Conversion Factor (LCF_t)

Exhibit 11.13 Histogram Transformed Used Amount Conversion Factor (UACF_t)

Exhibit 11.14 Linear Regression Fit for CCF

Exhibit 11.15 Linear Regression Fit for CEQ

Exhibit 11.16 Linear Regression Fit for LCF

Exhibit 11.17 Linear Regression Fit for UACF

Exhibit 11.18 Linear Regression Fit and Residuals for LCF

Exhibit 11.19 Transformed Linear Regression Fit for CCF_t

Exhibit 11.20 Transformed Linear Regression Fit for CEQ_t

Exhibit 11.21 Transformed Linear Regression Fit for LCF_t

Exhibit 11.22 Transformed Linear Regression Fit for UACF_t

Exhibit 11.23 Beta Regression for LCF

Exhibit 11.24 Real-Fit Plot of Beta Regression for LCF

Exhibit 11.25 Real-Fit Regression of Beta Regression for LCF

Exhibit 11.26 Multinomial Logit Model

Exhibit 11.27 Calibration of Multinomial Logit Models: Comparison of Default Indicators and Estimated Default Probabilities

Exhibit 11.28 Real-Fit Diagram for the Default Probabilities

Exhibit 11.29 Calibration of Multinomial Logit Models: Comparison of Payoff Indicators and Estimated Payoff Probabilities

Exhibit 11.30 Real-Fit Diagram for the Payoff Probabilities

Exhibit 11.31 Cross-Sectional Data

Exhibit 11.32 CPH Model

Chapter 12: Bayesian Methods for Credit Risk Modeling

Exhibit 12.1 Probit Model with PROC LOGISTIC

Exhibit 12.2 MCMC Parameter Information for Probit Model

Exhibit 12.3 MCMC Parameter Summaries for Probit Model

Exhibit 12.4 MCMC Procedure Output for Probit Model

Exhibit 12.5 MCMC Procedure Output for Probit Model

Exhibit 12.6 MCMC Procedure Output for Probit Model

Exhibit 12.7 MCMC Diagnostics

Exhibit 12.8 MCMC Diagnostics

Exhibit 12.9 MCMC Diagnostics

Exhibit 12.10 MCMC Diagnostics

Exhibit 12.11 Diagnostic Plots

Exhibit 12.12 Diagnostic Plots

Exhibit 12.13 Diagnostic Plots

Exhibit 12.14 Diagnostic Plots

Exhibit 12.15 Summary Statistics

Exhibit 12.16 Diagnostic Plots

Exhibit 12.17 Diagnostic Plots

Exhibit 12.18 Diagnostic Plots

Exhibit 12.19 Diagnostic Plots

Exhibit 12.20 Summary Statistics

Exhibit 12.21 Diagnostic Plots

Exhibit 12.22 Diagnostic Plots

Exhibit 12.23 Diagnostic Plots

Exhibit 12.24 Summary Statistics

Exhibit 12.25 Diagnostic Plots

Exhibit 12.26 Diagnostic Plots

Exhibit 12.27 Summary Statistics

Exhibit 12.28 Diagnostic Plots

Exhibit 12.29 Diagnostic Plots

Exhibit 12.30 Various Likelihoods

Exhibit 12.31 Prior and Posterior Distributions

Exhibit 12.32 Summary Statistics

Exhibit 12.33 Diagnostic Plots

Exhibit 12.34 Probit Model

Exhibit 12.35 Summary Statistics

Exhibit 12.36 Diagnostic Plots

Exhibit 12.37 Diagnostic Plots

Exhibit 12.38 Diagnostic Plots

Chapter 13: Model Validation

Exhibit 13.1 Validation Framework (Basel Committee on Banking Supervision 2005a)

Exhibit 13.2 Example of Validation

Exhibit 13.3 Data Set Split-Up

Exhibit 13.4 Backtesting

Exhibit 13.5 Traffic Lights Approach

Exhibit 13.6 PSI for Two Variables across Time

Exhibit 13.7 Stability Test with Interactions

Exhibit 13.8 Out-of-Sample Association Statistics

Exhibit 13.9 Out-of-Time ROC Curves

Exhibit 13.10 Brier Scores

Exhibit 13.11 In-Sample Default Rates

Exhibit 13.12 Out-of-Time Default Rates and Tests

Exhibit 13.13 Hosmer-Lemeshow Statistics

Exhibit 13.14 Calibration Diagram

Exhibit 13.15 Out-of-Sample PD Predictions

Exhibit 13.16 Critical Values under Extended Binomial Model with Various Correlations

Exhibit 13.17 Critical Values under ASRF Model with Various Correlations

Exhibit 13.18 Beta Error for Simple Binomial Test

Exhibit 13.19 Beta Error for Extended Binomial Test under Correlations

Exhibit 13.20 Backtesting PD at Level 2

Exhibit 13.21 Backtesting PD at Level 1

Exhibit 13.22 Backtesting PD at Level 0

Exhibit 13.23 Action Plan for PD Backtesting

Exhibit 13.24 Backtesting LGD and EAD

Exhibit 13.25 Histograms of Actual and Predicted LGDs

Exhibit 13.26 Box Plots of Actual and Predicted LGDs

Exhibit 13.27 ROC for Predicted LGDs

Exhibit 13.28 Measures for Correlation and Association

Exhibit 13.29 Real-Fit Diagnostics

Exhibit 13.30 Linear Regression

Exhibit 13.31 Box Plots of Actual and Predicted LGDs

Exhibit 13.32 Scatter Plot of Actual and Predicted LGDs

Chapter 14: Stress Testing

Exhibit 14.1 Types of Stress Tests

Exhibit 14.2 DFAST “Baseline,” “Adverse,” and “Severely Adverse” Scenario

Exhibit 14.3 Expected Loss, Unexpected Loss, and Stressed Loss

Exhibit 14.4 Asset Correlations

Exhibit 14.5 Worst-Case Default Rate

Exhibit 14.6 Unexpected Loss (Capital)

Exhibit 14.7 Options for Averaging LGD

Exhibit 14.8 Example for Computing the Downturn LGD

Exhibit 14.9 Probit Model

Exhibit 14.10 Cumulative Distribution Function for Baseline PDs, Basel Worst-Case Default Rates, and Stressed PDs

Exhibit 14.11 Probit Model

Exhibit 14.12 Cumulative Distribution Function for Baseline and Stressed PDs under Consideration of Model Risk (Basic Stress Test)

Exhibit 14.13 Cumulative Distribution Function for Baseline and Stressed PDs under Consideration of Model Risk (Basic Stress Test and Multivariate Stress Test)

Credit Risk Analytics

Measurement Techniques, Applications, and Examples in SAS

Bart BaesensDaniel RöschHarald Scheule

Copyright © 2016 by SAS Institute. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-ondemand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Names: Baesens, Bart, author. | Rösch, Daniel, 1968– author. | Scheule, Harald, author.

Title: Credit risk analytics : measurement techniques, applications, and examples in SAS / Bart Baesens, Daniel Rösch, Harald Scheule.

Description: Hoboken, New Jersey : John Wiley & Sons, Inc., 2016 | Series: Wiley & SAS business series | Includes index.

Identifiers: LCCN 2016024803 (print) | LCCN 2016035372 (ebook) | ISBN 9781119143987 (cloth) | ISBN 9781119278344 (pdf) | ISBN 9781119278283 (epub)

Subjects: LCSH: Credit—Management—Data processing. | Risk management—Data processing. | Bank loans—Data processing. | SAS (Computer file)

Classification: LCC HG3751 .B34 2016 (print) | LCC HG3751 (ebook) | DDC 332.10285/555–ldc23

LC record available at https://lccn.loc.gov/2016024803

Cover image: Wiley

Cover design: © styleTTT/iStockphoto

To my wonderful wife, Katrien, and kids Ann-Sophie, Victor, and Hannelore.To my parents and parents-in-law. Bart BaesensTo Claudi and Timo Elijah. Daniel RöschTo Cindy, Leo, and Lina: a book about goodies and baddies. Harald Scheule

Acknowledgments

It is a great pleasure to acknowledge the contributions and assistance of various colleagues, friends, and fellow credit risk analytics lovers to the writing of this book. This text is the result of many years of research and teaching in credit risk modeling and analytics. We first would like to thank our publisher, John Wiley & Sons, for accepting our book proposal less than one year ago, and Rebecca Croser for providing amazing editing work for our chapters.

We are grateful to the active and lively scientific and industry communities for providing various publications, user forums, blogs, online lectures, and tutorials, which have proven to be very helpful.

We would also like to acknowledge the direct and indirect contributions of the many colleagues, fellow professors, students, researchers, and friends with whom we have collaborated over the years.

Last but not least, we are grateful to our partners, kids, parents, and families for their love, support, and encouragement.

We have tried to make this book as complete, accurate, and enjoyable as possible. Of course, what really matters is what you, the reader, think of it. The authors welcome all feedback and comments, so please feel free to let us know your thoughts!

Bart BaesensDaniel RöschHarald ScheuleSeptember 2016

About the Authors

Bart Baesens

Bart Baesens is a professor at KU Leuven (Belgium) and a lecturer at the University of Southampton (United Kingdom). He has done extensive research on big data and analytics, credit risk modeling, customer relationship management, and fraud detection. His findings have been published in well-known international journals and presented at top-level international conferences. He is the author of various books, including Analytics in a Big Data World (see http://goo.gl/kggtJp) and Fraud Analytics Using Descriptive, Predictive, and Social Network Techniques (see http://goo.gl/P1cYqe). He also offers e-learning courses on credit risk modeling (see http://goo.gl/cmC2So) and advanced analytics in a big data world (see https://goo.gl/2xA19U). His research is summarized at www.dataminingapps.com. He regularly tutors, advises, and provides consulting support to international firms with respect to their big data, analytics, and credit risk management strategy.

Daniel Rösch

Daniel Rösch is a Professor of Business and Management and holds the chair in Statistics and Risk Management at the University of Regensburg (Germany). Prior to joining the University of Regensburg in 2013, he was Professor of Finance and Director of the Institute of Banking and Finance at Leibniz University of Hannover from 2007 to 2013. He earned a PhD (Dr. rer. pol.) in 1998 for work on empirical asset pricing. From 2006 to 2011 he was visiting researcher at the University of Melbourne. Since 2011 he has been visiting professor at the University of Technology in Sydney. His research interests cover banking, quantitative financial risk management, credit risk, asset pricing, and empirical statistical and econometric methods and models. He has published numerous papers in leading international journals, earned several awards and honors, and regularly presents at major international conferences.

Rösch's service in the profession has included his roles as president of the German Finance Association, co-founder and member of the board of directors of the Hannover Center of Finance, and deputy managing director of the work group Finance and Financial Institutions of the Operations Research Society. He currently serves on the editorial board of the Journal of Risk Model Validation. Professor Rösch has worked with financial institutions and supervisory bodies such as Deutsche Bundesbank in joint research projects. Among others, his work has been funded by Deutsche Forschungsgemeinschaft, the Thyssen Krupp Foundation, the Frankfurt Institute for Finance and Regulation, the Melbourne Centre for Financial Studies, and the Australian Centre for International Finance and Regulation. In 2014 the German Handelsblatt ranked him among the top 10 percent of German-speaking researchers in business and management.

Harald Scheule

Harald “Harry” Scheule is Associate Professor of Finance at the University of Technology, Sydney, and a regional director of the Global Association of Risk Professionals. His expertise is in the areas of asset pricing, banking, credit and liquidity risk, home equity release, house prices in distress, insurance, mortgages, prudential regulation, securities evaluation, and structured finance

Scheule's award-winning research has been widely cited and published in leading journals. He currently serves on the editorial board of the Journal of Risk Model Validation. He is author or editor of various books.

Harry has worked with prudential regulators of financial institutions and undertaken consulting work for a wide range of financial institutions and service providers in Asia, Australia, Europe, and North America. These institutions have applied his work to improve their risk management practices, comply with regulations, and transfer financial risks.

Chapter 1Introduction to Credit Risk Analytics

Welcome to the first edition of Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS.

This comprehensive guide to practical credit risk analytics provides a targeted training guide for risk professionals looking to efficiently build or validate in-house models for credit risk management. Combining theory with practice, this book walks you through the fundamentals of credit risk management and shows you how to implement these concepts using the SAS software, with helpful code provided. Coverage includes data analysis and preprocessing, credit scoring, probability of default (PD) and loss given default (LGD) estimation and forecasting, low default portfolios, Bayesian methods, correlation modeling and estimation, validation, implementation of prudential regulation, stress testing of existing modeling concepts, and more, to provide a one-stop tutorial and reference for credit risk analytics.

This book shows you how to:

Understand the general concepts of credit risk management

Validate and stress test existing models

Access working examples based on both real and simulated data

Learn useful code for implementing and validating models in SAS

Exploit the capabilities of this high-powered package to create clean and accurate credit risk management models

WHY THIS BOOK IS TIMELY

Despite the high demand for in-house models, there is little comprehensive training available. Practitioners are often left to comb through piecemeal resources, executive training courses, and consultancies to cobble together the information they need. This book ends the search by providing a thorough, focused resource backed by expert guidance.

Current Challenges in Credit Risk Analytics

Commercial banks are typically large in size, and their fundamental business model continues to rely on financial intermediation by (1) raising finance through deposit taking, wholesale funding (e.g., corporate bonds and covered bonds), and shareholder capital, and (2) lending, which is a major source of credit risk.

Commercial bank loan portfolios consist to a large degree of mortgage loans, commercial real estate loans, and small and medium-sized enterprise (SME) company loans. SME loans are often backed by property collateral provided by the SME owners. The reliance of commercial bank loan portfolios on real estate is fundamental. Note that various types of mortgage loans exist. Examples are prime mortgages, subprime mortgages, reverse mortgages, home equity loans, home equity lines of credit (HELOCs), and interest-only loans, as well as variable, fixed-rate, and hybrid loans, to name a few.

Further loan categories include consumer loans (car loans, credit card loans, and student loans) and corporate loans. Loans to large companies also exist but compete with other funding solutions provided by capital markets (i.e., issuance of shares and corporate bonds).

Other sources of credit risk are fixed income securities (e.g., bank, corporate, and sovereign bonds), securitization investments, contingent credit exposures (loan commitments and guarantees), credit derivatives, and over-the-counter (OTC) derivatives.

Credit risk was at the heart of the global financial crisis (GFC) of 2007 to 2009 and is the focus of this book. Post GFC, prudential regulators have increased risk model requirements, and rigorous standards are being implemented globally, such as:

Implementation of Basel III: The Basel rules concern capital increases in terms of quantity and quality, leverage ratios, liquidity ratios, and impact analysis. We will discuss the Basel rules in more detail later.

Stress testing: Regulators require annual stress tests for all risk models.

Consistency across financial institutions and instruments: Regulators are currently identifying areas where regulation is applied in inconsistent ways.

Reinvigoration of financial markets (securitization): A number of markets, in particular the private (i.e., non-government-supported) securitization market, have declined in volume.

Transparency: Central transaction repositories and collection of loan-level data mean more information is collected and made available to credit risk analysts.

Increase of bank efficiency, competition, deregulation, and simplification: The precise measurement of credit risk is a central constituent in this process.

Risk model methodologies have advanced in many ways over recent years. Much of the original work was based in science where experiments typically abstracted from business cycles and were often applied within laboratory environments to ensure that the experiment was repetitive. Today, credit risk models are empirical and rely on historical data that includes severe economic downturns such as the GFC.

State-of-the-art credit risk models take into account the economic fundamentals of the data generating processes. For example, it is now common to include the life cycle of financial products from origination to payoff, default, or maturity while controlling for the current state of the economy. Another aspect is the efficient analysis of available information, which includes Bayesian modeling, nonparametric modeling, and frailty modeling. Risk models are extended to exploit observable and unobservable information in the most efficient ways.

Despite all these advancements, a word of caution is in order. All empirical risk models remain subject to model risk as we continue to rely on assumptions and the historical data that we observe. For example, it is quite common to obtain R-squared values of 20 percent for linear LGD and exposure at default (EAD) models. As the R-squared measures the fraction of the observed variation that is explained by the model, these numbers suggest that there is a considerable amount of variation that these models do not explain. Providing more precise models will keep us busy for years to come!

A Book on Credit Risk Analytics in SAS

In our academic research, we work with a number of software packages such as C++, EViews, Matlab, Python, SAS, and Stata. Similar to real languages (e.g., Dutch and German), being proficient in one package allows for quick proficiency in other packages.

In our dealings with credit risk analysts, their financial institutions, and their regulators, we realized that in the banking industry SAS is a statistical software package that has come to be the preferred software for credit risk modeling due to its functionality and ability to process large amounts of data. A key consideration in the industry for using SAS is its quality assurance, standardization, and scalability. We will discuss this point in the next chapter in more detail.

Most documentation available for statistical software packages has been developed for scientific use, and examples usually relate to repeatable experiments in medicine, physics, and mathematics. Credit risk analytics is multidisciplinary and incorporates finance, econometrics, and law. Training material in this area is very limited, as much of the empirical work has been triggered by the digitalization and emergence of big data combined with recent econometric advances. Credit risk analytics requires the consideration of interactions with the economy and regulatory settings, which are both dynamic and often nonrepeatable experiments. We learned a great deal from existing literature but continuously reached limits that we had to overcome. We have collected much of this research in this text to show you how to implement this into your own risk architecture.

Structure of the Book

This book contains 15 chapters. We deliberately focused on the challenges in the commercial banking industry and on the analysis of credit risk of loans and loan portfolios.

Following the introduction in the first chapter, the book features three chapters on the preparation stages for credit risk analytics. The second chapter introduces Base SAS, which allows you to explicitly program or code the various data steps and models, and SAS Enterprise Miner, which provides a graphical user interface (GUI) for users that aim to extract information from data without having to rely on programming. The third chapter introduces how basic statistics can be computed in SAS, and provides a rigorous statistical explanation about the necessary assumptions and interpretations. The fourth chapter describes how data can be preprocessed using SAS.

Next, we have included five chapters that look into the most modeled parameter of credit risk analytics: the probability of default (PD). The fifth chapter develops linear scores that approximate the default probabilities without the constraints of probability measures to be bounded between zero and one. Credit scores are often provided by external appraisers to measure default behavior. Examples are real estate indexes, bureau scores, collateral scores, and economic indicators. The sixth chapter discusses methodologies to convert scores and other pieces of information into default probabilities by using discrete-time hazard models. Discrete-time methods are relatively simple, and their estimation is robust and has become a standard in credit risk analytics. The seventh chapter builds further on this and estimates default probabilities using continuous-time hazard models. These models explicitly model the life cycle of a borrower and do not assume that observations for a given borrower are independent over time, which discrete-time hazard models often do. The eighth chapter discusses the estimation of default probabilities for low default portfolios, which is a particular concern for small portfolios in relation to large and/or specialized loans.

In the next section, we consider other important credit risk measures. In Chapter 9, we estimate default and asset correlations. We compute credit portfolio default rates and credit portfolio loss distributions using analytical and Monte Carlo simulation–based approaches, and show the reader how correlations can be estimated using internal data. The tenth chapter presents marginal loss given default (LGD) models and LGD models that condition on the selecting default event. The eleventh chapter discusses exposure at default (EAD) models, which are similar in structure to LGD models.

In the last part of the book, we discuss capstone modeling strategies that relate to the various models built in prior sections. Chapter 12 discusses Bayesian models, which allow the analyst to base the model estimation on the data set and prior information. The priors may stem from experts or information collected outside the analyzed system. We show how to implement Bayesian methods and where they might be most useful. Chapter 13 reviews concepts of model validation along with regulatory requirements, and Chapter 14 discusses stress testing of credit risk models by building credit risk measures conditional on stress tests of the macroeconomy, idiosyncratic information, or parameter uncertainty. Chapter 15 concludes the book.

The companion website (www.creditriskanalytics.net) offers examples of both real and simulated credit portfolio data to help you more easily implement the concepts discussed.

THE CURRENT REGULATORY REGIME: BASEL REGULATIONS

We take a closer look at the Basel I, Basel II, and Basel III Capital Accords. These are regulatory guidelines that were introduced in order for financial institutions to appropriately determine their provisions and capital buffers to protect against various risk exposures. One important type of risk is credit risk, and in this section we discuss the impact of these accords on the development of PD, LGD, and EAD credit risk models. The Basel regulations underly many aspects of credit risk analytics, and we will come back to the various issues in later chapters.

Regulatory versus Economic Capital

Banks receive cash inflow from various sources. The first important sources are bank deposits like savings accounts, term accounts, and so on. In return, the depositors receive a fixed or variable interest payment. Another source is the shareholders or investors who buy shares, which gives them an ownership in the bank. If the firm makes a profit, then a percentage can be paid to the shareholders as dividends. Both savings money and shareholder capital are essential elements of a bank's funding. On the asset side, a bank will use the money obtained to make various investments. A first investment, and part of a key banking activity, is lending. Banks will lend money to obligors so that they can finance the purchase of a house or a car, study, or go traveling. Other investments could be buying various market securities such as bonds or stocks.

Note that these investments always have a risk associated with them. Obligors could default and not pay back the loan, and markets could collapse and decrease the value of securities. Given the societal impact of banks in any economic system, they need to be well protected against the risks they are exposed to. Bank insolvency or failure should be avoided at all times, and the risks that banks take on their asset side should be compensated by appropriate liabilities to safeguard their depositors. These people should be guaranteed to always get their savings money back whenever they want it. Hence, a bank should have enough shareholder capital as a buffer against losses. In fact, we could include retained earnings and reserves and look at equity or capital instead. In other words, a well-capitalized bank has a sufficient amount of equity to protect itself against its various risks. Thus, there should be a direct relationship between risk and equity.

Usually, this relationship is quantified in two steps. First, the amount of risk on the asset side is quantified by a specific risk number. This number is then plugged into a formula that precisely calculates the corresponding equity and thus capital required. There are two views on defining both this risk number and the formula to be used.

The first view is a regulatory view whereby regulations such as Basel I, Basel II, and Basel III have been introduced to precisely define how to calculate the risk number and what formula to use. Regulatory capital is then the amount of capital a bank should have according to a regulation. However, if there were no regulations, banks would still be cognizant of the fact that they require equity capital for protection. In this case, they would use their own risk modeling methodologies to calculate a risk number and use their own formulas to calculate the buffer capital. This leads us to the concept of economic capital, which is the amount of capital a bank has based on its internal modeling strategy and policy. The actual capital is then the amount of capital a bank actually holds and is the higher of the economic capital and the regulatory capital. For example, Bank of America reports at the end of 2015 a ratio of total capital to risk-weighted assets using advanced approaches of 13.2 percent and a current regulatory minimum capital of 8 percent (this number will increase as Basel III is fully phased in). Therefore, the capital buffer is currently 5.2 percent.

Note that various types of capital exist, depending upon their loss-absorbing capacity. Tier 1 capital typically consists of common stock, preferred stock, and retained earnings. Tier 2 capital is of somewhat less quality and is made up of subordinated loans, revaluation reserves, undisclosed reserves, and general provisions. The Basel II Capital Accord also included Tier 3 capital, which consists of short-term subordinated debt, but, as we will discuss later, this has been abandoned in the more recent Basel III Capital Accord.

Basel I

The Basel Accords have been put forward by the Basel Committee on Banking Supervision. This committee was founded in 1974 by the G10 central banks. Nowadays, it counts 27 members. They meet regularly at the Bank for International Settlements (BIS) in Basel, Switzerland.

The first accord introduced was the Basel I Capital Accord, in 1988. As already mentioned, the aim was to set up regulatory minimum capital requirements in order to ensure that banks are able, at all times, to return depositors' funds. The Basel I Accord predominantly focused on credit risk and introduced the idea of the capital or Cooke ratio, which is the ratio of the available buffer capital and the risk-weighted assets. It put a lower limit on this ratio of 8 percent; in other words, the capital should be greater than 8 percent of the risk-weighted assets. We have been asked where this number comes from and speculate that it was an industry average at the time of implementation of the first Basel Accord. Changing the capital requirement by only a few percentage points is a challenging undertaking for large banks and takes many years. The capital could consist of both Tier 1 and Tier 2 capital, as discussed earlier.

In terms of credit risk, the Basel I Capital Accord introduced fixed risk weights dependent on the exposure class. For cash exposures, the risk weight was 0 percent, for mortgages 50 percent, and for other commercial exposures 100 percent. As an example, consider a mortgage of $100. Applying the risk weight of 50 percent, the risk-weighted assets (RWA) then become $50. This is the risk number we referred to earlier. We will now transform this into required capital using the formula that regulatory minimum capital is 8 percent of the risk-weighted assets. This gives us a required capital amount of $4. So, to summarize, our $100 mortgage should be financed by least $4 of equity to cover potential credit losses.

Although it was definitely a good step toward better risk management, the Basel I Accord faced some important drawbacks. First, the solvency of the debtor was not properly taken into account since the risk weights depended only on the exposure class and not on the obligor or product characteristics. There was insufficient recognition of collateral guarantees to mitigate credit risk. It also offered various opportunities for regulatory arbitrage by making optimal use of loopholes in the regulation to minimize capital. Finally, it considered only credit risk, not operational or market risk.

Basel II

To address the shortcomings of the Basel I Capital Accord, the Basel II Capital Accord was introduced. It consists of three key pillars: Pillar 1 covers the minimal capital requirement, Pillar 2 the supervisory review process, and Pillar 3 market discipline and disclosure. (See Exhibit 1.1.)

Exhibit 1.1 Pillars of the Basel II/III Regulation

Under Pillar 1, three different types of risk are included. Credit risk is the risk faced when lending money to obligors. Operational risk is defined as the risk of direct or indirect loss resulting from inadequate or failed internal processes, people, and systems, or from external events. Popular examples here are fraud, damage to physical assets, and system failures. Market risk is the risk due to adverse market movements faced by a bank's market position via cash or derivative products. Popular examples here are equity risk, currency risk, commodity risk, and interest rate risk. In this book, we will closely look at credit risk. The Basel II Capital Accord foresees three ways to model credit risk: the standard approach, the foundation internal ratings based approach, and the advanced internal ratings based approach. All boil down to building quantitative models for measuring credit risk.

All quantitative models built under Pillar 1 need to be reviewed by overseeing supervisors. This is discussed in Pillar 2. Key activities to be undertaken are the introduction of sound processes to evaluate risk, such as the internal capital adequacy assessment process (ICAAP) and supervisory monitoring.

Finally, once all quantitative risk models have been approved, they can be disclosed to the market. This is covered by Pillar 3. Here, a bank will periodically disclose its risk profile, and provide qualitative and quantitative information about its risk management processes and strategies to the market. The objective is to inform the investors and convince them that the bank has a sound and solid risk management strategy, which it hopes will result in a favorable rating, in order for the bank to attract funds at lower rates.

Basel III

The Basel III Capital Accord was introduced as a direct result of the GFC. It builds upon the Basel II Accord, but aims to further strengthen global capital standards. Its key attention point is a closer focus on tangible equity capital since this is the component with the greatest loss-absorbing capacity. It reduces the reliance on models developed internally by the bank and ratings obtained from external rating agencies. It also places a greater emphasis on stress testing. (See Exhibit 1.2.)

Exhibit 1.2 Basel III: Capital Requirements

Basel II

Basel III

Common Tier 1 capital ratio (common equity = shareholders' equity + retained earnings)

2% * RWA

4.5% * RWA

Tier 1 capital ratio

4% * RWA

6% * RWA

Tier 2 capital ratio

4% * RWA

2% * RWA

Capital conservation buffer (common equity)

—

2.5% * RWA

Countercyclical buffer

—

0%–2.5% * RWA

Note: RWA = risk-weighted assets.

For important banks, it stresses the need to have a loss-absorbing capacity beyond common standards. It puts a greater focus on Tier 1 capital consisting of shares and retained earnings by abolishing the Tier 3 capital introduced in Basel II, as it was deemed of insufficient quality to absorb losses. A key novelty is that it introduces a risk-insensitive leverage ratio as a backstop to address model risk. It also includes some facilities to deal with procyclicality, whereby due to a too cyclical nature of capital, economic downturns are further amplified. The Basel III Accord also introduces a liquidity coverage and net stable funding ratio to satisfy liquidity requirements. We will not discuss those further, as our focus is largely on credit risk. The new Basel III standards took effect on January 1, 2013, and for the most part will become fully effective by January 2019. Compared to the Basel II guidelines, the Basel III Accord has no major impact on the credit risk models themselves. It does, however, introduce additional capital buffers, as we will discuss in what follows.

The Tier 1 capital ratio was 4 percent of the risk-weighted assets (RWA) in the Basel II Capital Accord. It was increased to 6 percent in Basel III. The common Tier 1 capital ratio whereby common Tier 1 capital consists of common equity, which is common stock and retained earnings, but no preferred stock, was 2 percent of the risk-weighted assets in Basel II and is 4.5 percent of the risk-weighted assets in Basel III. A new capital conservation buffer is introduced that is set to 2.5 percent of the risk-weighted assets to be covered by common equity. Also, a countercyclical capital buffer is added, ranging between 0 and 2.5 percent of the risk-weighted assets.

As already mentioned, a non-risk-based leverage ratio is introduced that should be at least 3 percent of the assets and covered by Tier 1 capital. Very important to note here is that we look at the assets and not risk-weighted assets, as with the previous ratios. The assets also include off-balance-sheet exposures and derivatives. The idea here is to add this ratio as a supplementary safety measure on top of the risk-based ratios.

Basel III includes (relative to Basel II) the capital conservation buffer, the countercyclical capital buffer, and, if relevant, an additional capital ratio for systemically important banks.

Basel Approaches to Credit Risk Modeling