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Preface
5
Contents
9
I. Statistical Methods to Develop Rating Models
16
1. Introduction
16
2. Statistical Methods for Risk Classification
16
3. Regression Analysis
17
4. Discriminant Analysis
18
5. Logit and Probit Models
19
6. Panel Models
22
7. Hazard Models
23
8. Neural Networks
24
9. Decision Trees
25
10. Statistical Models and Basel II
26
References
27
II. Estimation of a Rating Model for Corporate Exposures
28
1. Introduction
28
2. Model Selection
28
3. The Data Set
29
4. Data Processing
30
4.1. Data Cleaning
30
4.2. Calculation of Financial Ratios
31
4.3. Test of Linearity Assumption
32
5. Model Building
34
5.1. Pre-selection of Input Ratios
34
5.2. Derivation of the Final Default Prediction Model
36
5.3. Model Validation
37
6. Conclusions
39
References
39
III. Scoring Models for Retail Exposures
40
1. Introduction
40
2. The Concept of Scoring
41
2.1. What is Scoring?
41
2.2. Classing and Recoding
42
2.3. Different Scoring Models
44
3. Scoring and the IRBA Minimum Requirements
45
3.1. Rating System Design
45
3.2. Rating Dimensions
45
3.3. Risk Drivers
46
3.4. Risk Quantification
46
3.5. Special Requirements for Scoring Models
47
4. Methods for Estimating Scoring Models
47
5. Summary
51
References
52
IV. The Shadow Rating Approach – Experience from Banking Practice
54
1. Introduction
54
2. Calibration of External Ratings
57
2.1. Introduction
57
2.2. External Rating Agencies and Rating Types
58
2.3. Definitions of the Default Event and Default Rates
59
2.4. Sample for PD Estimation
60
2.5. PD Estimation Techniques
61
2.6. Adjustments
62
2.7. Point-in-Time Adaptation
63
3. Sample Construction for the SRA Model
65
3.1. Introduction
65
3.2. Sample Types
66
3.3. External PDs and Default Indicator
69
3.4. Weighting Observations
71
3.5. Correlated Observations
71
4. Univariate Risk Factor Analysis
72
4.1. Introduction
72
4.2. Discriminatory Power
73
4.3. Transformation
74
4.4. Representativeness
77
4.5. Missing Values
78
4.6. Summary
80
5. Multi-factor Model and Validation
81
5.1. Introduction
81
5.2. Model Selection
81
5.3. Model Assumptions
82
5.4. Measuring Influence
85
5.5. Manual Adjustments and Calibration
87
5.6. Two-step Regression
88
5.7. Corporate Groups and Sovereign Support
88
5.8. Validation
89
6. Conclusions
90
References
91
V. Estimating Probabilities of Default for Low Default Portfolios
94
1. Introduction
94
2. Example: No Defaults, Assumption of Independence
96
3. Example: Few Defaults, Assumption of Independence
98
4. Example: Correlated Default Events
101
5. Potential Extension: Calibration by Scaling Factors
104
6. Potential Extension: The Multi-period case
107
7. Potential Applications
112
8. Open Issues
112
9. Conclusions
113
References
114
Appendix A
115
Appendix B
117
VI. A Multi-Factor Approach for Systematic Default and Recovery Risk1
120
1. Modelling Default and Recovery Risk
120
2. Model and Estimation
121
2.1. The Model for the Default Process
121
2.2. The Model for the Recovery
122
2.3. A Multi-Factor Model Extension
123
2.4. Model Estimation
125
3. Data and Results
126
3.1. The Data
126
3.2. Estimation Results
129
4. Implications for Economic and Regulatory Capital
133
5. Discussion
137
References
138
Appendix: Results of Monte-Carlo Simulations
139
VII. Modelling Loss Given Default: A “Point in Time”- Approach
142
1. Introduction
142
2. Statistical Modelling
144
3. Empirical Analysis
146
3.1. The Data
146
3.2. Results
149
4. Conclusions
153
References
154
Appendix: Macroeconomic variables
155
VIII. Estimating Loss Given Default – Experiences from Banking Practice
158
1. Introduction
158
2. LGD Estimates in Risk Management
159
2.1. Basel II Requirements on LGD Estimates – a Short Survey
159
2.2. LGD in Internal Risk Management and Other Applications
160
3. Definition of Economic Loss and LGD
162
4. A Short Survey of Different LGD Estimation Methods
164
5. A Model for Workout LGD
166
6. Direct Estimation Approaches for LGD
168
6.1. Collecting Loss Data – the Credit Loss Database
169
6.2. Model Design and Estimation
171
7. LGD Estimation for Defaulted Exposures
185
8. Concluding Remarks
188
References
189
IX. Overview of EAD Estimation Concepts
192
1. EAD Estimation from a Regulatory Perspective
192
1.1. Definition of Terms
192
1.2. Regulatory Prescriptions Concerning the EAD Estimation
193
1.3. Delimitation to Other Loss Parameters
194
1.4. EAD Estimation for Derivative Products
196
2. Internal Methods of EAD Estimation
199
2.1. Empirical Models
199
2.2. Internal Approaches for EAD Estimation for Derivative Products
201
3. Conclusion
210
References
210
X. EAD Estimates for Facilities with Explicit Limits
212
1. Introduction
212
2. Definition of Realised Conversion Factors
213
3. How to Obtain a Set of Realised Conversion Factors
216
3.1. Fixed Time Horizon
216
3.2. Cohort Method
217
3.3. Variable Time Horizon
218
4. Data Sets (RDS) for Estimation Procedures
220
4.1. Structure and Scope of the Reference Data Set
221
4.2. Data Cleaning
222
4.3. EAD Risk Drivers
226
5. EAD Estimates
228
5.1. Relationship Between Observations in the RDS and the Current Portfolio
228
5.2. Equivalence between EAD Estimates and CF Estimates
228
5.3. Modelling Conversion Factors from the Reference Data Set
229
5.4. LEQ = Constant
232
5.5. Usage at Default Method with CCF = Constant (Simplified Momentum Method):
233
6. How to Assess the Optimality of the Estimates
234
6.1. Type of Estimates
234
6.2. A Suitable Class of Loss Functions
235
6.3. The Objective Function
236
7. Example 1
238
7.1. RDS
238
7.2. Estimation Procedures
243
8. Summary and Conclusions
250
References
251
Appendix A. Equivalence Between two Minimisation Problems
252
Appendix B. Optimal Solutions of Certain Regression and Optimization Problems
253
Appendix C. Diagnostics of Regressions Models
254
Appendix D. Abbreviations
257
XI. Validation of Banks’ Internal Rating Systems - A Supervisory Perspective
258
1. Basel II and Validating IRB Systems
258
1.1. Basel’s New Framework (Basel II)
258
1.2. Some Challenges
259
1.3. Provisions by the BCBS
262
2. Validation of Internal Rating Systems in Detail
265
2.1. Component-based Validation
265
2.2. Result-based Validation
271
2.3. Process-based Validation
274
3. Concluding Remarks
276
References
277
XII. Measures of a Rating’s Discriminative Power – Applications and Limitations
278
1. Introduction
278
2. Measures of a Rating System’s Discriminative Power
280
2.1. Cumulative Accuracy Profile
281
2.2. Receiver Operating Characteristic
283
2.3. Extensions
287
3. Statistical Properties of AUROC
290
3.1. Probabilistic Interpretation of AUROC
290
3.2. Computing Confidence Intervals for AUROC
292
3.3. Testing for Discriminative Power
294
3.4. Testing for the Difference of two AUROCs
295
4. Correct Interpretation of AUROC
298
References
300
Appendix A. Proof of (2)
300
Appendix B. Proof of (7)
301
XIII. Statistical Approaches to PD Validation
304
1. Introduction
304
2. PDs, Default Rates, and Rating Philosophy
304
3. Tools for Validating PDs
306
3.1. Statistical Tests for a Single Time Period
307
3.2. Statistical Multi-period Tests
313
3.3. Discussion and Conclusion
318
4. Practical Limitations to PD Validation
318
References
320
XIV. PD-Validation – Experience from Banking Practice
322
1. Introduction
322
2. Rating Systems in Banking Practice
323
2.1. Definition of Rating Systems
323
2.2. Modular Design of Rating Systems
323
2.3. Scope of Rating Systems
325
2.4. Rating Scales and Master Scales
325
2.5. Parties Concerned by the Quality of Rating Systems
327
3. Statistical Framework
328
4. Central Statistical Hypothesis Tests Regarding Calibration
331
4.1. Binomial Test
332
4.1.2. Normal Approximation of the Binomial Test
333
4.2. Spiegelhalter Test (SPGH)
334
4.3. Hosmer-Lemeshow-Test (HSLS)
335
4.4. A Test for Comparing Two Rating Systems: The Redelmeier Test
336
5. The Use of Monte-Carlo Simulation Technique
338
5.1. Monte-Carlo-Simulation and Test Statistic: Correction of Finite Sample Size and Integration of Asset Correlation
338
5.2. Assessing the Test Power by Means of Monte-Carlo-Simulation
344
6. Creating Backtesting Data Sets – The Concept of the Rolling 12- Month- Windows
348
7. Empirical Results
351
7.1. Data Description
351
7.2. The First Glance: Forecast vs. Realised Default Rates
352
7.3. Results of the Hypothesis Tests for all Slices
352
7.4. Detailed Analysis of Slice ‘Jan2005’
354
8. Conclusion
356
References
357
Appendix A
359
Appendix B
360
XV. Development of Stress Tests for Credit Portfolios
362
1. Introduction
362
2. The Purpose of Stress Testing
363
3. Regulatory Requirements
364
4. Risk Parameters for Stress Testing
366
5. Evaluating Stress Tests
368
6. Classifying Stress Tests
369
7. Conducting Stress Tests
373
7.1. Uniform Stress Tests
373
7.2. Sensitivity Analysis for Risk Factors
375
7.3. Scenario Analysis
375
8. Examples
378
9. Conclusion
381
References
383
Contributors
384
Index
388
Contributors
384
Index
388
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