Contents
I. Statistical Methods to Develop Rating Models ................................................1
Evelyn Hayden and Daniel Porath
1. Introduction ...............................................................................................1
2. Statistical Methods for Risk Classification ...............................................1
3. Regression Analysis ..................................................................................2
4. Discriminant Analysis ...............................................................................3
5. Logit and Probit Models............................................................................4
6. Panel Models .............................................................................................7
7. Hazard Models ..........................................................................................8
8. Neural Networks .......................................................................................9
9. Decision Trees.........................................................................................10
10. Statistical Models and Basel II ..............................................................11
References ...................................................................................................12
II. Estimation of a Rating Model for Corporate Exposures ............................13
Evelyn Hayden
1. Introduction .............................................................................................13
2. Model Selection.......................................................................................13
3. The Data Set ............................................................................................14
4. Data Processing .......................................................................................15
4.1. Data Cleaning ..................................................................................15
4.2. Calculation of Financial Ratios........................................................16
4.3. Test of Linearity Assumption ..........................................................17
5. Model Building .......................................................................................19
5.1. Pre-selection of Input Ratios............................................................19
5.2. Derivation of the Final Default Prediction Model ...........................21
5.3. Model Validation .............................................................................22
6. Conclusions .............................................................................................24
References ...................................................................................................24
III. Scoring Models for Retail Exposures ..........................................................25
Daniel Porath
1. Introduction .............................................................................................25
2. The Concept of Scoring...........................................................................26
2.1. What is Scoring?..............................................................................26
2.2. Classing and Recoding.....................................................................27
2.3. Different Scoring Models ................................................................29
3. Scoring and the IRBA Minimum Requirements .....................................30
3.1. Rating System Design......................................................................30
3.2. Rating Dimensions...........................................................................30
x Contents
3.3. Risk Drivers..................................................................................... 31
3.4. Risk Quantification.......................................................................... 31
3.5. Special Requirements for Scoring Models....................................... 32
4. Methods for Estimating Scoring Models................................................. 32
5. Summary ................................................................................................. 36
References................................................................................................... 37
IV. The Shadow Rating Approach – Experience from Banking Practice ...... 39
Ulrich Erlenmaier
1. Introduction............................................................................................. 39
2. Calibration of External Ratings............................................................... 42
2.1. Introduction ..................................................................................... 42
2.2. External Rating Agencies and Rating Types ................................... 43
2.3. Definitions of the Default Event and Default Rates......................... 44
2.4. Sample for PD Estimation ............................................................... 45
2.5. PD Estimation Techniques............................................................... 46
2.6. Adjustments ..................................................................................... 47
2.7. Point-in-Time Adaptation................................................................ 48
3. Sample Construction for the SRA Model................................................ 50
3.3. External PDs and Default Indicator ................................................. 54
4. Univariate Risk Factor Analysis.............................................................. 57
4.1. Introduction ..................................................................................... 57
4.2. Discriminatory Power...................................................................... 58
4.3. Transformation ................................................................................ 59
4.4. Representativeness........................................................................... 62
4.5. Missing Values ................................................................................ 63
4.6. Summary.......................................................................................... 65
5. Multi-factor Model and Validation ......................................................... 66
5.1. Introduction ..................................................................................... 66
5.2. Model Selection ............................................................................... 66
5.3. Model Assumptions ......................................................................... 67
5.4. Measuring Influence ........................................................................ 70
5.5. Manual Adjustments and Calibration .............................................. 72
5.6. Two-step Regression ....................................................................... 73
5.7. Corporate Groups and Sovereign Support ....................................... 73
5.8. Validation ........................................................................................ 74
6. Conclusions............................................................................................. 75
References................................................................................................... 76
V. Estimating Probabilities of Default for Low Default Portfolios ................. 79
Katja Pluto and Dirk Tasche
1. Introduction............................................................................................. 79
2. Example: No Defaults, Assumption of Independence............................. 81
3. Example: Few Defaults, Assumption of Independence........................... 83
4. Example: Correlated Default Events....................................................... 86
5. Potential Extension: Calibration by Scaling Factors ............................... 89
Contents xi
6. Potential Extension: The Multi-period case ............................................92
7. Potential Applications .............................................................................97
8. Open Issues .............................................................................................97
9. Conclusions .............................................................................................98
References ...................................................................................................99
Appendix A ...............................................................................................100
Appendix B ...............................................................................................102
VI. A Multi-Factor Approach for Systematic Default and Recovery Risk...105
Daniel Rösch and Harald Scheule
1. Modelling Default and Recovery Risk ..................................................105
2. Model and Estimation ...........................................................................106
2.1. The Model for the Default Process ................................................106
2.2. The Model for the Recovery ..........................................................107
2.3. A Multi-Factor Model Extension...................................................108
2.4. Model Estimation...........................................................................110
3. Data and Results....................................................................................111
3.1. The Data.........................................................................................111
3.2. Estimation Results .........................................................................114
4. Implications for Economic and Regulatory Capital ..............................118
5. Discussion .............................................................................................122
References .................................................................................................123
Appendix: Results of Monte-Carlo Simulations .......................................124
VII. Modelling Loss Given Default: A “Point in Time”-Approach...............127
Alfred Hamerle, Michael Knapp, Nicole Wildenauer
1. Introduction ...........................................................................................127
2. Statistical Modelling..............................................................................129
3. Empirical Analysis ................................................................................131
3.1. The Data.........................................................................................131
3.2. Results............................................................................................134
4. Conclusions ...........................................................................................138
References .................................................................................................139
Appendix: Macroeconomic Variables.......................................................140
VIII. Estimating Loss Given Default – Experiences from Banking
Practice...............................................................................................................143
Christian Peter
1. Introduction ...........................................................................................143
2. LGD Estimates in Risk Management ....................................................144
2.1. Basel II Requirements on LGD Estimates – a Short Survey..........144
2.2. LGD in Internal Risk Management and Other Applications..........145
3. Definition of Economic Loss and LGD.................................................147
4. A Short Survey of Different LGD Estimation Methods........................149
5. A Model for Workout LGD...................................................................151
xii Contents
6. Direct Estimation Approaches for LGD................................................ 153
6.1. Collecting Loss Data – the Credit Loss Database.......................... 154
6.2. Model Design and Estimation........................................................ 156
7. LGD Estimation for Defaulted Exposures ............................................ 170
8. Concluding Remarks............................................................................. 173
References................................................................................................. 174
IX. Overview of EAD Estimation Concepts .................................................... 177
Walter Gruber and Ronny Parchert
1. EAD Estimation from a Regulatory Perspective................................... 177
1.1. Definition of Terms ....................................................................... 177
1.2. Regulatory Prescriptions Concerning the EAD Estimation ........... 178
1.3. Delimitation to Other Loss Parameters.......................................... 179
1.4. EAD Estimation for Derivative Products ...................................... 181
2. Internal Methods of EAD Estimation.................................................... 184
2.1. Empirical Models ........................................................................ 184
2.2. Internal Approaches for EAD Estimation for Derivative Products 186
3. Conclusion ............................................................................................ 195
References................................................................................................. 195
X. EAD Estimates for Facilities with Explicit Limits..................................... 197
Gregorio Moral
1. Introduction........................................................................................... 197
2. Definition of Realised Conversion Factors ........................................... 198
3. How to Obtain a Set of Realised Conversion Factors ........................... 201
3.1. Fixed Time Horizon....................................................................... 201
3.2. Cohort Method............................................................................... 202
3.3. Variable Time Horizon .................................................................. 203
4. Data Sets (RDS) for Estimation Procedures.......................................... 205
4.1. Structure and Scope of the Reference Data Set ............................. 206
4.2. Data Cleaning ................................................................................ 207
4.3. EAD Risk Drivers.......................................................................... 211
5. EAD Estimates ...................................................................................... 213
5.1. Relationship Between Observations in the RDS and the Current
Portfolio................................................................................................ 213
5.2. Equivalence between EAD Estimates and CF Estimates............... 213
5.3. Modelling Conversion Factors from the Reference Data Set ........ 214
5.4. LEQ = Constant ............................................................................. 217
5.5. Usage at Default Method with CCF = Constant (Simplified
Momentum Method)............................................................................. 218

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