1;Preface;5 2;Contents;9 3;I. Statistical Methods to Develop Rating Models;16 3.1;1. Introduction;16 3.2;2. Statistical Methods for Risk Classification;16 3.3;3. Regression Analysis;17 3.4;4. Discriminant Analysis;18 3.5;5. Logit and Probit Models;19 3.6;6. Panel Models;22 3.7;7. Hazard Models;23 3.8;8. Neural Networks;24 3.9;9. Decision Trees;25 3.10;10. Statistical Models and Basel II;26 3.11;References;27 4;II. Estimation of a Rating Model for Corporate Exposures;28 4.1;1. Introduction;28 4.2;2. Model Selection;28 4.3;3. The Data Set;29 4.4;4. Data Processing;30 4.4.1;4.1. Data Cleaning;30 4.4.2;4.2. Calculation of Financial Ratios;31 4.4.3;4.3. Test of Linearity Assumption;32 4.5;5. Model Building;34 4.5.1;5.1. Pre-selection of Input Ratios;34 4.5.2;5.2. Derivation of the Final Default Prediction Model;36 4.5.3;5.3. Model Validation;37 4.6;6. Conclusions;39 4.7;References;39 5;III. Scoring Models for Retail Exposures;40 5.1;1. Introduction;40 5.2;2. The Concept of Scoring;41 5.2.1;2.1. What is Scoring?;41 5.2.2;2.2. Classing and Recoding;42 5.2.3;2.3. Different Scoring Models;44 5.3;3. Scoring and the IRBA Minimum Requirements;45 5.3.1;3.1. Rating System Design;45 5.3.2;3.2. Rating Dimensions;45 5.3.3;3.3. Risk Drivers;46 5.3.4;3.4. Risk Quantification;46 5.3.5;3.5. Special Requirements for Scoring Models;47 5.4;4. Methods for Estimating Scoring Models;47 5.5;5. Summary;51 5.6;References;52 6;IV. The Shadow Rating Approach - Experience from Banking Practice;54 6.1;1. Introduction;54 6.2;2. Calibration of External Ratings;57 6.2.1;2.1. Introduction;57 6.2.2;2.2. External Rating Agencies and Rating Types;58 6.2.3;2.3. Definitions of the Default Event and Default Rates;59 6.2.4;2.4. Sample for PD Estimation;60 6.2.5;2.5. PD Estimation Techniques;61 6.2.6;2.6. Adjustments;62 6.2.7;2.7. Point-in-Time Adaptation;63 6.3;3. Sample Construction for the SRA Model;65 6.3.1;3.1. Introduction;65 6.3.2;3.2. Sample Types;66 6.3.3;3.3. External PDs and Default Indicator;69 6.3.4;3.4. Weighting Observations;71 6.3.5;3.5. Correlated Observations;71 6.4;4. Univariate Risk Factor Analysis;72 6.4.1;4.1. Introduction;72 6.4.2;4.2. Discriminatory Power;73 6.4.3;4.3. Transformation;74 6.4.4;4.4. Representativeness;77 6.4.5;4.5. Missing Values;78 6.4.6;4.6. Summary;80 6.5;5. Multi-factor Model and Validation;81 6.5.1;5.1. Introduction;81 6.5.2;5.2. Model Selection;81 6.5.3;5.3. Model Assumptions;82 6.5.4;5.4. Measuring Influence;85 6.5.5;5.5. Manual Adjustments and Calibration;87 6.5.6;5.6. Two-step Regression;88 6.5.7;5.7. Corporate Groups and Sovereign Support;88 6.5.8;5.8. Validation;89 6.6;6. Conclusions;90 6.7;References;91 7;V. Estimating Probabilities of Default for Low Default Portfolios;94 7.1;1. Introduction;94 7.2;2. Example: No Defaults, Assumption of Independence;96 7.3;3. Example: Few Defaults, Assumption of Independence;98 7.4;4. Example: Correlated Default Events;101 7.5;5. Potential Extension: Calibration by Scaling Factors;104 7.6;6. Potential Extension: The Multi-period case;107 7.7;7. Potential Applications;112 7.8;8. Open Issues;112 7.9;9. Conclusions;113 7.10;References;114 7.11;Appendix A;115 7.12;Appendix B;117 8;VI. A Multi-Factor Approach for Systematic Default and Recovery Risk1;120 8.1;1. Modelling Default and Recovery Risk;120 8.2;2. Model and Estimation;121 8.2.1;2.1. The Model for the Default Process;121 8.2.2;2.2. The Model for the Recovery;122 8.2.3;2.3. A Multi-Factor Model Extension;123 8.2.4;2.4. Model Estimation;125 8.3;3. Data and Results;126 8.3.1;3.1. The Data;126 8.3.2;3.2. Estimation Results;129 8.4;4. Implications for Economic and Regulatory Capital;133 8.5;5. Discussion;137 8.6;References;138 8.7;Appendix: Results of Monte-Carlo Simulations;139 9;VII. Modelling Loss Given Default: A "Point in Time"- Approach;142 9.1;1. Introduction;142 9.2;2. Statistical Modelling;144 9.3;3. Empirical Analysis;146 9.3.1;3.1. The Data;146 9.3.2;3.2. Results;149 9.4;4. Conclusions;153 9.5;References;154 9.6;Appendix: Macro