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

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