1. Sydney December 11, 2006 Seite 1 Lessons from implementations of Basel II and for Solvency II - Credit Rating Models for the Banking Book of Banks

2. Sydney December 11, 2006 | 24.06.2015Seite 2 Credit Risk Credit risk is key for the business model of a universal bank Hence, for core credit segments (retail, corporates, banks,…) rating models were established long before Basel II Rating systems actually in place were not implemented from scratch Typically, they are a hybrid models blending the existing ones with newer approaches (external data, KMV, RiskCalc, statistical models)

3. Sydney December 11, 2006 | 24.06.2015Seite 3 What‘s new: Definition of Default Institute’s View: Definition of Default according to the Rating Agencies and according to Basel II are almost identical Argumentation: Similar semantic definition Analysis of internally observed defaults delivers no statistical evidence of underestimating the PD (binomial test based on a sample containing 14 defaults)  indirect argument that definitions are similar

4. Sydney December 11, 2006 | 24.06.2015Seite 4 Definition of Default BaFin‘s View: Definition of Default according to the Rating Agencies and according to Basel II are different. Argumentation: Compared to banks, rating agencies are not able to observe all criteria belonging to the Basel II definition of default (asymmetric information) There even exist differences between the default definition of Rating agencies, e.g. Moody´s refers primarily to rated bonds rather than to other liabilities as for example bank loans

5. Sydney December 11, 2006 | 24.06.2015Seite 5 Definition of Default Analysis of the validation data: 400 datasets carry a default flag 53 of these include an external rating from these 53 the external rating reflects a default state in only 14 cases  The ratio 53/14 is an indication that there are differences between the default definitions

6. Sydney December 11, 2006 | 24.06.2015Seite 6 Definition of Default However, the ratio 53/14 overestimates the effect: Rating agencies may react after the institute has observed a default (time delay) Credit officer does not necessarily update the information about the external rating for internally defaulted obligors Further analysis performed by the institute suggests a scaling factor of about 1.2 between internal and external default rates for this sample.

7. Sydney December 11, 2006 | 24.06.2015Seite 7 Case Study: Module Corporates 1. initial situation model developing process (MDP) 2. design of rating system „Corporates“ 2.1. pooling standards 2.2. quantitative part 2.3. qualitative part 2.4. creditworthiness rating 2.5. support / burden and transfer stop 3. validation

8. Sydney December 11, 2006 | 24.06.2015Seite 8 1. Initial Situation MDP basic proceeding pool project data used: quantitative ratios out of annual balance sheet and qualitative ratios (questionnaires), default information provided data transformation on risk points between 0 and 100. Higher value means higher risk. determinating weights by means of which these risk points are included in the total score (using logistical regressions and adjustment of experts) estimation of PD allocated to a score with logistical regression classifying of these individual PD in a master scale

9. Sydney December 11, 2006 | 24.06.2015Seite 9 data base for model development and validation

10. Sydney December 11, 2006 | 24.06.2015Seite 10 1. initial situation MDP poor data quality of ratios ratios out of annual balance sheet are characterized by numerous and extreme outliers in approx. 30% of all observations at least one ratio is outside of the 1% or 99% quantile ratios of the qualitative section are in some cases significantly beyond the respective range -examples are given on the subsequent pages

11. Sydney December 11, 2006 | 24.06.2015Seite 11 Bagplot of Balance sheet data

12. Sydney December 11, 2006 | 24.06.2015Seite 12 Equity capital rate 0,5% to 99,5% quantile

13. Sydney December 11, 2006 | 24.06.2015Seite 13 fixing five parameters (0,25,50,75,100) and the ranges of value allocated to these five parameters generation of clusters depending on regions and sectors Clustering has a strong impact on model developing processes Clustering is based on profound expert know-how (e.g. external consultancy) especially for foreign clusters: external experts  regular check of clustering required Transformation of the quantitative ratios in risk points

14. Sydney December 11, 2006 | 24.06.2015Seite 14 equity capital rate according to clustering high absolute frequency with 100 risk points for non-defaulted borrowers

15. Sydney December 11, 2006 | 24.06.2015Seite 15 2.1. Pooling Standards 1. population switching to gross and net liability according to economic point of view method of pool partner is unknown 2. completeness of data set different definitions of input box of pool partners (optional or compulsory entry) can result in different filling rate of pool input. example: key figure „short-range supplier credit target“  obliging guidelines for an agreement on a consistent proceeding for all pool partners are meaningful

16. Sydney December 11, 2006 | 24.06.2015Seite 16 Analyses by BaFin reconstruction of modeling and score computation on basis of the sample used for the development Given the data and the model as described in the documentation the error was about 100% Analog model development and score computation using own estimation of parameters of logistical regression maintaining data transformation (risk points and according limits) analysis of impact on allocation of borrowers in rating grades and estimation of PD.

17. Sydney December 11, 2006 | 24.06.2015Seite 17 Re-traceability of calculations estimation of parameters could be traced back by means of documentations and subsequent questioning (relative deviation under 0,1%) estimation of parameters for the quantitative ratios are sensitive with regard to different treatment of missing values (relative deviation of more than 20% using the substitution method applied for validation) estimation of parameters for the qualitative ratios are sensitive with regard to outliers, especially beyond the interval [0,100] (relative deviation of more than 15% for significant parameters, more than 50% for less significant ones) influence of individual extreme outliers on the coefficients used for the estimation of PD: 1,5% on the intercept, 2,5% on the slope (3544 observations, relative deviation)

18. Sydney December 11, 2006 | 24.06.2015Seite 18 comparison bank’s Model with the purely statistical model

19. Sydney December 11, 2006 | 24.06.2015Seite 19 Difference of rating grades impacts on total borrowers in- sample: Expert-driven model assigns worser rating grades impacts on defaulted borrowers: Expert-driven model assigns too optimistic rating grades

20. Sydney December 11, 2006 | 24.06.2015Seite 20 Comparison of discriminatory power variations of discriminatory power can be mainly observed in the lower areas for bad borrowers

21. Sydney December 11, 2006 | 24.06.2015Seite 21 estimation of PD impacts on the determined PD estimation of parameter with logistical regression yields different results  different functional relation between score and PD: expert- driven model more conservative für low scores (good borrowers), to progressive for higher scores (bad borrowers) different distribution of scores different distribution of PD small variation in average, but strong impact on single borrowers

22. Sydney December 11, 2006 | 24.06.2015Seite 22 conclusions Due to the high importance of qualitative ratios, quality assurance of inputs is treated with special importance. The influence of experience of credit experts on the different steps of modeling should be checked within validation. In-sample shows the expert-based model weaknesses especially with regard to the allocation of worse borrowers. Analog analysis should be executed out-of-sample and out-of-time.

23. Sydney December 11, 2006 | 24.06.2015Seite 23 Data for model development process and validation

24. Sydney December 11, 2006 | 24.06.2015Seite 24 Data

25. Sydney December 11, 2006 | 24.06.2015Seite 25 Summary Statistics

26. Sydney December 11, 2006 | 24.06.2015Seite 26 B 1 : Equity Capital Ratio

27. Sydney December 11, 2006 | 24.06.2015Seite 27 Boxplot of equity capital ratio C

28. Sydney December 11, 2006 | 24.06.2015Seite 28 Trimming of Variable B 1

29. Sydney December 11, 2006 | 24.06.2015Seite 29 Boxplot of equity capital ratio C γ

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32. Sydney December 11, 2006 | 24.06.2015Seite 32 Estimates by QRM

33. Sydney December 11, 2006 | 24.06.2015Seite 33 Influence of an Outlier

34. Sydney December 11, 2006 | 24.06.2015Seite 34 Descriptive analysis of default probability mean value and standard deviation mean value as per model: 0.95% standard deviation as per model: 2.09% mean value with expert influence: 0.96% standard deviation with expert influence: 1.84% Deviations (Model - expert-driven model) mean value: -0.0015% minimum: -22.23% maximum: 23.54%

35. Sydney December 11, 2006 | 24.06.2015Seite 35 estimation of default probability effects on the calculated default probability estimation of parameters by means of logistic regression is providing other results for coecients – another function connecting score and default probability: PD curve of expert-driven model proves to be more conservative in lower score area (good borrower)and more progressive in the upper score area (bad borrowers) other distribution of scores – other distribution of default probability high impact on individual borrowers

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47. Sydney December 11, 2006 | 24.06.2015Seite 47 analysis of defaults

48. Sydney December 11, 2006 | 24.06.2015Seite 48 influence of expertise on the model The expertise of credit department has a vital influence on the model building process: following the existing model → model selection selection of the analysed variables → selection of variables determination of cluster and class limits for the allocation of risk points → data transformation determination of weights of quantitative variables determination of weights of quantitative partial score and the qualitative variables → determination of score function definition of qualitative variables, evaluation of qualitative variables → subjective evaluation

49. Sydney December 11, 2006 | 24.06.2015Seite 49 Analysis of the resulting effects tracing back the model building process and score computation on basis of the data set submitted to the subvisors analog model building process and score computation using the parameter estimation of the logistic regression and maintaining the risk points and class limits) analysis of eects of the assignment of rating classes to borrowers and the estimation of default probability

50. Sydney December 11, 2006 | 24.06.2015Seite 50 Some conclusions Due to the high importance of the qualitative variables and the sensitivity of parameter estimation concerning outliers, quality assurance of input is attached special importance. The influence of expertise of credit departments on the dierent steps of modeling should be checked within the validation process. In-Sample shows the expert-driven model weaknesses especially with regard to allocation of bad borrowers. analogue analysis should be checked out-of-sample and out-of- time.