Transcript Definition of Default

Lessons from implementations of Basel II
and for Solvency II
Credit Rating Models for the Banking Book of
Banks
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Credit Risk
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Credit risk is key for the business model of a universal
bank
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Hence, for core credit segments (retail, corporates,
banks,…) rating models were established long before
Basel II
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Rating systems actually in place were not implemented
from scratch
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Typically, they are a hybrid models blending the existing
ones with newer approaches (external data, KMV,
RiskCalc, statistical models)
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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
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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
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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
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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.
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Case Study: Module Corporates
1. initial situation model developing process (MDP)
2. design of rating system „Corporates“
2.1.
2.2.
2.3.
2.4.
2.5.
pooling standards
quantitative part
qualitative part
creditworthiness rating
support / burden and transfer stop
3. validation
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1. Initial Situation MDP
basic proceeding
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pool project
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data used: quantitative ratios out of annual balance sheet and
qualitative ratios (questionnaires), default information provided
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data transformation on risk points between 0 and 100. Higher
value means higher risk.
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determinating weights by means of which these risk points are
included in the total score (using logistical regressions and
adjustment of experts)
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estimation of PD allocated to a score with logistical regression
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classifying of these individual PD in a master scale
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data base for model development and validation
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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
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Bagplot of Balance sheet data
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Equity capital rate 0,5% to 99,5% quantile
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Transformation of the quantitative ratios in risk
points
• 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
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equity capital rate according to clustering
high absolute frequency
with 100 risk points for
non-defaulted borrowers
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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
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Analyses by BaFin
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reconstruction of modeling and score computation on basis of the
sample used for the development
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Given the data and the model as described in the documentation
the error was about 100%
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Analog model development and score computation using own
estimation of parameters of logistical regression maintaining data
transformation (risk points and according limits)
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analysis of impact on allocation of borrowers in rating grades and
estimation of PD.
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Re-traceability of calculations
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estimation of parameters could be traced back by means of
documentations and subsequent questioning (relative deviation
under 0,1%)
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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)
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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)
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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)
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comparison bank’s Model with the purely
statistical model
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Difference of rating grades
impacts on total borrowers insample:
Expert-driven model assigns
worser rating grades
impacts on defaulted borrowers:
Expert-driven model assigns too
optimistic rating grades
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Comparison of discriminatory power
variations of discriminatory power
can be mainly observed in the
lower areas for bad borrowers
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estimation of PD
impacts on the determined PD
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estimation of parameter with logistical regression yields different
results  different functional relation between score and PD: expertdriven model more conservative für low scores (good borrowers), to
progressive for higher scores (bad borrowers)
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different distribution of scores
 different distribution of PD
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small variation in average, but strong impact on single borrowers
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conclusions
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Due to the high importance of qualitative ratios, quality assurance of
inputs is treated with special importance.
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The influence of experience of credit experts on the different steps of
modeling should be checked within validation.
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In-sample shows the expert-based model weaknesses especially with
regard to the allocation of worse borrowers.
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Analog analysis should be executed out-of-sample and out-of-time .
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Data for model development process and
validation
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Data
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Summary Statistics
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B1 : Equity Capital Ratio
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Boxplot of equity capital ratio C
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Trimming of Variable B1
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Boxplot of equity capital ratio Cγ
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Estimates by QRM
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Influence of an Outlier
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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%
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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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analysis of defaults
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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
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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
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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-oftime.
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