Credit Risk Management
Dr. Lukas Prorokowski
Credit Risk Management
About me:
Dr Lukas Prorokowski
Deputy Head of Validation at
Banque International a
Luxembourg
Lukas.Prorokowski@gmail.com
Lukas Prorokowski
About the unit:
This unit will be divided into the
following blocks:
• Theory
• Practitioner’s Insights
• Case Studies
• Practical Exercises (excel)
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model risk
managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested (with case studies)?
Credit Risk Management
• What is Credit Risk management?
• It is a continuous process of:
• Identifying risk
• Analysing risk
• Modelling risk
• Mitigating risk
• Monitoring risk
• Predicting risk
Identify
Analyse
Quantify
Mitigate
Monitor
Credit Risk Management
• Mitigation of Credit Risk
In the banking practice, credit risk mitigation constitutes an important element of risk
management complementing the core credit risk modelling and estimation, counterparty
credit quality checks and setting the risk appetite.
There are several credit risk mitigation techniques among which applying the collateral
haircuts is most prominent across the banking industry:
• Holding collateral as security against granted credit lines;
• Transferring risk to special purpose vehicles;
• Implementing credit limits;
• Netting and collateral arranging for exposures from derivative instruments.
Credit Risk Management
• Mitigation of Credit Risk
What is the most common collateral accepted by banks?
• Cash & Gold
• Bonds (fixed income instruments)
• Funds
• Equities
Three Lines of Defence Model
• Three Lines of Defence
Credit Risk Management is conducted through the 3 Lines of Defence model. All lines are
coordinating tasks to set up the governance framework.
• Credit Risk Modelling Team
• Credit Risk Data Management Team
• Model Implementation Team
• Model Risk Manager (Credit Risk Unit)
First Line of
Defence
• Model Validation (Independent Model
Validation Unit)
Second Line
of Defence
• Internal Audit
Third Line of
Defence
CRO
Three Lines of Defence Model
• First Line of Defence
• Credit Risk Modellers (Credit Risk Modelling Team):
• are responsible for all model development activities comprising methodology, design and prototype
construction. They provide the documentation throughout the development and keep it updated with
changes in the model.
• test the credit risk model, check its accuracy and identify its limitations → inform the Model User on
the model’s usage limits.
• Manage, with the support of the Model Implementation Team, the model implementation → define
the specifications, review the planning and the implementation and oversee the model testing.
• Keeping the Model Risk Manager (Credit Risk Unit) informed about the evolution of the credit risk
model (e.g. recalibration, redevelopment, change in scope).
Model
Documentation
Modelling
Team
Review Model
Documentation
Validation
Team
Three Lines of Defence Model
• First Line of Defence
• Credit Risk Data Management Teams:
• The input data is one component of a credit risk model, and the Data Management Team is
responsible for the activities related to the data quality. With the support of the Credit Risk Modelling
Team, which identifies the required data for the model, the Management Team is responsible for the
assessment of data completeness and appropriateness with the model design.
• Manage, in close collaboration with the Model Implementation Team, the implementation of the data
including: the source, collection, storage, validity and traceability of the data.
• Keep the Senior Management (CRO) informed about data quality and improvement areas.
• Monitor the Data Quality and tak the appropriate actions to maintain a high level of data quality.
Data Quality
Assurance
Data
Team
Review Model
Data
Validation
Team
Three Lines of Defence Model
• First Line of Defence
• Model Implementation Teams:
• The Model Implementer is responsible for ensuring that the correct implementation takes place,
whilst the Model Developer (Credit Risk Modelling Team) remains accountable for the end-results.
• Model implementation is usually managed on a day-to-day basis by IT based on the Model Developer’s
requirements. For models which do not require IT, the role of Model Implementer can be assumed by
the Model Developer.
• Manage the dataflow between all involved systems. Implement the model data in accordance with the
Model Data Manager’s (Credit Risk Data Management Team) specifications.
• Ensure that the access rights to the model implementation and data source are securely managed.
Grant access to
systems
Implementation
Team
Review Credit
Rating Systems
Validation
Team
Three Lines of Defence Model
• First Line of Defence
• Model User:
• Responsible to operate the model in a manner consistent with the approved model documentation.
• Assists the Model Developer in defining the purpose of the model
• Informs the Credit Risk Modelling Team of exceptions and overrides.
• Keeps the Senior Manager (CRO) informed about the quality and deficiencies of the model output.
• Reports unexpected model behaviour or deficiencies to the Credit Risk Modelling Team.
• Provides and maintains up-to-date procedures for model usage.
Overrides &
Feedback
Model
User
Overrides
&
Feedback
Modelling
Team
Analyse
Overrides
Validation
Team
Three Lines of Defence Model
• First Line of Defence
• Model Risk Manager (Credit Risk Unit – CRU):
• The Model Risk Manager is responsible for establishing credit risk management standards.
• Oversees the compliance with the Model Risk Management policies and procedures.
• Maintains the model inventory tool.
• Provides information to the Senior Management (CRO) about significant source of model risk, model
development flaws and implementation failures.
• Manages the model’s versioning, especially ensuring that the correct version of the model is properly
disseminated.
• Communicates with other team of the First and Second Line of Defence.
Latest version of
model
document
CRU
Review Model
Document
Validation
Team
Obligation
16
Obligation 16:
The Supervised Entity shall ensure that
the process for drafting the model
development report is transparent and
valid. If changes to the model
development report are necessary after
the deliberations and model approval at
IRSPC, the correct version of the report
shall be re-presented to IRSPC and RPC.
The IRSPC and/or RPC shall explicitly
require a re-presentation of the report at
the committee and include an action
point in the minutes.
Deadline
31.12.17
Status
R
Response:
No Versioning of the Modelling Documentation
0.X
• Draft in development
1.X
• Final Draft
• Out for comment
2.X
• Under review
3.X
• Out for Risk Policy Committee
(RPC) approval
4.X
• Post PRC/MRC
Three Lines of Defence Model
• First Line of Defence
• Model Owner:
• The Model Owner is responsible for many aspects of the model lifecycle and ensures that the model is
properly developed, implemented, documented and used.
• Ensures that the credit risk model has undergone appropriate validation and approval processes,
prompt identification of model change.
• Model Owners should be sufficiently senior within the Bank to be able to interact with the other
actors concerned throughout the model lifecycle.
• The role of Model Owner will be usually assumed by the Model Risk Manager.
Model
Owner
Model
Risk
Manager
Three Lines of Defence Model
• Second Line of Defence
• Internal Model Validation (Independent Model Validation Unit)
• As a second line of defence, Internal Model Validation is responsible for independently verifying that
the model proposed for use by the Credit Risk Modelling Team is fit for its intended purpose.
• Internal Model Validation has explicit authority and independence to challenge related stakeholders
and to present issues and highlight deficiencies.
• Internal Model Validation is responsible for validating the key aspects of models:
Model Design Data Quality
Model
Implementation
Model
Performance
Model Validation Governance Process
Three Lines of Defence Model
• Third Line of Defence
• Internal Audit
• Internal Audit is the third line of defence, and is independent from any other functions.
• its role is not to duplicate model risk management activities but rather to ensure that the first two
lines of defence are operating effectively.
• Reviews model validation reports and confirming their compliance with the Validation Policy.
• Confirms that the model governance is compliant with the Bank’s expectations and the applicable
regulatory requirements (especially the independence of the validation function).
• Reviews annually the framework for Pillar I and IFRS9 models and their related parameters (including
compliance with all applicable requirements).
Validation
Report
Validation
Team
Review
Validation
Report
Internal
Audit
Three Lines of Defence Model
• Committees
• Several Committees are established to consolidate the Model Risk Governance and to
provide adequate follow-up and decisions:
• Approves the Model Risk Governance Framework
Board of Directors
• Oversees Model Risk and Model Performance
Board Risk Committee
• Ensures the comprehensiveness and the consistency of the policies
and procedures related to credit risk model concernsRisk Policy Committee
• Oversees the lifecycle of each model, approves validation reports
and performance reportsModel Risk Committee
• Makes the final decision during the MRC meeting in case of a
disagreementEscalation Committee
• Monitors the use of credit risk model and reviews the rating process
Rating Committee
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model risk
managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested (with case studies)?
Regulatory Framework for Credit Risk
• Basel II:
• credit risk measurement approach:
Standardised
• Use of regulatory
prescribed weights for
exposure classes;
• Over-reliance on
agency ratings;
• Some flexibility on the
choice of risk weight
assignment.
FIRB (Foundation)
• Use of own models for
Probability of Default
(PD) – subject to the
regulatory approval;
• Use of regulatory
prescribed LGD models
(e.g. regulatory floors).
AIRB (advanced)
• Use of own models for:
• PD
• LGD
• EAD
• Credit risk models are
subject to regulatory
review.
MODEL COMPLEXITY
Standardised Approach
The Basel Committee allows for two approaches of calculating sovereign risk weights to be made:
• In the first case, banks can rely on external ratings mapped to specific risk weights.
• In the second case, banks can use scores assigned to sovereign exposures by Export Credit Agencies (ECA). However, the
methodology of calculating the ECA’s scores must be aligned to the OECD-agreed principles and approved by the
supervisor.
• Against this backdrop, only a limited number of sovereigns are assigned the ECA’s scores. On the other hand, there are
sovereign exposures that lack external ratings.
Reliance on External Agency Ratings:
Rating: AAA to AA- A+ to A- BBB+ to BBB- BB+ to B- Below B- Fallback
Risk Weight: 0% 20% 50% 100% 150% 100%
Reliance on ECA’s Scores:
Score: 0 to 1 2 3 4 to 6 7
Risk Weight: 0% 20% 50% 100% 150%
Standardised Approach
Scenario Script Description
Scenario 1 S1 Bank relies only on the agency ratings when calculating risk weights
Scenario 2 S2 Bank relies only on the ECA’s scores when calculating risk weights
Scenario 3 S3 Bank toggles between the agency ratings and ECA’s scores to achieve the lowest risk weights
(liberal approach)
Scenario 4 S4 Bank toggles between the agency ratings and ECA’s scores to achieve the highest risk weight
(conservative approach)
Scenario 5 S5 Smoothed approach proposed in this paper
Aggregated results of the capital
charges achievable under different
scenarios: S1 – use of agency ratings;
S2 – use of ECA’s scores; S3- liberal
approach; S4- conservative approach;
S5- smoothed approach. The currency
used in this simulation is EURO. The
original exposure to the entire data
sample is EUR 137,000.
137 000
119 700
145 600
116 400
148 900
132 650
0
20 000
40 000
60 000
80 000
100 000
120 000
140 000
160 000
Original
Exposure
Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5
Risk Weighted Capital (EUR)
Regulatory Framework for Credit Risk
• Basel II:
• Our focus:
• Apart from Basel II, what are other regulations that encompass credit risk?
AIRB (advanced)
• Use of own models for:
• PD
• LGD
• EAD
• Credit risk models are subject
to regulatory review.
Regulatory Framework for Credit Risk
CRR
CRD IV
TRIM
New
Definition
of Default
EBA GL
AnaCredit
IFRS 9
BCBS 239
EBA’s Guidelines on PD estimation, LGD estimation
and the treatment of defaulted exposures
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Exposure Assignment
Art.
173(1)(a) of
Reg. (EU)
575/2013
For exposures to corporates, where an
institution uses the PD/LGD approach,
assignment of exposures and periodic
reviews of assignments shall be
completed or approved by an
independent party that does not
directly benefit from decisions to
extend the credit.
R
• Check if the Validation Report goes through the
relevant Committee (in this case: MRC) for the
final approval.
• Check the composition of the Committee is
made in a way that does not directly benefit
from decisions to extend the credit.
Art.
173(1)(c) of
Reg. (EU)
575/2013
The institution shall have an effective
process to obtain and update relevant
information on obligor characteristics
that affect PDs.
R
• Check if the relevant databases feed correctly to
the model and are maintained by the Model
Implementation Team and supervised by the
Credit Risk Data Management Team.
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Use of Model
Art. 174(a)
of
Reg. (EU)
575/2013
The model shall have good predictive power
and capital requirements shall not be
distorted as a result of its use. The input
variables shall form a reasonable and
effective basis for the resulting predictions.
The model shall not have material biases.
£
How can you prove that a credit risk model
has good predictive power?
Art. 174(b)
of
Reg. (EU)
575/2013
The institution shall have in place a process
for vetting data inputs into the model, which
includes an assessment of the accuracy,
completeness and appropriateness of the
data.
£
Who provides data quality assurance?
Who validates the data quality report?
Art. 174(c)
of
Reg. (EU)
575/2013
The data used to build the model shall be
representative of the population of the
institution's actual obligors or exposures. £
Who checks data representativeness, data
completeness and data accuracy?
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Use of Model
Art. 174(a)
of
Reg. (EU)
575/2013
The model shall have good predictive power
and capital requirements shall not be
distorted as a result of its use. The input
variables shall form a reasonable and
effective basis for the resulting predictions.
The model shall not have material biases.
R
How can you prove that a credit risk model
has good predictive power?
• Compare realised vs. predicted
• Calibration backtesting
• Override analysis
Art. 174(b)
of
Reg. (EU)
575/2013
The institution shall have in place a process
for vetting data inputs into the model, which
includes an assessment of the accuracy,
completeness and appropriateness of the
data.
R
Who provides data quality assurance?
• Data Management Team
Who validates the data quality report?
• Validation Team
Art. 174(c)
of
Reg. (EU)
575/2013
The data used to build the model shall be
representative of the population of the
institution's actual obligors or exposures. R
Who checks data representativeness, data
completeness and data accuracy?
• Data Management Team
• Validation Team
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Documentation of Rating System
Art. 175(2)
of
Reg. (EU)
575/2013
The institution shall document the rationale
for and analysis supporting its choice of
rating criteria.
£
Where do you look for the documentation of
the rationale for the methodological choices
of the credit risk model?
Art.
175(4)(b) of
Reg. (EU)
575/2013
Where the institution employs statistical
models in the rating process, the institution
shall document their methodologies. This
material shall establish a rigorous statistical
process including out-of-time and out-ofsample
performance tests for validating the
model.
£
The out-of-time (OOT) sample is the sample
that includes additional years of observations
to the portfolio that was used for model
development.
Why model validation should be performed on
OOT sample?
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Documentation of Rating System
Art. 175(2)
of
Reg. (EU)
575/2013
The institution shall document the rationale
for and analysis supporting its choice of
rating criteria.
R
Where do you look for the documentation of
the rationale for the methodological choices
of the credit risk model?
Model Development Document
Art.
175(4)(b) of
Reg. (EU)
575/2013
Where the institution employs statistical
models in the rating process, the institution
shall document their methodologies. This
material shall establish a rigorous statistical
process including out-of-time and out-ofsample
performance tests for validating the
model.
R
The out-of-time (OOT) sample is the sample
that includes additional years of observations
to the portfolio that was used for model
development.
Why model validation should be performed on
OOT sample?
To capture changes to the portfolio of obligors
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Data Maintenance
Art.
176(1)(a) of
Reg. (EU)
575/2013
For exposures to corporates, where an
institution uses the PD/LGD approach set out
in Article 155(3), institutions shall collect and
store: complete rating histories on obligors
and recognised guarantors.
£
Where do you store complete ratings?
Rating System Database maintained by the
Model Implementation Team.
What are the common issues with storing
complete rating histories?
A common issue is that a database is
producing missing values for the rating and
indicating that an entity in non-rated, where in
fact the entity has a final rating.
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Overall Requirements for Estimation
Art.
179(1)(a) of
Reg. (EU)
575/2013
In quantifying the risk parameters to be
associated with rating grades or pools,
institutions shall apply the following
requirements: an institution's own estimates
of the risk parameters PD, LGD, conversion
factor and EL shall incorporate all relevant
data, information and methods. The
estimates shall be derived using both
historical experience and empirical evidence,
and not based purely on judgemental
considerations. The estimates shall be
plausible and intuitive and shall be based on
the material drivers of the respective risk
parameters. The less data an institution has,
the more conservative it shall be in its
estimation.
R
The Validation Team should confirm that:
• A rating is obtained via a statistical and
quantitative part, and an expert,
qualitative/judgmental part.
• There is enough historical data containing
default events to make meaningful
conclusions.
• The model is reactive to macro-conditions
and stressed risk parameters.
• The model discriminates well between
good and bad obligors.
Regulatory Framework for Credit Risk
• CRR:
Regulation Issue
Compliance
Check
Evidence
Validation
Art. 185(a)
of
Reg. (EU)
575/2013
Institutions shall have robust systems in place
to validate the accuracy and consistency of
rating systems, processes, and the estimation
of all relevant risk parameters. The internal
validation process shall enable the institution
to assess the performance of internal rating
and risk estimation systems consistently and
meaningfully.
R
A credit risk model is subject to a robust
system of validation:
• initial validation upon development;
• backtesting validation on an annual basis;
• annual review.
Art. 185(b)
of
Reg. (EU)
575/2013
Institutions shall regularly compare realised
default rates with estimated PDs for each
grade and, where realised default rates are
outside the expected range for that grade,
institutions shall specifically analyse the
reasons for the deviation.
R
The realised vs. predicted PD estimates are
regularly compared and analysed through:
• backtesting on an annual basis;
• backtesting validation on an annual basis:
• annual review.
Regulatory Framework for Credit Risk
Regulatory Framework for Credit Risk
• TRIM:
Regulation Issue
Compliance
Check
Evidence
Data Requirements
Art.
7(a)(b)(c)
of
TRIM
Institutions are expected to establish a
complete framework which assesses the
quality of the data considered for use in the
modelling and risk quantification process
including:
(a) Its completeness and appropriateness;
(b) The soundness of the process for vetting
data inputs (especially with regard to missing
data, outliers and categorical data);
(c) The representativeness of modelling data.
£
Who assesses data completeness and
appropriateness?
Who assesses the soundness of the process
for vetting data inputs and the
representativeness of the modelling data?
Regulatory Framework for Credit Risk
• TRIM:
Regulation Issue
Compliance
Check
Evidence
Data Requirements
Art.
7(a)(b)(c)
of
TRIM
Institutions are expected to establish a
complete framework which assesses the
quality of the data considered for use in the
modelling and risk quantification process
including:
(a) Its completeness and appropriateness;
(b) The soundness of the process for vetting
data inputs (especially with regard to missing
data, outliers and categorical data);
(c) The representativeness of modelling data.
R
Who assesses data completeness and
appropriateness?
• Data Management Team
• Validation Team
Who assesses the soundness of the process
for vetting data inputs and the
representativeness of the modelling data?
• Validation Team
Regulatory Framework for Credit Risk
• TRIM:
Regulation Issue
Compliance
Check
Evidence
Drivers for risk differentiation
Art. 18
of
TRIM
Institutions should ensure that there are no
overlaps in the range of application of
different models and that each obligor or
facility to which the IRB approach should be
applied can clearly be assigned to one
particular rating system.
R
CASE: Slotting Model
Within the corporate exposure class,
institutions shall separately identify as
specialised lending exposures:
• (a) the exposure is to an entity which was
created specifically to finance or operate
physical assets(SPV);
• (b) the contractual arrangements give the
lender a substantial degree of control over
the assets and the income that they
generate;
• (c) the primary source of repayment of the
obligation is the income generated by the
assets being financed.
Regulatory Framework for Credit Risk
• TRIM on Internal Validation:
• In the context of rating systems, the term “validation” encompasses a range of processes
and activities that contribute to an assessment of whether ratings adequately
differentiate risk, and whether estimates of risk components appropriately characterise
the relevant aspects of risk.
• The main role of the internal validation function is to ensure an adequate quality of the
rating systems and their compliance with the relevant requirements.
• The validation process and content are expected to be consistent across rating systems.
However, it is not expected that institutions develop a unique validation process, as the
relevant tests may differ from one rating system to another.
• The institution should ensure that any statistical tests or confidence intervals used by the
bank are appropriate from a methodological point of view (or sufficiently conservative).
• Overrides should not only be monitored but also assessed as part of the validation
process on an annual basis.
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model risk
managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested (with case studies)?
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model risk
managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested (with case studies)?
Credit Risk Modelling
• Definition of a Model:
• “(…) the term model refers to a quantitative method, system, or approach that applies
statistical, economic, financial, or mathematical theories, techniques, and assumptions to
process input data into quantitative estimates.” – Federal Reserve System
Input
• Assumptions
• Data
• Scenarios
• Expert Judgment
Process
• Methodology
• Implementation
• Calculation
Engine
• Aggregation
Use
• Quantitative
Estimates
• Forecasts
• Limitation
• Management
decision support
Credit Risk Modelling
• Definition of a Model:
Input
• Assumptions
• Data
• Scenarios
• Expert Judgment
Process
• Methodology
• Implementation
• Calculation
Engine
• Aggregation
Output
• Quantitative
Estimates
• Forecasts
Credit Risk Modelling
• Expected Credit Loss (ECL)
• IFRS 9 introduces a forward-looking ECL model. Banks will now be required to consider
historic, current and forward-looking information (including macro-economic data) in the
credit risk modelling.
Risk Parameter Basel Model IFRS 9 Model
Measurement timespan • 12 months average PD. • 12 months PD; or
• Remaining life of the underlying
exposure.
Look-back period • Long-run average-based PD • PIT PD
Reflection of stressed
conditions
• Downturn LGD;
• Reflection of a significant stress period
• Current LGD
• Forward-Looking PD/LGD
• Reflection of economic conditions
Recovery cost • Direct and indirect costs • Only direct costs
EAD historical data • 5 years for retail exposures
• 7 years for sovereign, corporate and
bank exposures
• No specific requirements
Credit Risk Modelling
• Expected Credit Loss (ECL)
• Existing credit risk models can be used to feed into the ECL, however the IFRS 9 gaps should
be eliminated:
IFRS 9 Gap Description Gap Assessment
Unbiased
The ECL model must reflect an unbiased and
probability-weighted amount that is determined
by evaluating a range of possible outcomes. The
models should provide the most accurate and
unbiased estimates of default probability (PD
models), loss rates (LGD models) and exposure
amounts (EAD).
• Backtesting reveals that the model produces
estimates that are significantly above or below the
predictions for the whole portfolio;
• Model is designed with a built-in bias;
• There is no alignment of model estimates with
actual observations;
• Model contains built-in floors and adjustments;
• Model has specification bias.
Credit Risk Modelling
• IFRS 9 Gaps
IFRS 9 Gap Description Gap Assessment
PIT
The ECL model must be a relative model to
include the assessment of a significant increase in
credit risk.
• The model specifications do not reflect systemic
credit risk;
• The model specifications do not explain why the
fundamental obligor factors are suitable to capture
the absolute default risk;
• The model is not subject to periodical empirical
tests comparing predictions to actual results.
Forward
looking
The ECL model should use the forward-looking
information for the assessment purposes.
Especially macroeconomic factors should be
incorporated to the extent that these factors are
material drivers of the model estimates.
• The model relies only on the past information to
determine the estimates;
• The macroeconomic factors are not incorporated
into the model.
Credit Risk Modelling
• IFRS 9 Gaps:
• Model Documentation:
• Backtesting Report
• Model Development Report
• Annual Review (previous year)
IFRS 9 Gap Description Gap Assessment
Term
Structure
The maximum period for the ECL is the maximum
contractual period over which the bank is
exposed to credit risk.
• The model does not estimate a term structure over
the life of a specific transaction;
• The model estimate is limited to a 12-month
horizon.
Credit Risk Modelling
• Basel Models:
EAD is seen as
an estimation
of the extent
to which a
bank may be
exposed to a
counterparty
in the event
of, and at the
time of, that
counterparty’s
default.
EAD
LGD is the
share of an
asset that is
lost when a
borrower
defaults:
Normal
Downturn
LGD
PD is the risk
that the
borrower will
be unable or
unwilling to
repay its debt
in full or on
time:
TTC
PIT
PD
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model
risk managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested (with case studies)?
Credit Risk Model Validation
• Model Validation is responsible for validating the following key aspects of
models:
• The relevance of the data used;
• The model design: theoretical soundness, assumptions and developmental evidence;
• The implementation; and
• The model performance.
• Analyses and tests that should be performed at least on an annual basis:
Backtesting
Portfolio
Analysis
Input Data Overrides
Other
Quant Tests
Initialisation
stage
Strategy
definition
Methodology
and Model
Design
Implement
ation
Disseminat
ion
Monitoring
Maintenan
ce
Credit Risk Model Validation
Model Validation takes place at three separate stages within the model lifecycle
framework, namely:
• Methodology and Model Design;
• Implementation; and
• Monitoring stages. Model
Overview
Replication of
the Model
Review of
methodological
choices
Robustness check
Model
Design Model Risk
Regulatory
Compliance
Backtesting
Model
performance
Model acceptance
Monitoring
Credit Risk Model Validation
Model Risk: Model risk occurs primarily from three sources:
• On the input: The quality of model outputs depends on the quality of input
data and assumptions, and errors in inputs or incorrect assumptions will lead to
inaccurate outputs.
• On the process: The model may have fundamental errors and may produce
inaccurate outputs when viewed against the design objective and intended
business uses. Errors can occur at any point from design through
implementation. In addition, shortcuts, simplifications or approximations used
to manage complicated problems could compromise the integrity and reliability
of outputs from those calculations.
• On the model usage: The model may be used incorrectly or inappropriately. We
need to understand the limitations of a model to avoid using it in ways that are
not consistent with the original intent.
Credit Risk Model Validation
Model Risk Management: Model Risk Rating (MRR)
• The MRR process underpins the model risk management. It is an additional analysis
to cover model-specific areas. By the industry practice (e.g. RBS, HSBC), the MRR is
assessed by the model materiality and model quality.
• For Validation:
• The Validation Team must ensure that every model has the MRR assigned;
• The Validation Team must use the expert knowledge to propose a new MRR at
each annual review;
• The MRR must be updated on an annual basis in a way that ensures the audit trail
of previous MRRs.
• Notwithstanding the model risk assessment during the annual review, the MRR
can be subject to a change if new relevant factors come to light that have not
been covered during the annual review.
• The Validation Team must present the MRR during the Model Risk Committee
(MRC). Areas of high risk materiality must be investigated and commented during
MRC.
Credit Risk Model Validation
MRR Dimension Description
Model Materiality Assessment of the size of the portfolio to which the model is used in terms of EAD and RWA.
Assessment of the impact of the portfolio size on the bank’s capital and the influence on other
models.
Data Assessment if the risk data is collected to a sufficient standard in terms of accuracy and
completeness to support current and future model lifecycle events. Investigation of missing and
erroneous data items (e.g. decimals, units).
Model Specification Assessment if the model is correctly specified (e.g. specified in a way that creates potential risk by
basing the model only on judgemental factors or having a Point-in-Time PD model that does not
respond to the credit cycle).
Model Implementation Assessment if the model itself or a complex system set-up causes the implementation difficulties
(e.g. a model is coded into more than one system causing various outputs depending on the system
used or a model is overly too complex that prevents the implementation).
Model
Use
Assessment if the model is used correctly. Analysis of the number of overrides (e.g. a high number
of overrides caused by the lack of an on-going model training for the new staff). Assessment if the
model outputs are misused or extended to other processes beyond the primary approved purpose
of the model.
Model Performance Assessment if the model is working as expected (e.g. identification of any breaches of the agreed
model performance metrics and thresholds, failed backtesting).
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model risk
managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested (with case studies)?
Learning Outcome
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model risk
managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested (with case studies)?
Backtesting of Credit Risk Models
• Backtesting is a model validation process that compares the internal model’s estimates with
the actual realised observations.
• The purpose of initiating a backtesting exercise is to evaluate the predictive power and
performance of a model and how the model performs over time. Backtesting serves to flag
model deterioration, when a backtested model starts to underestimate or overestimate risk.
• The backtesting process assesses the following characteristics of the internal models:
calibration, discrimination and stability.
Backtesting Process Validation Focus
Calibration Assessment of the deviation of the internal model’s estimates from the realised
observations.
Discrimination Assessment of the extent to which bad realised observations are assigned low
internal model’s estimates and the good realised observations are assigned high
estimates.
Stability Assessment of the changes to the population over time that affect the
appropriateness of the internal model.
Backtesting of Credit Risk Models
• It should be ensured that the validation team has its own access to the relevant databases
that are used to generate the backtesting dataset.
• The validation should focus on the following aspects of the backtesting dataset:
Portfolio Aggregation Validation Focus
Aggregation over initialisation
points,
not overlapping,
fixed time horizons
Validation should consider the following points:
• Does the observation window increase relevant to the increase in the time horizon?
• Is the observation window large enough to guarantee statistically significant results?
• Does the observation window include a diversified range of market conditions?
• Does the observation window allow for periods of sound model performance in
normal macro-conditions to mask bad performance during the period of stress?
• Can the resulting data be considered independent with appropriate statistical tests
applied?
Backtesting of Credit Risk Models
Portfolio Aggregation Validation Focus
Aggregation over initialisation
points,
overlapping,
fixed time horizons
Validation should consider the following points:
• Does the observation window increase relevant to the increase in the time horizon?
• Does the observation window enhance the ability to discriminate between the good
vs. bad model performance due to the overlaps?
Aggregation over
varying time horizons,
fixed initialisation points
Validation should consider the following points:
• Does the observation window capture model’s performance changes resulting from
later recalibrations and reparametrisation of the model?
• Does the aggregation lead to the robust assessment of model performance?
• Does the observation window enhance the ability to discriminate between the good
vs. bad model performance at different time horizons?
Backtesting of Credit Risk Models
Portfolio Aggregation Validation Focus
Aggregation over
varying time horizons,
varying initialisation points
Validation should consider the following points:
• Does taking forecasts with different time horizons initialised on a number of dates
affect the clarity of results?
• Does the aggregation lead to the robust assessment of model performance?
• Does the observation window enhance the ability to discriminate between the good
vs. bad model performance at different time horizons?
Aggregation over
credit facilities,
risk factors,
obligors
Validation should consider the following points:
• Does the aggregation lead to the increase of default instances or other exceptions for
a given observation window?
• Does the aggregation capture the way in which dependencies between risk factors,
obligors or credit facilities are modelled?
Backtesting of Credit Risk Models
• Calibration – Empirical Example: Brier Score
The Brier score is also known as the Mean Square Error (MSE). The Brier score is a common
way of verifying the accuracy of the probability forecast that relates to a specific event with
the estimated probability known. The Brier score can only be used for the binary outcomes,
where there is only two possible realisations: default/non-default.
For N obligors with individual PD estimates !" and with the #" being a default indicator that
takes the value of 1 for default and the value of 0 for non-default, the Brier score takes the
following formula:
MSE =
$
%
∑(#" − !")* [1]
The Brier score is small for the high PD estimates assigned to defaults and low PD estimates
assigned to non-defaults. The low Brier score indicates the good calibration of a rating model.
The Brier score can only tell about how accurate the forecast was, but cannot inform about the
accuracy of the forecast if compared with anything else. The validation team should look at the
specific aspect when validating the calibration by using the Brier score:
• Is the obtained score low enough to conclude about the model’s accuracy of predicting
defaults?
Backtesting of Credit Risk Models
• Calibration – Empirical Example: Brier Score
Specifically for the TRIM exercise, the validation team is required to have pre-defined actions
in place that correspond to certain values of the Brier score.
Traffic Lights for Brier Score
Traffic
Light
Values Description
Dark Green 0.0 ≤ Brier score ≤ 0.1 Indication that the model is very well calibrated (conservatively calibrated).
Green 0.1 < Brier score ≤ 0.5
Indication that the model is calibrated with no significant divergence between the
estimates and realisations.
Yellow 0.5 < Brier score ≤ 0.7
Indication that the observed realisations are in line with the model estimates. There is
no significant difference, but the model can be recalibrated in order to increase its
accuracy.
Orange 0.7 < Brier score ≤ 0.9
Indication that the model is weakly calibrated and significant differences appear
between the observed realisations and model estimates.
Red 0.9 < Brier score ≤ 1.0 The model is wholly inaccurate and the recalibration is needed.
Backtesting of Credit Risk Models
• Calibration – Empirical Example: Brier Score
For the backtesting results of both PD models, the null hypothesis is tested by using the
Spiegelhalter’s z-statistic, which allows for a formal assessment of the calibration of the
targeted PD models:
Z(!,") =
∑$%&
'
()$* +$)(-* .+$)
∑$%&
'
-*.+$
/+$(-* +$)
[2]
The null hypothesis of perfect calibration is rejected at the confidence level “α” if the following
applies:
Z(!, ") > 2-* 3/. [3]
2008-2015 Backtesting Dataset (Appendix)
Population
N
PD Model Brier Score
B(!,")
Spiegelhalter’s Z-statistic
Z(!,")
P-value
< α
CI
α = 0.05
4153 MidCorp 0.034532 7.524517 0.000199 95%
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
In practice, the discriminatory power of the mid-corporate PD models is assessed by means of
the AUROC, CAP and AR. As a rival statistical tool to the aforementioned methods, the
Goodman and Kruskal’s Gamma is used to validate the discriminative power of a PD model.
The Goodman and Kruskal’s Gamma is applied to assess the consistency of allocating good
ratings to less risky obligors and bad rating to the highly risky obligors. The Null Hypothesis
states that the validated PD model discriminates between highly risky and less risky obligors
with the gamma coefficient being applied to test this hypothesis:
The value of the gamma coefficient is compared with the test statistics (z-critical from the
tables). If the test statistic is higher, then one cannot reject the null hypothesis. The gamma
coefficient is specified by the following formula:
! =
#$%#&
#$'#&
[4]
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
! =
#$ − #&
#$ + #&
Under the TRIM framework, the results of the gamma coefficient should be interpreted in
accordance with the predefined levels included in relevant internal policies:
Traffic
Light
Values Description
Dark Green 0.8 < ! ≤ 1.0 Very strong discrimination between the good and bad obligors
Green 0.6 < ! ≤ 0.8 Strong discrimination between the good and bad obligors
Yellow 0.4 < ! ≤ 0.6 Neutral discrimination between the good and bad obligors
Orange 0.1 < ! ≤ 0.4 Weak discrimination between the good and bad obligors
Red ! ≤ 0.1 Very weak discrimination between the good and bad obligors
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
The gamma coefficient’s z-value is compared with the z-critical values from the tables and, if
lower, then one cannot reject the null hypothesis that there is a difference in the populations
(the rating discriminates between highly risky and less risky obligors):
z = ! ∗
#$% #&
'()* +,)
[5]
First Step:
1) Divide the backtesting dataset between the good and bad obligors. How?
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
1) Divide the backtesting dataset between the good and bad obligors. How?
• You need a cut-off point!
• the distinction between the good and bad obligors is usually set for the cut-off point for
the non-investment grade bonds with the rating below BBB-. In doing so, the obligors
with adequate capacity to meet their financial commitments are separated from the
obligors that are vulnerable in the near term and facing major on-going uncertainties
rendering them inadequate to meet their financial commitments.
MidCorp PD model:
Rating Non Defaults Defaults
Good (AAA to BBB-) 1950 19
Bad (BB+ to CCC) 1485 78
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
The analysis of the above table reveals the following facts placing the gamma coefficient in the
green flag of the predefined traffic lights:
• The number of concordant pairs “N_c” is: 152100
• The number of discordant pairs “N_d” is: 28215
• The Gamma Coefficient “γ” is: 0.687047
MidCorp PD model:
Rating Non Defaults Defaults
Good (AAA to BBB-) 1950 19
Bad (BB+ to CCC) 1485 78
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
1) The Gamma Coefficient “γ” is: 0.687047 but….
• The z-values (6.756) is significantly over the z-critical values from the tables. Thus, there
are no grounds to assume that the model discriminates between highly risky and less
risky obligors, as the null hypothesis can be rejected.
• What do you do then? Clearly the model seems to be OK for the discriminatory power.
Yule’s Q
• Yule’s Q is the measure of the discriminatory power and association between bad/good
differentiations and defaults.
• Yule’s Q is always a number between -1 and 1 and constitutes the statistical measure of
discrimination for a 2x2 confusion matrix.
• Unlike the gamma coefficient, Yule’s Q does not require tests of significance, and hence
the TRIM inspection does not insist on providing the proof of robustness for the Yule’s Q
findings.
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
However, Yule’s Q should be referenced to predefined standards (e.g. traffic lights):
Traffic
Light
Values Description
Dark Green Yule’s Q = 1
Perfect association between the good/bad ratings of the obligors and
defaults. The model has very strong discrimination.
Green 0.7 ≤ Yule’s Q < 1
Very strong association between the good/bad ratings of the obligors
and defaults. The model has strong discrimination.
Yellow 0.5 ≤ Yule’s Q < 0.7
Substantial association between the good/bad ratings of the obligors
and defaults. The model has good discrimination.
Orange 0.3 ≤ Yule’s Q < 0.5
Moderate association between the good/bad ratings of the obligors
and defaults. The model has weak discrimination.
Red Yule’s Q ≤ 0.3
Negligible or inversed association between the good/bad ratings of
the obligors and defaults. The model has very weak discrimination.
Backtesting of Credit Risk Models
• Discrimination – Empirical Example: Gamma Coefficient & Yule’s Q
1) The Gamma Coefficient “γ” is: 0.687047 but….
2) The Yule’s Q is 0.687047 indicating a very strong association between the good/bad ratings
and defaults (green flag of the predefined traffic lights).
Backtesting of Credit Risk Models
• Stability – Empirical Example: Population Stability Index (PSI)
In practice, the stability of the PD models is assessed by means of the PD rating migration
matrix, analysis of the changing macroeconomic conditions and the changing business
landscape.
The validation team is advised to apply measures of the population stability in order to
investigate how much the underlying portfolio of obligors has changed over time rending a
credit risk model obsolete and inadequate:
PSI = ∑"( $%",'()*'+% − $%",./0.().1% 2 ln
567,89:;8<%
567,=>?=9:=@%
) [6]
Where “i” denotes the rating class (e.g. AAA), $%",'()*'+ is the actual distribution of obligors
per rating “i” and $%",./0.().1 is the expected distribution of obligors per rating “i” taken from
the reference year that is the previous year and/or the development year.
Backtesting of Credit Risk Models
• Stability – Empirical Example: Population Stability Index (PSI)
Under the TRIM framework, the results of the PSI should be referenced to the predefined
levels that allow for actionable decisions to be taken:
Traffic
Light
Values Description
Dark Green 0.00 ≤ PSI < 0.05 Population remains very stable over time.
Green 0.05 ≤ PSI < 0.10 Negligible shift in the population over time. Population remains stable.
Yellow 0.10 ≤ PSI < 0.25
Minor shift in the population over time. Population remains relatively
stable.
Orange 0.25 ≤ PSI < 0.50
Moderate shift in the population over time. Population remains unstable.
Red 0.50 ≤ PSI
Significant shift in the population over time. Population remains unstable.
Backtesting of Credit Risk Models
• Stability – Empirical Example: Population Stability Index (PSI)
Rating Class 2008 2009 2010 2011 2012 2013 2014 2015
AAA 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
AA+ 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
AA 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
AA- 0.00% 0.20% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
A+ 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
A 0.00% 0.00% 0.20% 0.40% 0.40% 0.00% 0.00% 0.00%
A- 0.00% 0.00% 0.00% 0.00% 0.00% 0.20% 0.20% 0.20%
BBB+ 0.40% 1.00% 1.00% 0.60% 1.50% 2.40% 1.30% 1.40%
BBB 15.10% 12.30% 9.40% 10.60% 12.70% 13.80% 15.20% 15.00%
BBB- 14.70% 15.80% 14.00% 16.70% 13.50% 14.60% 12.20% 13.50%
BB+ 23.20% 19.20% 19.80% 15.50% 14.20% 19.60% 16.30% 21.10%
BB 15.90% 15.20% 15.40% 16.50% 16.30% 14.60% 15.90% 15.30%
BB- 13.20% 13.20% 11.20% 11.80% 11.60% 12.00% 15.20% 11.20%
B+ 4.10% 2.20% 4.20% 4.50% 4.40% 7.30% 3.60% 5.40%
B 1.60% 2.20% 4.20% 2.60% 3.20% 2.20% 1.60% 1.80%
B- 0.60% 1.20% 1.20% 0.60% 2.50% 2.20% 2.00% 2.00%
CCC 0.40% 0.20% 0.00% 0.80% 0.80% 1.70% 1.40% 1.80%
NR 0.20% 0.20% 0.00% 0.00% 0.40% 0.40% 0.00% 0.40%
PSI 6.94% 4.30% 3.19% 4.87% 12.07% 8.85% 4.84%
Backtesting of Credit Risk Models
• Stability – Rating Migration Matrix
AAA AA+ AA AA- A+ A A- BBB+ BBB BBB- BB+ BB BB- B+ B B-
CCC
NR
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 2 3 0 1 0 0 0 0 0 0 1
0 0 0 0 0 0 4 45 14 4 0 0 0 0 0 0 12
0 0 0 0 0 0 0 9 24 15 5 2 0 0 0 0 10
0 0 0 0 0 0 1 5 16 34 14 3 3 0 0 1 4
0 0 0 0 0 0 0 2 3 22 33 9 5 1 1 0 8
0 0 0 0 0 0 0 0 3 10 14 31 7 0 6 2 4
0 0 0 0 0 0 0 0 0 4 1 4 7 0 1 0 3
0 0 0 0 0 0 0 0 0 0 2 1 0 4 0 0 2
0 0 0 0 0 0 0 0 0 1 3 1 1 2 2 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 1
0 0 0 0 0 0 0 7 3 11 2 2 0 1 0 0 14
0 0 0 0 0 1 7 71 63 102 74 53 23 9 10 8 59
Learning Outcome Summary
• Credit Risk Management
How is credit risk managed within a bank? What are the credit risk mitigation techniques?
• Three Lines of Defence Model
What is the governance framework for credit risk management?
• Regulatory Framework for Credit Risk Management
What is the regulatory background for credit risk management? What is the difference between the
Standardised, Foundation and Advanced approach to credit risk measurement?
• Credit Risk Modelling
What are the common models for credit risk: Probability of Default (PD); Loss Given Default (LGD);
Exposure at Default (EAD); Expected Credit Loss (ECL)?
• Credit Risk Model Validation
What is the internal model validation function? What is a credit risk model lifecycle? How is model risk
managed by a bank?
• Backtesting of Credit Risk Models
How are credit risk estimates backtested?