Credit Risk Irb Approach2
Transcript of Credit Risk Irb Approach2
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Credit RiskInternal Rating Based Approach
Laurent Balthazar
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AgendaAgenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
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AgendaAgenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
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1. Introduction to IRB: The 3 pillars
Basel Committee
• The BCBS was formed in 1974 by the Group of 10 central bank governors following the failure of West German bank BankhausHerstatt
• Committee members include representatives from Belgium, Canada, France, Germany, Italy, Japan, Luxembourg, the Netherlands, Spain, Sweden, Switzerland, the U.K. and the U.S.
• From its inception, its primary mission has been to promote stability in the global banking system in the pursuit of two guiding principles
• No foreign banking system should escape supervision• Supervision must be adequate for all banks operating internationally
• Its primary objective is to formulate standards, guidelines and best practices that individual authorities will implement
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1. Introduction to IRB: The 3 pillars
The 3 pillars: mutual re-enforcement
Pillar 1 : menu of evolutionary approaches• Credit risk• Operational risk• Market risk
Pillar 2 : 4 principles• Internal assessment• Supervisory review• Capital > minimum• Supervisory intervention
Pillar 3 : disclosure requirements
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1. Introduction to IRB: The 3 pillars
Scope of application
Holding => Basel 2 rules apply
International Bank => Basel 2 rules apply
International Bank => Basel 2 rules apply
International Bank => Basel 2 rules apply
Domestic Bank => Control of national supervisor
Investment Bank => Control of national supervisor CRD Directive
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1. Introduction to IRB: The 3 pillars
Treatment of participations – Financial Companies
Financial companies (Insurance excluded)
Majority-owned / Controlled
DeductedSignificant investment(e.g. EU : 20%-50%)
Deducted or consolidated on a pro rata basis
Risk Weighted
Minority investments
Minor investment(e.g. EU < 20%)
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1. Introduction to IRB: The 3 pillars
Treatment of participations – Insurance CompaniesInsurance companies
Majority-owned / Controlled
Deducted or other method (national
discretion)
Significant investment(e.g. EU : 20%-50%)
Deducted or other method (national
discretion)Risk Weighted
Minority investments
Minor investment(e.g. EU < 20%)
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1. Introduction to IRB: The 3 pillars
Treatment of participations – Insurance CompaniesCommercial companies
Majority-owned / Controlled and Minority
investments
Amounts of participations up to 15% of banks capital (individual exposure) or 60% of banks
capital (aggregated exposure)
Deducted Risk Weighted
Amounts superior to those thresholds
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1. Introduction to IRB: Pillar 1
Pillar 1 : menu of evolutionary approachesCredit risk• STA• FIRBA• AIRBAOperational risk• BIA• STA• AMAMarket risk• STA• AMA
Economic Models
Rough weights
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1. Introduction to IRB: Pillar 1
Pillar 1 : solvency ratio
Total Eligible Capital
Credit Risk
- Standard Approach- IRBF Approach- IRBA Approach
Market Risk
- Standard Approach- Internal Model Approach
Operational Risk
- Basic Indicator Approach- Standardized Approach- Advanced Measurement Approach
≥ 8%
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1. Introduction to IRB: Credit risk
Credit risk
Standard approach• Continuation of Basel 88 • New: internal ratings (+ asset class): 0%, 20%, 50%, 100%, 150%
Foundation Internal Rating Based Approach• RWA= f (PD, LGD, EAD, M, Confidence level, Correlation)• Banks estimates only PD
Advanced Internal rating Based Approach• RWA= f (PD, LGD, EAD, M, Confidence level, Correlation)• Banks estimates PD, LGD, EAD, M
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1. Introduction to IRB: Why IRB ?
Why choosing IRB ?
Standard approach
• Simpler, less requirements• Not always more capital requirements
IRB• If there should be only one reason:
Banks should be managed in a economical way !
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1. Introduction to IRB: Why IRB ?
Why choosing IRB ?
•Complex function integrating risk parameters• Derived from state of the art economical model
• Simple weights• No economical foundationPortfolio Risk
Assessment
• Internal ratings and PD• All portfolio might be covered• Internal LGD• Extended recognition of collateral
• Only external ratings• Implied PD given by regulator• Large part of portfolio unrated (externally)• No explicit LGD• Limited recognition of collateral
Individual Risk Assessment
IRBStandardSTD vs IRB
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1. Introduction to IRB: Why IRB ?
Why choosing IRB ? => Macro view
% are contribution from portfolios to total capital changeAverage gain for advanced approaches
QIS 3 – G10 Banks Standard Approach FIRB approach AIRB approach Portfolio Group 1 Group 2 Group 1 Group 2 Group 1 Corporate 1% -1% -2% -4% -4% Sovereign 0% 0% 2% 0% 1%
Bank 2% 0% 2% -1% 0% Retail -5% -10% -9% -17% -9% SME -1% -2% -2% -4% -3%
Securitised assets 1% 0% 0% -1% 0% Other 2% 1% 4% 3% 2%
Overall Credit Risk 0% -11% -7% -27% -13% Operational risk 10% 15% 10% 7% 11% Overall Change 11% 3% 3% -19% -2%
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1. Introduction to IRB: Why IRB ?
Why choosing IRB ? Macro view
View by individual portfolioRetail are the winners, Equity and sovereign the losers
QIS 3 – G10 Banks Standard Approach FIRB approach AIRB approach Portfolio Group 1 Group 2 Group 1 Group 2 Group 1 Corporate 1% -10% -9% -27% -14% Sovereign 19% 1% 47% 51% 28%
Bank 43% 15% 45% -5% 16% Retail (Total) -21% -19% -47% -54% -50% - Mortgage -20% -14% -56% -55% -60%
- Non-Mortgage -22% -19% -34% -27% -41% - Revolving -14% -8% -3% -33% 14%
SME -3% -5% -14% -17% -13% Specialised Lending 2% 2% n.a. n.a. n.a.
Equity 6% 8% 115% 81% 114% Trading book 12% 4% 5% 4% 2%
Securitised assets 86% 61% 103% 62% 129%
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1. Introduction to IRB: Why IRB ?
Why choosing IRB ? Micro view
Min and Max impact at bank levelAverage variation low, but at individual bank level might be very important
QIS 3 – G10 Banks Standard Approach FIRB approach AIRB approach Group 1 Group 2 Group 1 Group 2 Group 1
Maximum 84% 81% 55% 41% 46% Minimum -15% -23% -32% -58% -36% Average 11% 3% 3% -19% -2%
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1. Introduction to IRB: From proposal to law
IRB in national laws
3-level structure
• Basel Committee : recommendations and best practices
• EU : directives
• Countries : local law
open options
open options
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1. Introduction to IRB: Exposure classes
Exposures class => Determine the risk weight function
1) Corporate, sovereign, banks: same function (>< Standard)• Corporate:
- SME specific treatment (adjustment of RWA)- Specialized Lending: SPV, reimbursement based on cash-flows of
financed asset.
Real estate with high volatility. To be defined by regulators.
High volatility Commercial real estate
High correlation between PD and cash flows generated by the property
Income producing real estate
e.g.: oil, metals, crops …Commodities financee.g.: ships, aircrafts, satellites …Object financee.g.: power plant, chemical plants, mines…Project finance
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1. Introduction to IRB: Exposure classes
• Sovereign:- Countries- Central banks- Multilateral Development Banks- Public Sector Entities (PSE) considered as sovereigns by regulators
(tax raising power)- International organizations RW 0% in standard (e.g.: BIS, IMF …)
• Banks:- Financial institutions- PSE not considered as sovereigns
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1. Introduction to IRB: Exposure classes
2) Retail: 3 functions (>< Standard)
• Mortgages:- Exposure covered by residential mortgage- No size limit- If rented must be limited
• Qualifying revolving exposures:- Exposures: revolving, unsecured, uncommitted- On private person- Max 100.000 EUR- Bank must demonstrate low volatility of loss rate
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1. Introduction to IRB: Exposure classes
• Other retail:- Loans on a group < 1Mio EUR- Large number of exposures in portfolio- Must be managed on a pool basis- Individual analysis does not prevent mass treatment
3) Equity: 1 function (but standard method allowed in IRB)
- Recovery only by selling or when bankruptcy occurs- No obligation form issuer - Obligation from issuer but: can be delayed, reimbursement can be
done in equity- Includes securities when income is function of equity- Includes securities eligible as Tier 1
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1. Introduction to IRB: Exposure classes
4) Eligible purchased receivables: function Corp or retail
- Claims purchased to another counterparty- can be retail or corporate in function of the nature of the claim
5) Securitisation exposure: special treatment: Standard or SF
- Not based on legal definition but economical one- Securitised exposure as soon as there are at least 2 tranches - Special attention as often used for regulatory capital arbitrage
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1. Introduction to IRB: Terminology
IRB ingredients
Symbol Name Comments
PD Probability of Default It is the probability that the counterparty will not meet its financial obligations
LGD Loss Given Default It is the expected amount of loss that will be
incurred on the exposure in case the counterparty defaults
EAD Exposure at Default
It is the expected amount of exposure at the time when a counterparty will default (the expected
drawn-down amount for revolving lines or the off-balance sheet exposure times its CCF)
M Maturity The average maturity of the exposure
ρ Asset correlation A measure of association between the evolution of assets returns of the various counterparties
CI Confidence Interval The degree of confidence used to compute the economic capital
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1. Introduction to IRB: Terminology
IRB : sources of parameters estimation
NB: ρ and CI always given by regulators
IRB Foundation IRB Advanced Exposure type Internal data Regulators data Internal data Regulators data
Corporate, Sovereigns, Banks, Eligible
purchased receivables Corp
PD LGD, EAD, M PD, LGD, EAD, M
Retail, Eligible Purchased receivables
retail Internal PD, LGD, EAD, M mandatory
Equity PD/LGD approach or market based approach
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1. Introduction to IRB: Terminology
IRB : for each exposure class, 3 components
1. Risk Components
2. Risk weight function
Capital requirements
3. Minimum Requirements
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1. Introduction to IRB: Roll out
Principle: if IRB, must apply to all asset classes.
Exceptions:
• Specialized Lending• Securitisation• Non-material exposures
For the rest:
• Roll out plan• Timing and resources• To be approved by regulators
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1. Introduction to IRB: Transition period
Transition period of 3 years• Beginning at implementation (31/12/2006 IRBF, 31/12/2007 IRBA)• Data requirements may be relaxed :
2000 2001 2002 2003 2004 2005 2006 2007 2008 2010
LG D : 7 years
E AD : 7 years
PD : 5 years(*)
R etail: 5 years (*)
R ating system : 3 years (*)
Relaxed: 2 years
Parallelrun
Transition period: 3 years
2009
(*): re laxed during transition period
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1. Introduction to IRB: Transition period
Transition period of 3 years
• But Capital Gains are limited
• 2009 … ?
Approach From Year-end 2005
From Year-end 2006
From Year-end 2007
From Year-end 2008
IRBF Parallel run 95% floor 90% floor 80% floor IRBA - AMA Parallel run or
impact studies Parallel run 90% floor 80% floor
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Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
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2. Credit risk in IRB: PD Minimum Requirements
Dimension of rating system
• Corporate, Sovereign and Banks
- 2 dimensions: PD and LGD (>< issue rating !)- 2 exposures on same borrower => same rating (except sover. Ceiling and
guarantees)- There must be policies to guide to classification in a rating grade
• Retail
- Exposures must be classified in homogenous pools that share risk characteristics- For each pool a PD must be estimated (and LGD and EAD)
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2. Credit risk in IRB: PD Minimum Requirements
Rating structure
• Corporate, Sovereign and Banks
- Concentration issue (no more 30% in one grade)=> Concentrated portfolio ex: PSE at Dexia ?- Min 7 pass ratings and 1 for default
• Retail
- Number of pools and number of exposures in each pool sufficient to validate PD, LGD and EAD parameters
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2. Credit risk in IRB: PD Minimum Requirements
Rating criteria
- There must be clear and coherent definition to classify exposures in rating grades, which means:
• Consistency across businesses, departments and geographical locations• Third parties (auditors, regulators…)should be able to reproduce the process
- Bank should integrate all available information- An external rating can be a basis but other info must be incorporated
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2. Credit risk in IRB: PD Minimum Requirements
Rating horizon
- PD on 1 year- Ratings on longer horizon- Rating: reimbursement capacity under adverse economic conditions- PIT Vs. TTC issues (procyclicality…)
Today
Business Cycle
Time
PIT rating
Average TTC rating
Stress TTC rating
?
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2. Credit risk in IRB: PD Minimum Requirements
Use of models: Current market practices
SME Portfolio
Corporate portfolio
Retail portfolio
Bank and sovereign portfolio
Weight of scoring model in final rating
Weight of human expert in final rating
Statistical Models
Constrained expert models
Expert Models
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2. Credit risk in IRB: PD Minimum Requirements
Use of models:
Requirements
- May be used as a primary input for the rating- But only uses a subset of available info => cannot be the only tool- Human oversight necessary- The bank has to demonstrate the discriminatory power of the model- The bank must have procedures to check quality of inputs- Bank must demonstrate that the dataset used for construction isrepresentative of the bank borrower- Human judgment must integrate elements not taken into account in the model- Ongoing monitoring, validation and assessment of the quality of the model
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2. Credit risk in IRB: PD Minimum Requirements
Documentation of rating system
- The bank must document extensively its IRB system- Documentation should highlight:
rating criteriarating responsibilitiesrating exceptionsreview frequency (in principles min 1 per year)management overview
- Documentation of default definition- If a model is used:
Mathematical hypothesisValidation out of the time and out of the sampleModel weaknesses
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2. Credit risk in IRB: PD Minimum Requirements
Coverage
- Each Corp/ sovereign/ Bank exposure should have a facility rating- Each retail exposure should be classified in a pool- Each guarantor should be rated
Integrity
- Independency of the rater (FO / RM separation)- Yearly review (may be done by sampling for retail)- Efficient procedures to collect new info on a borrower
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2. Credit risk in IRB: PD Minimum Requirements
Overrides
- Overrides = change to the model rating - The bank must define in which cases it is allowed- Overrides must be identified and followed separately- Each guarantor should be rated
Data maintenance
- The bank must collect and historize all the data necessary for re-rating - Corporate, Sovereign, Banks: Store rater name, rating data, Default Rates, Migrations- Retail: Store data that allows to classify in pools, observed DR
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2. Credit risk in IRB: PD Minimum Requirements
Corporate governance and oversight
- The board must validate main aspects of the rating system and must understand it - There must be regular discussion about the rating system quality between management and risk control.- Ratings included in reporting to senior management- The bank must have an independent risk control unit: model development, monitoring, policies …- Independent review at least once a year by audit or other similar independent function
⇒ Regulators will look at reports of meetings (Board, Risk Control, audit…), and they will question them !
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2. Credit risk in IRB: PD Minimum Requirements
Use of internal rating systems
Ratings and PD must be used for
- Credit Approval- Risk Management- Economic Capital Allocation- Corporate Governance
⇒ PD’s of Basel 2 and Internal PD’s might be different (e.g.:pricing…) but coherency must be demonstrated.
IRB Compliant systems must be used at least 3 years before implementation
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2. Credit risk in IRB: PD Minimum Requirements
Overall requirements
- PD must be long term average of 1 year default rates (except for retail)- Pooling authorized but data must be comparable- Estimations must be grounded in experience- Economic climate at the time of collection must be taken into account- Usually a margin of error is included => conservatism
⇒ Often not enough data internally: conservative bias that might not be used for internal risk management
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2. Credit risk in IRB: PD Minimum Requirements
Default definition
90 days delayUnlikely to pay
- Default indicators:Non accrued statusProvisionsSelling at material lossRestructuration with lower NPVFilled for bankruptcy
- Retail: default might be at facility or obligor level (no contagion mandatory)
Calibration issue !
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2. Credit risk in IRB: PD Minimum Requirements
Re-ageing policy
Regulators do not want the bank to play with rules:
There must be a clear policy for past due credits:
Who can approve them ?Minimum age of facility to be eligible for re-ageingNumber of re-ageing authorized per facilityNew risk assessment for re-aged facilities
Use test (treatment of re-aged exposures >< defaulted exposures)
Overdrafts
If new limit, must be communicated to the client ! (no internal game)
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2. Credit risk in IRB: PD Minimum Requirements
Requirements specific to PD estimation
Corporate, sovereigns, banks:
- Internal long run experience must be incorporated- Judgment must be taken into account- If mapping to external data: default definition and rating criteria must be documented - Minimum 5 years of data
Retail
- Internal data should be primary source- It should integrate seasoning effects in case of portfolio growth
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2. Credit risk in IRB: PD Minimum Requirements
Requirements specific to qualifying purchased receivables
- Legal certainty: the bank must ensure it has control on reimbursements- Monitoring of the quality of the pools:
correlation between seller and receivablessellers/ servicers monitoringfraud detectionhistorical data on the poolconcentration monitoring
- The bank must be able to verify that the seller/ servicer respect the contract covenants
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2. Credit risk in IRB: PD Minimum Requirements
Validation of internal estimates
- The bank must have clear policies and pre-defined triggers to determine when the deviation between expectations and observed values should lead to a review of the parameters
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2. Credit risk in IRB: PD operational implementation
How to estimate a PD on each exposure and fulfilling those requirements ?
Operational development of a rating framework
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2. Credit risk in IRB: PD operational implementation
1st issue: do we need a model ?
• Not mandatory in Basel 2 text
• Even, in CP3 warning about the use of models
⇒ But: how to fulfill requirements otherwise ?
• Uses only a part of the info• Is correct in 80% of the cases• Cannot treat outliers• If fundamental underlying characteristics of the population changes, the model does not integrate it
• Systematic in the rating process
• Can be reproduced by third parties
• Statistical tests can prove discriminatory power
Models weaknessesModel advantages
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2. Credit risk in IRB: PD operational implementation
Solution: take the best of the 2 worlds
⇒ Construct a rating framework that combines the use of models with human oversight and adjustment (constrained expert model)
Basel 2 Credit Analyst
Automated
Scoring Model
Traditional
Expert analysis
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2. Credit risk in IRB: PD operational implementation
Which quantitative technique to use ?
1) Regression techniques
- Multivariate Discriminant Analysis
- Ordinary Least Square
- Logistic regressione.g. Logistic regression
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2. Credit risk in IRB: PD operational implementation
2) Structural Models: e.g. KMV
Current asset value
Current value of debts
Potential value of assets in the future
1 year
PD= f (asset value, asset volatility, debt value)
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2. Credit risk in IRB: PD operational implementation
3) Expert systems: e.g. Decision trees
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2. Credit risk in IRB: PD operational implementation
4) Inductive learning: e.g. Neural Networks
Inputs
Results
TRIAL
MODIFY
Wi
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2. Credit risk in IRB: PD operational implementation
Comparison
Criteria Statistical techniques
Inductive learning techniques Structural models
Applicability + + - (Limited to listed companies)
Empirical validation (out of the sample and out of the time
tests)
+ + +
Statistical validation + - (No weights that can be statistically
tested)
n.a. (Parameters must not be statistically tested as they are derived from an
underlying financial theory)
Economical validation
+ (We can see if the weights of the various ratios
corresponds to the weight expected by
specialists)
+ (The impact of the ratios can be
estimated using sensitivity analysis)
++ (Structural models are the only
derived from a financial theory)
Market reference
++ (Riskcalc of Moodys, Fitch IBCA
scoring models, various models used by central banks of
France, Italy, UK…)
+ (No model directly based on neural networks to the extend of our
knowledge, but a model of S&P is based on Support
Vector Machines that is derived from NN)
+ KMV model
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2. Credit risk in IRB: PD operational implementation
Finding data: 3 sources
• Default data- Most objective
- But often scarce data
- Basel 2 definition ?
• External ratings- Especially for certain portfolios (Corp, Sovereign, Banks)
- Indirect way to modelize defaults
• Internal ratings- When no other data available
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2. Credit risk in IRB: PD operational implementation
Regression techniques
• Default data- Binary issue (default=1, not default=0)
- e.g. Binary logistic regression
• Ratings- Multi-class issue
- e.g. Ordered logistic regression
- Rating coding: AAA=1, AA+=2, AA=3, … B-=16, CCC=17
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2. Credit risk in IRB: PD operational implementation
How many models to construct ?
• Should integrate- Number of type of counterparties (retail, Corp, banks…)
- Model by sector, region … => Data availability issue !
- Model use outside its development population (Generic Vs
Specific model)
• 2003 Study- US banks: 5 non retail and 3 retail on average
- European banks
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2. Credit risk in IRB: PD operational implementation
Sector issue ?
• A specific model may be constructed on a given sector, or sector variable may be included (1/0)
• But pay attention !- More overfitting risk
- Variation in sector fundamentals not anticipated
- e.g.: utilities sector and deregulation
- e.g.: sensitivity to the stage of business cycle if few data
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2. Credit risk in IRB: PD operational implementation
Modelization steps1. Data collection and cleaning
5. Validation
2. Univaried analysis
3. Ratio transformation
4. Regression analysis
6. Calibration
7. Test phase
8. Production
Regular
Feed-Back
to Credit
analysts
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2. Credit risk in IRB: PD operational implementation
1. Data collection and cleaning
- Which data sources are available ? => Internal, external DB, data pooling …
- What kind of data do they contain ? => potential explanatory variable (fin. statements, age …)
- What is the quality of the data ?=> Missing values, extreme values …=> Potential bias (survivor bias, size bias …)
- How to clean the data ?=> rating or default date vs fin. Statement availability => replacing or excluding missing values=> polluted data (Shareholders, country ceiling …)
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2. Credit risk in IRB: PD operational implementation
- Rating distribution issue
Which distribution ?=> Bell shaped ? => Flat ?=> keeping concentration ?
Classical distribution
02468
101214
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
rating
freq
uenc
y
Concentrations
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
rating
freq
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2. Credit risk in IRB: PD operational implementation
- Fraction issue
Which ratio is the best ?- denominator negative values ! - Ordering !
=> Those values have to be treated
Profit / Equity Equity/ LT fin debt Profit Equity Result Equity LT fin Debt Result
10 100 10% - 10 100 -10% -10 10 -100% -10 -100 10% -100 10 -1000%
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2. Credit risk in IRB: PD operational implementation
- Treatment of size variable
=> To get good results in regression analysis, variable distributions should not be too far from the bell shape
=> Some variable may need to be transformed
Frequency of total assets
0
200
400
600
800
1000
1200
1400
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734
420,7
7584
0,816
1,260
,858
1,680
,899
2,100
,940
2,520
,981
2,941
,022
3,361
,063
3,781
,105
4,201
,146
4,621
,187
5,041
,228
Assets in 000 EUR
Freq
uenc
y
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2. Credit risk in IRB: PD operational implementation
- Studying outliers
• “Quick and dirty” model to identify outliers
• May we find a reason for that ?
• if it is the case, can we exclude those observations ?
=> Pay attention to keep objectivity and to document choices
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2. Credit risk in IRB: PD operational implementation
- Analysts feed-back
=> OK with potential variable ?
=> OK with treatment of missing values ?
=> OK with treatment of extreme values ?
=> OK with sample composition ?
=> ratio definition ?
=> Outliers excluded ?
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2. Credit risk in IRB: PD operational implementation
2. Univaried analysis
- Study of the relationship between each variable and the average PD / the average rating
Graph 11.5 ROA - default dataset
0%
10%
20%
30%
40%
50%
60%
-20% -10% 0% 10% 20% 30%
ROA
Ave
rage
Def
ault
rate
Graph 11.4 ROA - rating dataset
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-15.0% -10.0% -5.0% 0.0% 5.0% 10.0% 15.0% 20.0% 25.0%
ROA
Rat
ing
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2. Credit risk in IRB: PD operational implementation
- Univariate predictive power
- Shape of the relationship (monotonic or not)
- What is the range of efficiency ?
- Does the relationship make sense ?
0
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Cash/ ST debts
Rat
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e.g. Liquidity ratio on large corporate rating dataset
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2. Credit risk in IRB: PD operational implementation
- Analysts feed-back
=> Does the relationship makes sense ?
=> OK with rejected ratios ?
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2. Credit risk in IRB: PD operational implementation
3. Ratio transformation
- Can be done in many ways:
Polynomial function (e.g. Moody’s uses DR)Cap: minimum and maximum values
- Mandatory for non monotonic ratios, usefull for other
- Univaried analysis can be a basis for Caps
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2. Credit risk in IRB: PD operational implementation
- Analysts feed-back
=> Does the function makes sense (no overfitting) ?
=> Does min and max values seems reasonable ?
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2. Credit risk in IRB: PD operational implementation
4. Regression analysis
- e.g. Logistic regression
- Divide sample in construction and backtesting sample
- Selection process:
ForwardBackwardStepwiseManual
- Choose a performance measure: economic vs statistical
[ ])...(exp11
2211 cxbxb +++−+=π
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2. Credit risk in IRB: PD operational implementation
- Analysts feed-back
=> OK with selected variables ?
=> Replacing ratios with correlated one even if less performing ?
=> Model acceptance is key issue
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2. Credit risk in IRB: PD operational implementation
5. Validation
- On construction sample and on backtesting sample, ideally out of the sample and out of the time.
- Performance measures:
- Accuracy ratio (default)- Cumulative notch difference (ratings)- Cost function
Economic tests- p. value- Log likelihood- Wald test- R squared- Goodness of fit
Statistical tests
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2. Credit risk in IRB: PD operational implementation
- Main tools
CND
0%10%20%30%40%50%60%70%80%90%
0 1 2 3
Perfect model
Tested model
100%
0%
% of defaults
ScoreDefault rate of the sample
Naive model
AR
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2. Credit risk in IRB: PD operational implementation
- Benchmarking performances:
• Publicly available models (Altman, gloubos grammatikos …)• External commercial tools• Performance level published by other banks• Best ratio• Blind tests
=> but performance depends on particular sample characteristics !
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2. Credit risk in IRB: PD operational implementation
- Analysts feed-back
=> opinion on model performance
=> opinion on zone where model is under performing
=> rating stability versus reactivity
=> weight of the different variables (e.g.: size for Corp at Dexia)
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2. Credit risk in IRB: PD operational implementation
6. Calibration
- If default dataset is used:
• Does it correspond to Basel 2 definition• If not, which adjustments (constant over rating scale) ?
- If rating dataset:
• Which source of info on default (e.g. public statistics of rating agencies) ?• Coherence of reference dataset and default definition
=> Calibration function of application (pricing, Basel 2 …)
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2. Credit risk in IRB: PD operational implementation
7. Test phase
- Double run of some month for the analysts- Feed back from analysts (validation)- Detection for underperformance
8. Production
- Building definitive IT tools (feed back from analyst on user-friendliness)
80
2. Credit risk in IRB: PD operational implementation
Qualitative assessment
- Scoring tool delivers a first rating, but only based on financial assessment
- Qualitative elements have to be integrated
=> in analyst freedom ?
=> or scorecard approach ? +-
-+SubjectivityFlexibility
81
2. Credit risk in IRB: PD operational implementation
Qualitative scorecard
- Develop list of questions with credit analysts- Expert weighting of questions- Rate a sample of counterparties- Study link between qualitative score and rating- If ok, combines qualitative score and financial score
Qualitative score
Very good Good Neutral Bad Very BadAAA 0 0 0 -6 -7AA 1 0 0 -5 -6A 2 1 0 -4 -5
BBB 3 2 0 -3 -4BB 4 3 0 -2 -3B 5 4 0 -1 -2Fi
nanc
ial s
core
Impact in steps
82
2. Credit risk in IRB: PD operational implementation
Typical rating sheet
83
2. Credit risk in IRB: PD operational implementation
Typical rating system structureScoring module based on financial ratios=> Financial rating
Overruling of the analyst=> Final rating before sov ceiling
Qualitative scorcard basedOn a list of questions=> Qualitative score
Potential second rating after sovereign ceiling
Combination of both=> Model rating
84
2. Credit risk in IRB: PD operational implementation
Pre-defining the overrulings
- Shareholders- New credit- Exceptional year- …
=> Allows a more formal follow up of them
85
2. Credit risk in IRB: PD operational implementation
Typical timing (15 months)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Data collection and cleaning
Univariate analysis
Model Construction
Test phase
IT tools definition
Training and
production
Final validation and first
backtesting
86
2. Credit risk in IRB: PD operational implementation
Organizational issue
- We have a model to systematize the rating process- But there is still freedom for the analyst- Statistical development is not complicated, but will the model be used correctly ?
=> operational implementation in organizational structure is the key
Model developers Credit analysts
Quality control
87
2. Credit risk in IRB: PD operational implementation
Quality control: role
- Function appearing in a lot of banks
- Main roles:
• Control that models are applied correctly• Quality of the inputs• Coherency of answers to questions• Support model use and testing
=> Main role: analysis of overrulings
=> This function is key for regulators (reports)
88
2. Credit risk in IRB: PD operational implementation
Quality control: functioning
Credit Analysts
Model developers
Independent review (senior analyst)
Fill ratios and qualitative scorecards
Model rating
Give the final rating to the
borrower
Analysts rating
Difference is within accepted
degree of freedom (e.g. 1 step)
Both analysts and model agrees on the rating – no additional control needed
No agreement on overruling:
discussion (rating
committee)
Agreement on overruling: report to developers
Regular joint back-testing of the model
89
2. Credit risk in IRB: PD operational implementation
Organization at Dexia
- Who is involved in rating models ?
=> Risk= too much control …
Model developer
Credit analysts
Quality Control
Validation department
Rating Committee
AuditGroup of rating follow up
Rating system
90
2. Credit risk in IRB: PD operational implementation
Conclusions on setting up rating models
Key issues for success
- Data, Data, Data …
- Model acceptance by users => Integration of experts in the whole development process
- Support from senior management => resistance to change (micro view >< macro view)
- Role of quality control => also for model acceptance
91
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
92
2. Credit risk in IRB: LGD Minimum requirements
Basic requirements for LGD estimation in IRBA
- History of recovery data in databases- Conservative bias- Business cycle of collected data taken into account- Compliance with Basel 2 default definition- A LGD must be estimated on each facility- Min = long run default weighted average loss rate
Corporate, Bank, Sovereign
- Min 7 years of history
Retail
- Min 5 years of history
93
2. Credit risk in IRB: LGD measures
How to estimate an LGD on each exposure and fulfilling those requirements ?
Operational measurement of LGD
94
2. Credit risk in IRB: LGD measures
Introduction
- Requirements are less numerous than for PD- Might seems easier at a first sight
But …
- less research than on PD- More country specific issues- When going in the details, complexity increases importantly
Challenge…
- PD is based on fixed event at a given date- LGD is a dynamic issue that may last several years
95
2. Credit risk in IRB: LGD measures
Source of LGD data
Market LGD
- Secondary bonds prices- Objective as assets can effectively be sold
Implied LGD
- Derived from asset pricing model- e.g. Bond spreads
Workout LGD
- Effective recoveries after workout process- Discounted at time of default
96
2. Credit risk in IRB: LGD measures
Quality of LGD data
Market LGD
- limited to listed bonds- Secondary prices OK if it is the policy of the bank- If default weighted, might be bias because of demand / supply
Implied LGD
- no standard asset pricing models- e.g. Bond spreads: part of PD, LGD, Liquidity, influence of interest rates …
Workout LGD
- Internal data, objective- few historical data available in most cases
97
2. Credit risk in IRB: LGD measures
Workout LGD
- Economical loss => including costs and discount effects
EADr
tseriesre
LGDt
tt∑ +−
−=)1(
coscov
1
EAD is directly linked to LGD
=> Both should be treated at the same time
98
2. Credit risk in IRB: LGD measures
Example
- A default occurs on a facility of 1 Mio EUR- At the time of default, the facility is used for 500.000 EUR- There is a cost for a legal procedure of 1.000 euro one year after the default- After 2 years the bankruptcy is pronounced and the bank is paid back 0.2 Mio EUR-The discount rate is 5%
%64000.500
05.1000.200
05.11000
12
=+
−
−=LGD
99
2. Credit risk in IRB: LGD measures
Issues around LGD Computation
1. Costs
2. Null LGD
3. Default duration
4. Discount rate
100
2. Credit risk in IRB: LGD measures
1. Costs
- All costs (direct + indirect) should be integrated
- Scope: legal department, credit analysis, risk monitoring … limit ?
- Allocation key for indirect cost: fix, by exposure amount, …
=> Not important at portfolio level, but might be important at facility level (pricing …)
101
2. Credit risk in IRB: LGD measures
2. Null LGD
- LGD might be bull or negative (when contract penalties, or settlement through physical collateral)
• A/ Integrating negative values in average LGD ?• B/ Censoring data (min 0%) ?• C/ Censoring LGD + PD for coherency ?
⇒ B preferred by regulators⇒ C coherent but changes Basel 2 default definition⇒ A …
102
2. Credit risk in IRB: LGD measures
3. Default duration
- If credit is called by the bank at default => OK- But if it is not the case (intensive care), what is the treatment of …
• Lines at default that do not exist at the end ?• Drawn dawn amounts after default (LGD or EAD) ?• Changes of collateral
Default Credit is called
End of workout process
- Lines paid back- New lines- New collateral
- Lines arefrozen
- Recovery process
103
2. Credit risk in IRB: LGD measures
4. Discount rate
- One of the more fundamental questions- Basel 2 text not clear on this issue
‘Firms should use the same rate as that used for an asset of similar risk. They should not use the risk free rate or the firm’s hurdle rate…’ (CP 189, FSA)
‘A bank must establish a discount rate that reflects the time value of money and the opportunity cost of funds to apply to recoveries and costs. The discount rate must be no less than the contract interest rate on new originations of a type similar to the transaction in question, for the lowest-quality grade in which a bank originates such transactions. Where possible, the rate should reflect the fixed rate on newly originated exposures with term corresponding to the average resolution period of defaulting assets’ (pub 8/4/03, Federal Reserve).
104
2. Credit risk in IRB: LGD measures
- Then, in principle market rates for such assets
• But how to estimate ? By comparing secondary market prices of bonds with future cash-flows from worked out recoveries
• Basel 2 default definition >< market (rating agencies)
• Assets without secondary markets (e.g. Mortgages) ?
• Historical rates or implied future ones (Rf 70’s 10%, 90’s 4%)?
105
2. Credit risk in IRB: LGD measures
- Impact might be important: Study of Moral and Oz (2002) on Spanish mortgages
- Applied 3 scenarios
• Rate specific to each facility (rate before default)• Average discount rate (ranging from 2% to 6%)• Forward rates on several periods
⇒ Discount rate +1% = increase of LGD by 8%
⇒ Using different forward rates (rolling period 900 days) results in a maximum difference of 20%
106
2. Credit risk in IRB: LGD measures
Public studies
- Often banks do not have sufficient internal data
- Public studies usually rely on market LGD
Author Period Sample LGD Type Statistics Altman and
Vellore 1982-2001 1.300 Corporate bonds Market - Average 62.8%
- PD and LGD correlated
Araten, Michael and
Peeyush 1982-1999
3.761 large Corporate loans of
JP Morgan Workout
- Average 39.8% - Stand. Dev. 35.4% - Min/ Max (on single loan) –10%/173%
Ciochetti 1986-1995 2.013 commercial mortgages Workout
- Average 30.6% - Min/ Max (annual) 20%/38%
Eales and Edmund 1992-1995
5.782 customers (large consumer loans and small business loans) from Westpac Banking Corp
(Australia), 94% secured loans
Workout
- Average business loan 31%, Median 22% - Average Consumer loans 27%, Median 20% - Distribution of LGD on secured loans is unimodal and skewed towards low LGD - Distribution of LGD on unsecured loans is bimodal
Gupton and Stein 1981-2002
1800 defaulted loans, bonds and preferred stocks
Market
- Beta distribution fits recovery - Small number of LGD<0
Hamilton, Parveen,
Sharon and Cantor
1982-2002 2.678 bonds and
loans (310 secured)
Market
- Beta distribution skewed toward high recoveries - Average LGD 62.8%, Median 70% - Average LGD secured 38.4%, Median 33% - PD and LGD correlated
107
2. Credit risk in IRB: LGD measures
Main findings
- High volatility of LGD
- LGD distributions far from normal
Bimodal distribution
01020304050607080
0% 10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
LGD
Freq
uenc
y
Unimodal (Beta ?) distribution
010203040506070
0% 10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
LGD
Freq
uenc
y
108
2. Credit risk in IRB: LGD measures
LGD drivers
- Moody’s launched a model Losscalc that try to predict LGD
- What influences the LGD level
• Seniority• Secured/ unsecured
• The rating• The country
• The industry• Macro economic drivers• Capital structure
Clear, no doubt
Seems confirmed by several studies
More data needed to confirm
109
2. Credit risk in IRB: LGD measures
PD/ LGD correlation
- One of the most crucial and controversial issue in the industry- Often modeled as a fix parameter in risk management- Most recent studies tend to show that it is correlated- But based on market LGD … supply / demand bias ?
=> Study of Altman: fixed LGD against moderate correlation with PD. 30% of difference for capital at 99.9%
30.1%
29.6%
Diff fix/ correl
1053
564
Correlated LGD
814
437
Volatile LGD
809
435
Fixed LGD
99.9% VAR
99% VAR
Statistic
110
2. Credit risk in IRB: LGD measures
Stressed LGD
‘A bank must estimate an LGD for each facility that aims to reflect economic downturn conditions where necessary to capture the relevant risks…In addition, a bank must take into account the potential for the LGD of the facility to be higher than the default-weighted average during a period when credit losses are substantially higher than average... For this purpose, banks may use averages of loss severities observed during periods of high credit losses, forecasts based on appropriately conservative assumptions, or other similar methods.’
(see article 468 of ICCMCS)
=> Link to PD / LGD correlation issue
111
2. Credit risk in IRB: LGD measures
Arguments against stressed LGD
- The industry had an important reaction against this issue- LGD is the more sensitive parameters in capital requirements, they argued:
• Already conservative bias in other parameters (PD, CCF,…)• Add-on of 6% (Madrid compromise)• Correlation hypothesis high against market standards• Double default effect limited• Conservatism in collateral valuation• Diversification of different portfolios (sectors, geographical locations …)• Diversification of product types
=> An additional stress on LGD is not necessary, and correlation at global level has still to be proved
112
2. Credit risk in IRB: LGD measures
Advanced Basel IIcompliance
Model complexity
LGD RecoveryLGD Basel II(transitions)
LGD Basel II(costs
add-ons)Basic
Complex
Step 1 Step 2… 3
::
113
2. Credit risk in IRB: LGD measures
Assess Loss Given Default and...Basic stepping stones
• First step• rely on the most observable data, on a best effort basis• start from a legal fixed point, namely the recovery world• take the obtained results as a Basel II conservative point of view
• Second step• translate the “recovery” results to the Basel II world
• Third step• enhance the results by costs estimation
Increase afterwards the modelling complexity
… solve the EAD issues at the same timeAs similar data sources addressed
114
2. Credit risk in IRB: LGD measures
...PUK
NLL
Country dimension
B
Advanced Basel IIcompliance
Model complexity
Step 1 Step 2… 3
Complex::
Basic
115
2. Credit risk in IRB: LGD measures
The country dimension• brings a lot of issues related to
• the processes (e.g. legal framework)• the data chains (less developed), and the necessity of,• and… the inherent scarcity of the data
• and therefore forces us to retain a pragmatic approachIt is our aim
• to privilege the developments where this can be ensured on a larger data scale,)• to derive from the Loss Given Default rates developments rates for the other
countries (= second direction), by applying an expert country correction coefficient function of:
• the legal framework• internal or external benchmarks
116
2. Credit risk in IRB: LGD measures
Conclusions on LGD measures
- Fewer focus received from the industry up to now
- But has the greater influence on capital level
- Principles are easy but in practice we face a lot of questions
- Most banks will start with “recovery LGD” as a prudent first guess
- LGD very dependant on local regulation => limited international data pooling
- Stressed LGD required by regulators will be discussed
117
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
118
2. Credit risk in IRB: EAD requirements and examples
Basic requirements for EAD estimation in IRBA
- History of exposure data in databases
- Conservative bias
- Business cycle of collected data taken into account
- Compliance with Basel 2 default definition
- A CCF must be estimated on each facility
- On balance min EAD= exposure
- Off-balance: EAD must estimate possible drawn dawn amount at defaultand after default
- Long run average default weighted, with safety margin if correlation between PD and EAD
119
2. Credit risk in IRB: EAD requirements and examples
Corporate, Bank, Sovereign
- Min 7 years of history
Retail
- Min 5 years of history
2 types of EAD
- The one linked to the behavior of the client: will he draw its line, will it use its guarantee
- The one linked to derivatives instruments, they are function of the evolution of risk parameters (interest rates, exchange rates,…)
120
2. Credit risk in IRB: EAD requirements and examples
EAD linked to client behavior
- CCF have to be estimated on each product type (e.g. double CCF for guarantee lines ?)
- E.g. CCF of foundation approach
0% - Commitments unconditionally cancellable without prior notice.
20% -Short term self-liquidating trade-related contingencies (e.g.: documentary credit collateralized by the underlying goods) - Undrawn commitments with an original maturity of maximum 1 year
50% - Transaction related contingencies (e.g.: performance bonds) - Undrawn commitments with an original maturity greater than 1 year
100%
- Direct credit substitutes (e.g.: general guarantees of indebtedness…) - Sale and repurchase agreements - Forward purchased assets - Securities lending
121
2. Credit risk in IRB: EAD requirements and examples
EAD= Current exposure + CCF x undrawn part of credit line
- For LGD we need to look at default time and after- For EAD we need to look at default time, after, and before
⇒Is the CCF 100% ? Bank penalized for a good management of risky clients ?
Line
Exposure
Default1 year before
122
2. Credit risk in IRB: EAD requirements and examples
Current Mark-to-Market
Add-on = Potential Mark-to-Market or
OTC Derivatives contract residual maturity
Credit Risk
Maturity
Total Credit Risk = Current Credit Risk + Add-On
EAD linked to market parametersOTC Derivatives Credit Risk is a function of two major drivers :
• The Current Credit Risk: equal to current Mark-to-Market• The Potential Future Credit Risk or Add-On: due to potential future evolution of
Mark-to-Market
123
2. Credit risk in IRB: EAD requirements and examples
Forward BuyNov 2002
The current value of a transaction: assessed by calculating the value this transaction would have if it were immediately hedged in the financial markets.
Default
Default
Negative Mark-to-Market
Positive Mark-to-Market
Negative MtM: The value of the transaction is negative. The transaction is ‘out of the money’. The counterparty has a credit exposure on Fortis Bank.
Positive MtM: The value of the transaction is positive. The transaction is ‘in the money’. Fortis Bank has a credit exposure on the counterparty.
124
2. Credit risk in IRB: EAD requirements and examples
Maturity
Add-On
OTC Derivatives contract residual maturity
Reflect the evolution of the OTC Derivatives Credit Risk in the future
?
• Modelled as depending on the future volatility of the market risk factors underlying the derivative contract
• Statistically build by MB Risk Management: comparable methodology to assessment of market Risk
125
2. Credit risk in IRB: EAD requirements and examples
Regulatory add-on
For instance, if a bank has concluded a 3 years interest rate swap with another bank, on a notional amount of 1000 EUR whose market value is currently 10 EUR, the credit-equivalent would be
10 EUR (MTM value) + 1000 EUR × 0.5% (PFE) = 15 EUR
Residual
Maturity
Interest
rate
Exchange rate
and gold Equity
Precious
metal
Other
commodities
≤ 1 year 0.0% 1.0% 6.0% 7.0% 10.0%
1 – 5 years 0.5% 5.0% 8.0% 7.0% 12.0%
≥ 5 years 1.5% 7.5% 10.0% 8.0% 15.0%
126
2. Credit risk in IRB: EAD requirements and examples
In order to reduce Economic Derivatives Credit Risk, it is possible to apply the following Credit Risk Mitigation Factors:
• derivatives collateral management: securities posted to cover net MtM above a specified trigger
• derivatives close-out netting: Offsetting of receivables and liabilities in case of an event of default of the counterparty (only with MtM deals)
• break clause: bilateral contingent option to early cancellation at pre-fixed dates
127
2. Credit risk in IRB: EAD requirements and examples
Definition: Offsetting of receivables and liabilities in case of an event of default of the counterparty (only with MtM deals)
Conditions requested by Regulator for each counterparty to apply Close-Out Netting :
• Signed Master Agreement with the counterparty.• Favourable legal opinion on the Close-Out Netting in the country of incorporation of
the counterparty • Legal opinion define the products and type of counterparty (corporate, bank, financial
institution, etc...) that can be accepted in a Close-Out Netting process. Offsetting takes place within Netting Pools : set of transactions that are eligible
for Close-Out NettingCountries allowing corporates to apply for Close-Out Netting: Australia, Austria,
Canada, Denmark, Finland, Hong-Kong, Ireland, Italy, Japan, The Netherlands, Norway, Portugal, Singapore, UK, USA, South Africa, Sweden, Switzerland
128
2. Credit risk in IRB: EAD requirements and examples
Exposure calculation in case of netting
The PFE is adapted with the following formula:
0.4+0.6×NGR
with NGR being the ratio of the netted MTM value (set to zero if negative) to the gross positive MTM values.
=> Offset of collateral agreement partially recognized at the add-on level
129
2. Credit risk in IRB: EAD requirements and examples
Example
Notional CCF MTMContract 1 1000 EUR 1.0% +100 EURContract 2 2000 EUR 5.0% -30 EURContract 3 3000 EUR 6.0% -40 EUR
NGR = 30 EUR (netted MTM of 100 – 30 – 40) / 100 EUR (sum of positive MTM)=0.3
PFE (without netting)=(1000 × 1% + 2000 × 5%+ 3000 × 6%)= 290 EUR
PFE (corrected for netting) = (0.4 + 0.6 × 0.3) × 290 EUR = 168.2 EUR
Credit-equivalent = 30 EUR (net current exposure)+168.2EUR= 198.2 EUR
130
2. Credit risk in IRB: EAD requirements and examples
Derivatives collateral management implies • Daily Mtm value calculation• Daily Margin calls if the Net Current Mark-to-Market is bigger than a predefined
threshold• Threshold often equal to zero in order to eliminate the capital consumption• Only Cash and OECD government bonds are accepted as collateral• Internal Add-ons are less severe (one month add-on is used)• Documented by a Credit Support Annex to ISDA AgreementsExample : FX deal collateralised - Residual maturity : 4 years
1Y 2Y 3Y 4Y
Maturity
Add-on value [% of the Notional Amount]
6m1m
14.0%
11.5%
9.2%
7.0%
4.9%3.5%
One month Add-on due to collaterisation
131
2. Credit risk in IRB: EAD requirements and examples
• Total maturity is considered to select add-ons curve.• Break-clause date reflects date at which the credit risk exposures stops
Maturity
Add-on value [% of the Notional Amount]
Break-Clause Date Deal Maturity Date
Credit Risk Exposures
132
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
133
2. Credit risk in IRB: Maturity requirements and examples
Maturity calculation
- In IRBF, fixed at 2,5 years (6 months for repo style transactions)
- In IRBA calculated as
- Min 1 year, Max 5 years
- If the bank cannot apply the formula => Final maturity
- Netting: average maturity
- National discretion: break of the 1 year min (e.g.: Repo, Forex, Securities Lending…)
∑∑
CFtCF
134
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
135
3. Understanding RWA function
Goal of part 3: understanding the formula …
136
3. Understanding RWA function
1. The RWA function
2. What is a risk ?
3. Correlation issue
4. The Merton process
5. The formula: stressed default rate
6. The formula: Confidence Interval
7. The formula: expected loss deduction
8. The formula: Maturity adjustment
9. The formula: Madrid issue
10. Weaknesses of the approach
137
3. Understanding RWA function
1. The RWA function
PD
LGD
EAD
Maturity
Correlation
Confidence interval
IRB
FIR
BA
Regulators
Full model recognition:
Basel 3 ?
F(x) = Capital requirements
Capital requirements / 8%= RWA
138
3. Understanding RWA function
2. What is a risk ?
- Formula delivers capital to cover credit risk
- But what is a risk ?
A/ Next year salaries of employees
B/ Next year credit loss on large retail portfolio
C/ Next year amortized value of the building
D/ Next year revenue on corporate business line
=> Risk is the Unexpected
139
3. Understanding RWA function
Expected versus unexpected loss
• Expected loss • Anticipated average annual loss rate• Foreseeable cost of doing business• Differentiated cost of risk recovered through pricing
• Unexpected loss• Unforeseeable • Unanticipated Losses • Requires balance sheet cushion of capital• Differentiated capital sustained with appropriate return
140
3. Understanding RWA function
3. Correlation issue
- What creates the risk is the correlation of defaults (simul 3% PD)
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
100 500 1,000 10,000 50,000
Portfo lio size
defa
ult r
ate
Year 1Year 2Year 3Year 4Year 5Year 6Year 7Year 8Year 9Year 10
141
3. Understanding RWA function
- S&P historical default rates
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
Year
Def
ault
rate
Average
Deviation ? = Basel 2
issue
142
3. Understanding RWA function
4. The Merton process
- Default generating process- E.g.: assets=100, expected return=10%, volatility of asset value 20%,
debt=80
0%2%4%6%8%
10%12%14%16%18%20%
0.0
20.0
40.0
60.0
80.0
100.
0
120.
0
140.
0
160.
0
180.
0
200.
0
Assets and debts value
Freq
uenc
y
Assets value Debts
143
3. Understanding RWA function
- Correlation is introduced in Basel 2 as:
R(A) = w1 R(E) + w2 R(a) R(B) = w1 R(E) + w2 R(b)
Total Return of
companies
Correlated
Return of economy
Systemic risk
Stand alone Return of
companies
Idiosyncratic risk
144
3. Understanding RWA function
5. The formula: stressed default rate
⎟⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ1
)()( 11 CIPD
Asset correlation(Inverse)Normal
distribution
Probability of default
Confidence interval
With some statistical developments …
145
3. Understanding RWA function
- The formula allows to estimate the loss distribution
0.0010.0020.0030.0040.0050.0060.0070.0080.0090.00
100.00
0.15
%0.
33%
0.40
%0.
46%
0.51
%0.
56%
0.61
%0.
66%
0.70
%0.
75%
0.80
%0.
85%
0.90
%0.
96%
1.02
%1.
08%
1.15
%1.
23%
1.32
%1.
43%
1.57
%1.
76%
2.06
%2.
93%
Default rate
Freq
uenc
y
Corp: PD 1%, Correl 20%
=> Basel 2 capital= 14.6%
Qual. Rev. Expo: PD 1%, Correl 4%=> Basel 2 capital= 4.1%
0.0020.0040.0060.0080.00
100.00120.00140.00160.00180.00200.00
0.00
%0.
03%
0.05
%0.
08%
0.11
%0.
14%
0.17
%0.
21%
0.26
%0.
31%
0.36
%0.
42%
0.50
%0.
58%
0.68
%0.
79%
0.93
%1.
10%
1.32
%1.
60%
1.99
%2.
58%
3.69
%7.
81%
Default rate
Freq
uenc
y
146
3. Understanding RWA function
- The different risk classes are associated to different risk weighting function, the only difference is correlation
SME
Retail
Large CorporatesUL
UL
UL
147
3. Understanding RWA function
6. The formula: Confidence Interval
⎟⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ1
)()( 11 CIPD
Confidence interval ?
- Used for all statistical measures
- Signification: not enough capital =>
Accepted Bankruptcy
- Calibration: Desired PD ?
148
3. Understanding RWA function
- Used for all statistical measures
1 Year PD CIAAA 0.01% 99.99%AA+ 0.02% 99.98%AA 0.03% 99.97%AA- 0.04% 99.96%A+ 0.05% 99.95%A 0.06% 99.94%A- 0.07% 99.93%
BBB+ 0.18% 99.82%BBB 0.34% 99.66%BBB- 0.72% 99.28%BB+ 0.91% 99.09%BB 1.15% 98.85%BB- 2.68% 97.32%B+ 3.95% 96.05%B 9.07% 90.93%B- 13.84% 86.16%
⎟⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ1
)999.0()( 11 PD
⇒ Basel 2 calibrated for A- / BBB+ bank
149
3. Understanding RWA function
7. The formula: expected loss deduction
Risk= Unexpected
⇒ Expected loss is a cost that should be integrated in the pricing
⇒ Up to know only PD was considered, we introduce LGD
PDPD
−⎟⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ1
)999.0()( 11
xLGDPDPD
⎥⎥⎦
⎤
⎢⎢⎣
⎡−⎟
⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ1
)999.0()( 11
150
3. Understanding RWA function
• Likelihood that losses will exceed the sum of Expected Loss (EL) and Unexpected Loss (UL)
• 100% minus this likelihood = confidence level• Capital set according to the gap between EL and VaR, and EL is covered by
provisions or revenues, likelihood that the bank will remain solvent over a one-year horizon = confidence level.Under Basel II, capital is set to maintain a supervisory fixed confidence level
151
3. Understanding RWA function
8. The formula: Maturity adjustment
- Input = PD 1 year => output = capital 1 year
- Why not 5 years ? Why not until maturity of the credit ?
We can work on 1 year horizon because we suppose that we can sell all the bank assets …
Assets
100 EUR credit BBB(e.g. 20Bp EL
5% at 99.9%
5 years)
Liabilities
5 EUR capital
95 EUR debt
Enough ?
152
3. Understanding RWA function
Stressed year !
- 5 EUR loss because of default => covered by capital
- 95 EUR of credit still at risk and no more capital => we sell them
- But …
Assets
100 EUR credit BBB (20 Bp EL
5% at 99.9%
5 years)
Liabilities
5 EUR capital
95 EUR debt
New rating year end
% of portfolio Spread New value
AAA 0% 0.05% 0.0AA 5% 0.10% 4.8A 10% 0.20% 9.5
BBB BBB 50% 0.30% 47.5Spread BB 20% 1.00% 18.50.30% B 10% 2.00% 8.9
Default 5%Intitial Value Final Value
95 89Delta
-6
153
3. Understanding RWA function
- Regulators used MTM credit VAR models to calibrate Basel 2 formula
- And smoothed results through regression
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
1 2 3 4 5
Maturity
Reg
ulat
ory
capi
tal
0.1% PD0.5% PD1.0% PD1.5% PD
154
3. Understanding RWA function
- The formula:
))5.2(1()5.11(
11
)999.0()( 11
xbMxxb
xLGDxPDPD
−+−⎥
⎥⎦
⎤
⎢⎢⎣
⎡−⎟
⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ
))²ln(05478.011852.0( PDxb −=
155
3. Understanding RWA function
9. The formula: Madrid issue
- Madrid compromise: regulators accepted EL deduction but introduced a
corrective factor (6% add-on)
With ))²ln(05478.011852.0( PDxb −=
06.1))5.2(1()5.11(
11
)999.0()( 11
xxbMxxb
xLGDxPDPD
−+−⎥
⎥⎦
⎤
⎢⎢⎣
⎡−⎟
⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ
May be reviewed based on QIS 5 results
156
3. Understanding RWA function
SUMMARY
06.1))5.2(1()5.11(
11
)999.0()( 11
xxbMxxb
xLGDxPDPD
−+−⎥
⎥⎦
⎤
⎢⎢⎣
⎡−⎟
⎟⎠
⎞⎜⎜⎝
⎛
−
+ −−
ρφρφ
φ
Stressed DR RecoveriesEL
deduction
Maturity adjustment
(MTM)
Safety margin
ProbaDefault
Asset correl
(Merton) CI for BBB+ / A- rating
157
3. Understanding RWA function
10. Weaknesses of the approach
- Critics of the industry
• Correlation structure too simplistic
• 5 year cap for Maturity adjustment
• Unique confidence interval
• Concentration risk not recognized (single name and industry)
• Fixed LGD
• Single approach (Merton type) kills research
=> Internal credit VAR models ? Future of Basel 3 ?
158
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
159
3. Detailed issues of Risk quantification
1. Calibration of RW functions
2. Correlation level
3. Example of RWA
4. Specialized lending
5. Equity exposures
6. Purchased receivables
160
3. Detailed issues of Risk quantification
1. Calibration of RW functions
The calibration intended in CP 2 (January 2002)
QIS2 results (Spring 2002)G10 average, after incorporating someof the working paper proposals
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
Operationalrisk
Creditrisk
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
Source: CBF
Operationalrisk
Creditrisk
The calibration intended in CP 2 (January 2002)
QIS2 results (Spring 2002)G10 average, after incorporating someof the working paper proposals
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
Operationalrisk
Creditrisk
Operationalrisk
Creditrisk
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
Source: CBF
Operationalrisk
Creditrisk
Operationalrisk
Creditrisk
161
3. Detailed issues of Risk quantification
Source: CBF
The calibration aimed at for in CP3
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
Review of the Standardised Approach calibration
QIS2.5(Nov.2001)
Further review of the IRB calibration
QIS3(Oct.2002)
G10 average, after incorporating someof the working paper proposals
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
QIS2 results (Spring 2002)
Operat.risk
Creditrisk
Operat.risk
Creditrisk
Source: CBF
The calibration aimed at for in CP3
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
Review of the Standardised Approach calibration
QIS2.5(Nov.2001)
Further review of the IRB calibration
QIS3(Oct.2002)
G10 average, after incorporating someof the working paper proposals
0102030405060708090
100110120130
Cur
rent
Acc
ord
Stan
dard
ised
App
roac
h
Foun
datio
nIR
B
QIS2 results (Spring 2002)
Operat.risk
Creditrisk
Operat.risk
Creditrisk
Operat.risk
Creditrisk
Operat.risk
Creditrisk
162
3. Detailed issues of Risk quantification
2. Correlation level
SME
Retail
Large CorporatesUL
ULUL
4%QRE
15%
16%-3%(function of PD)
8% - 20%(function of Turnover
and PD)
12%-24%(function of PD)
Mortgages
Other retail
SME
Corp, Sovereign, Banks
High because of maturity
European pressure
163
3. Detailed issues of Risk quantification
Retail Correlation
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00%
PD
Cor
rela
tion
Asset correlation for corporate portfolios
10%
12%
14%
16%
18%
20%
22%
24%
26%
0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00%
PD
Ass
et c
orre
l
Corporate Other retail
164
3. Detailed issues of Risk quantification
SME
0.01
%
0.80
%
1.70
%
2.60
%
3.50
%
4.40
%
5.30
%
6.20
%
7.10
%
8.00
%
8.90
%5
25
455.0%
10.0%
15.0%
20.0%
25.0%
Correl
PD
Turnover Mios EUR
165
3. Detailed issues of Risk quantification
Impact on SME: a revised pricing ? Customer Condition
SharedFixed Costs
Marginal Costs
Transfer price
Options:• Reservation• Max. Price• Early Term.
Market price
Provision(Expected Loss)
ALM
Cré
dits
Profit margin
Bus
ines
s Li
ne
Capital(Unexpected Loss)
CostsProduct
Cost BL
YES
NO
?
Funding
166
3. Detailed issues of Risk quantification
Capital Required For €100 Unsecured Loan Basel I €100 X 100% X 8% = €8.00 Corporate Retail
20% €1.60 50% €4.00 100% €8.00
Basel II Standardised Approach
€100 X
150%
X 8% =
€12.00
€100 X 75% X 8% = €6.00
€5m €50m
*11.3% - 14.4% €0.90 to €1.16 4.45% €0.36 X
€100 X 8% = X
Basel II IRB Approach (PD 0.03% to 20%; LGD 45%)
188% to 238%
X 8% =
€15.07 to €19.06
€100 X
100.3% €8.02
From Basel II Annex 3 *Shows Firm –size adjustment effect for Sales of €5m and €50m
167
3. Detailed issues of Risk quantification
3. Example of RWA
PD (%) BRW PD (%) BRW140.03190.05290.1450.2700.4810.51000.7
1 125192224633315482105881562520
Original calibration !
168
3. Detailed issues of Risk quantification
Risk Weight IRBF / Standard
0,00%
50,00%
100,00%
150,00%
200,00%
250,00%
300,00%
0,00%
0,05%
0,14%
0,33%
0,75%
1,30%
2,00%
3,00%
5,00%
10,00
%
Risk Weight IRBFCorporateRisk weight IRBF SME
Risk Weight StandardECAI RATEDRisk Weight StandardECAI UNRATED
BBB+ BB+ BB- B+
169
3. Detailed issues of Risk quantification
Maturity : 2,5y Sovereign Retail Other RetailLGD : 45% Corporate Residential Retail Qualifiying
PD Bank Mortgage Revolving0.03% 14.44% 4.15% 45.00% 0.98%0.05% 19.65% 6.23% 6.63% 1.51%0.10% 29.65% 10.69% 11.16% 2.71%0.25% 49.47% 21.30% 21.15% 5.76%0.40% 62.72% 29.94% 28.42% 8.41%0.50% 69.71% 35.08% 32.36% 10.04%0.75% 82.78% 46.46% 40.10% 13.80%1.00% 92.32% 56.40% 45.77% 17.22%1.30% 100.95% 67.00% 50.80% 21.02%1.50% 105.59% 73.45% 53.37% 23.40%2.00% 114.86% 97.94% 57.99% 28.92%2.50% 122.16% 100.64% 60.90% 33.98%3.00% 128.44% 111.99% 62.79% 38.66%4.00% 139.58% 131.63% 65.01% 47.16%5.00% 149.86% 148.22% 66.42% 54.75%6.00% 159.61% 162.52% 67.43% 61.61%10.00% 193.09% 204.41% 75.54% 83.89%15.00% 221.54% 235.72% 88.60% 103.89%20.00% 238.23% 253.12% 100.28% 117.99%
THE 4 CURVES
RISK WEIGHTED ASSET DERIVATION for Corporate, Sovereign, Bank & Retail Exposures
June 2004Without 1.06 conservative factor
170
3. Detailed issues of Risk quantification
4. Specialized lending
250%140%120%95%HVCRE (Basel II not CAD III)
B- C-BB- or B+BB+ or BBBBB- or better
More than 2,5 years
250%115%70%50%Less than 2,5 years
PF,OF,CF,IPRE
WeakSatisfactoryGoodStrong
If NO PD/LGD Corporate Criteria Approach ⇒Supervisory Risk Weights Estimates („Slotting Grid Approach“):
171
3. Detailed issues of Risk quantification
5. Equity exposures
Approaches:
• PD/LGD based approach (same as Corporate (LGD 90%), 5 years maturity)
• a methodology based on market risk and stress testing (target: equities heldmainly for capital gains purposes)
• Simple risk weight• Internal models (VAR)
172
3. Detailed issues of Risk quantification
Equity exposures subject to PD/LGD Method• PD determined according to methods for corporate exposures.
minimum PD’s :• 0.09% for exchange traded equity exposures where investment is part of long-term
customer relationship• 0.09% for non-exchange traded equity exposures where returns on the investment
based on regular and periodic cash flows not derived from capital gains• 0.40% for exchange traded equity exposures including other short positions • 1.25% for all other equity exposures including other short positions
• LGDPrivate equity exposures in sufficiently diversified portfolios 65%All other exposures 90%
• MaturityM assigned to all exposures shall be 5 years
173
3. Detailed issues of Risk quantification
Simple Risk Weight Approach• Risk weight (RW) = 190% for private equity exposures in sufficiently diversified
portfolios.• Risk weight (RW) = 290% for exchange traded equity exposures.• Risk weight (RW) = 370% for all other equity exposures.• Risk-weighted exposure amount = RW * exposure value
Internal Models Approach• Potential loss on the institution’s equity exposures using internal value-at-risk
models subject to the 99th percentile, one-tailed confidence interval of the difference between quarterly returns and an appropriate risk-free rate computed over a long-term sample period, multiplied by 12.5.
• Risk weighted exposure amounts at individual level not less than the sum of minimum risk weighted exposure amounts required under the PD/LGD Approach and the corresponding expected loss amounts multiplied by 12.5.
174
3. Detailed issues of Risk quantification
6. Purchased receivables
Retail – “top-down” approach
Corporate:• If such receivables are purchased, banks are expected to estimate the risk
of their default (“bottom-up” approach). • The alternative "top-down“ approach is possible as long as:
• receivables are purchased from third parties,• must not be subject to netting agreements,• if not secured by collateral, their maturity must not exceed 1 year,• concentration limits must be kept.
Note.: „top-down“ means that claims are viewed as one package, each separate claim is not analyzed
175
3. Detailed issues of Risk quantification
• Within the IRB approach bank is expected to calculated not only the capital requirement for default risk (like for any other exposures) but also capital requirement for so called „dilution risk“
• The essence of dilution risk is the possible existence of a counter-claim of the debtor against the original creditor.
• For the purpose of calculating the RW for such risk, into the corporate risk function is set LGD = 100 % and the portion of expected loss from the exposure will be equal to PD.
• When the receivable is secured by a guarantee, the procedure is the same as for IRB approach for corporate exposures, regardless whether the guarantee covers the risk of default, dilution risk or both.
176
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
177
4. Credit risk mitigation
1. General issues
2. Funded Versus Unfunded
3. Funded
a. Financial collateral eligibleb. Calculationc. Other collateral eligibled. Calculation
4. Unfunded
a. Eligible instrumentsb. Calculation
178
4. Credit risk mitigation
1. General issues
• Institutions using both the standardized approach, or foundation IRB, may take into consideration the effect of Credit Risk Mitigation (CRM) during RW calculation.
• All possible credit risk mitigation methods must be legally enforceable in all relevant countries.
• In addition, institutions must ensure the efficiency of the entire process and address risks connected therewith.
• Institutions must always ensure compliance with minimum requirements for CRM procedures.
• If all defined requirements are met, the institution may decrease the value of RW or EL in compliance with CAD.
• No exposure with a CRM instrument may have a RW higher than an identical, but unprotected exposure.
• In cases when CRM has been incorporated in the calculation of RWA, the provision on CRM is not further applied.
179
4. Credit risk mitigation
2. Funded Versus Unfunded
Credit Risk Mitigation instruments may be funded or unfunded
For funded instruments the following is required:• Sufficient liquidity of the underlying assets and their low volatility• The institution has the right to keep or sell the assets in case of default or
other contractually determined credit event occurrence• The degree of correlation between the value of the asset and creditworthiness
of the debtor may not be inappropriately high
For unfunded instruments the following is required:• The providing entity is sufficiently trustworthy (CAD sets binding list of eligible
providers)
180
4. Credit risk mitigation
3. Funded: a) Financial collateral eligibleCollateral approach Simple approach Comprehensive approach
Impact on RWA
Covered exposure receives the risk weight of the collateral
with a minimum of 20%
Exposures are reduced by the value of collateral and the net result is risk weighted
as unsecured • Cash on deposits at the issuing banks • Gold • Debt securities rated by ECAI at least: BB- for sovereigns (and
assimilated PSE), BBB- for other, A-3/P3 for short term • Unrated debt securities if they are: issued by a bank, senior, liquid,
listed on recognized exchange • Equities (including convertibles bonds) included in a main index • UCITS (Undertakings for Collective Investments in transferable
Securities) and mutual funds if: quoted daily and invest only in the instruments above
Eligible collateral
• Equities (including convertibles bonds) not included in a main index but listed on a recognized exchange
• UCITS and mutual funds which include such equities
181
4. Credit risk mitigation
Eligibility
• Low correlation between the creditworthiness of the debtor and the value of the collateral.
• Operational requirements – sufficient documentation, risk management processes connected with collateral, at least semi-annual frequency of re-pricing and in cases when the collateral is held by a third party such party may not report it among its assets.
• In addition, under the simple approach with respect to financial collateral it is required that residual maturity of the collateral is not shorter than the residual maturity of the exposure.
182
4. Credit risk mitigation
3. Funded: b) Calculation for financial collateral
• In order to mitigate the capital requirement, banks may use the simple approach replacing the risk weight of the counterparty by the risk weight of the collateral. However simple approach is NOT allowed within IRB.
• Comprehensive (FCCM) approach:• allows a greater ratio of offsetting the exposure by collateral through decreasing
the value of the exposure by the value of the collateral. • The principle of this approach is that the market value of the collateral is adjusted
for the haircut representing the estimate of volatility of such collateral. A different haircut is allocated to the exposure itself. The level of such haircut may be determined:
• by the regulator,• through an estimate made by the bank (VaR model).
• In case the collateral is denominated in a different currency than the exposure itself, another haircut considering currency risk is applied
183
4. Credit risk mitigation
Comprehensive approach
Adjusted value of exposure (E*) is calculated as follows:
E* = max{0,[E × (1+HE) – C × (1-HC-HFX)]}
where:E = is the exposure value according to the standardized or IRB approachHE = discount (haircut) applicable to the given exposureC = present value of the collateral receivedHC = discount (haircut) applicable to the collateralHFX = discount (haircut) for the currency mismatch between collateral and exposure
The relevant haircuts can be calculated in two ways:• use of regulatory estimates,• bank’s own estimates.
184
4. Credit risk mitigation
Haircuts proposed by regulators
Collateral Residual Maturity Sovereign (and assimilated) issuers Other issuers
AAA to AA- and A1 securities
≤ 1 year > 1 year, ≤ 5 years
> 5 years
0.5% 2.0% 4.0%
1.0% 4.0% 8.0%
A+ to BBB- and A2 / A3 / P-3 and unrated
bank securities
≤ 1 year > 1 year, ≤ 5 years
> 5 years
1.0% 3.0% 6.0%
2.0% 6.0%
12.0% BB+ to BB- All 15.0% Not eligible
Main index equities and gold 15.0% Other equities listed on a recognised
exchange 25.0%
UCITS / Mutual funds Highest haircut applicable to any security in which the fund can invest
Cash in the same currency 0.0% Collateral and exposures in different
currencies 8.0%
185
4. Credit risk mitigation
Haircuts adjustment
- Those haircuts are for a 10 day holding period and should be adjusted for other effective holding period with
186
4. Credit risk mitigation
The following minimum holding period should be used
• If there is no daily remargining or revaluation, the minimum holding period has to be adapted upward.
• To transform the supervisory haircuts for the ten days holding period to haircuts adapted for the transaction-holding period, banks have to use the square root of time formula.
20 daysSecured loans10 daysOther capital market transactions5 daysREPO type transactions
187
4. Credit risk mitigation
Worked out example
Example :a bank has a three years BBB bond as collateral to cover a three years secured lending operation. The bond is marked to market every week. The bond issuer is a corporate and the face value is 100 EUR. The haircut is calculated as follow:
• The supervisory haircut for a three years BBB bond issued by a corporate is 6% • The minimum holding period for secured lending is 20 business days• As the bond is not revaluated daily but weekly (every five business days), the
minimum holding period must be adapted to 24 (as there are five days instead of one between revaluations)
• Then the supervisory haircut that is based on a ten days holding period is scaled up using the square root of time formula
• The value of the bond is then 100 EUR x (1-9.3%)= 90.7 EUR.
%3.91024%0.6 == xHaircut
188
4. Credit risk mitigation
Internal measurement of haircuts
- Internal VAR models may be used to estimate haircuts but subject to following requirements
Qualitative criteria Quantitative criteria - Estimated haircuts must be used in
day to day risk management - Risk measurement system must be
documented and used in conjunction with internal exposures limits
- At least annual review by the audit of the risk measurement framework
- Use of the 99th percentile, one-tailed confidence interval
- Use of minimum holding periods as for supervisory haircuts
- Liquidity of the collateral taken into account when determining the minimum holding period
- Minimum one year of historical data, updated at least every three months
189
4. Credit risk mitigation
Zero haircuts for Repo transaction
At national discretion, some collateral can receive zero haircuts when used in REPO-style transactions
- if exposures and collaterals are cash or sovereign
- in the same currency
- there is a daily remargining
- the maximum liquidation period is four days
- with core market participants (sovereigns, central banks, banks…).
190
4. Credit risk mitigation
Netting agreements
AE = max [0; (Σ E - Σ C + Σ (Es x Hs) + Σ (Efx x Hfx))]
With AE = Adjusted Exposure
Σ E = sum of exposures (positive and negative)
Σ C = sum of the values of received collaterals
Es = absolute values of net positions in a given security
Hs = haircut appropriate to Es
Efx = absolute value of the net position in a currency different from the settlement currency
Hfx = haircut appropriate for currency mismatch
191
4. Credit risk mitigation
3. Funded: c) Other collateral eligible
Real estate collateral (CRE / RRE)• Monitoring the market price of the real estate - with at least an annual
frequency. In case of loans above 3 mill. € or above 5 % of own capital, an independent appraisal must be performed every 3 years.
• Documentation for all approved types of real estate.• The real estate must be properly insured.
Financial receivables • Claims <1y, repayment will occur through the commercial or financial flows
related to the underlying assets of the borrower.• Legal certainty: the bank can take control of it• Risk management requirements (collection cost, concentration risk, …)
192
4. Credit risk mitigation
Other collateral
Regulators should ensure that:
• Liquid markets• Public prices
Banks requirements:
• First claim• Loan agreements should describe valuation procedure• For inventories: physical inspection• Collateral accepted, valuation methods should be described in banks
procedures
193
4. Credit risk mitigation
3. Funded: d) Other collateral calculation
IRBF
1/ Minimum collateralization test2/ collateral haircut3/ New LGD
Collateral type Minimum collateralisation
Collateral Haircut Final LGD
Receivables 0% 125% 35%
CRE / RRE 30% 140% 35%
Other physical collateral 30% 140% 40%
194
4. Credit risk mitigation
IRBF Worked out example
Exposure of 100 EUR secured by a commercial real estate of 40 EUR would be valued as follows
• 40 EUR / 100 EUR = 40% which is superior to the 30% minimum collateralisation level.
• haircuted by 140%, 40 EUR/140%= 28.6 EUR. • LGD applied on the part of the exposure corresponding to the haircuted value
would be 35%.
⇒The LGD on the 100 EUR exposure would then be 45% (assuming senior corporate exposure) on 71.4 EUR and 35 % on 28.6 EUR.
195
4. Credit risk mitigation
IRBA
• the rules are less strict as any kind of collateral can be recognized
• deduction from the exposure to compute the capital requirements
• as long as the bank has historical data to support its valuation (at least 7 years of data on average recovery value on the various types of collaterals it plans to use).
⇒ Collateral effect in IRBA is much more important
196
4. Credit risk mitigation
Maturity mismatch
Maturity mismatch is a situation when the residual maturity of the credit protection instrument is shorter than the one of the given exposure.
Maturity of exposure is defined as the longest possible residual period until the debtor meets its obligations (maximum 5 years).
Maturity of protection is defined as the shortest possible delay when the credit protection can be cancelled.
Calculation:• In general, the value of CRM instrument is multiplied by:
• where:• t … is maturity of protection (in years)• T … is maturity of exposure (in years)
,25,025,0
−−
Tt
197
4. Credit risk mitigation
4. Unfunded a) Eligible instruments
Recognized unfunded CRM: only the following credit protection providers of unfunded protection may be recognized in IRBF:
• central banks and sovereigns,• local governments and PSE,• multilateral development banks,• international organizations (with a 0 % RW with the standardized
approach),• Financial institutions,• corporate with A- minimum• Must cover capital and interest
IRBA:
• No limit
198
4. Credit risk mitigation
Beside above mentioned instruments some types of credit derivativesmay also be used.
Some of them are treated as unfunded (=guarantees)
• Credit Default Swaps: if protection is similar to guarantees• Total Return Swaps: except if premiums included in P&L and fluctuation of asset
values not in MTM
Some of them as funded (=collateral)
• Cash funded CLN: considered as collateralized transaction
199
4. Credit risk mitigation
Requirements: Guarantees
- Guarantor should be rated (annual review)- Effect of guarantor can be recognized in PD or LGD (IRBA) - Cannot result in RWA inferior to a direct exposure to guarantor- Guarantee should be written, unconditional, non-cancellable, up to maturity
Requirements: Credit derivatives
- Credit events should cover: default, bankruptcy, restructuration with lower NPV (or partial recognition)
- The one who determines default cannot be protection seller alone- If a reference asset is used: should be at least pari passu, same issuer
200
4. Credit risk mitigation
4. Unfunded b) Calculation
Base case: substitution
• For the secured part of exposure (coverage adjusted for currency and maturity haircut), PD of the credit protection provider is used instead of PD of debtor (and LGD if better).
• The uncovered part of the exposure still has a PD of the debtor and LGD according the underlying exposure.
• The value of Guarantee must always be adjusted in case of a currency mismatch between the exposure and protection instrument of a currency haircut HFX (the haircut is calculated in the same way as under the financial collateral comprehensive method):
)H(1GG FX* −×=
201
4. Credit risk mitigation
Critics of the industry
• No recognition of double default effect (e.g. AA covered by AA no effect) => No incentive for those efficient risk management tools
• But simple PD product supposes independence => again a correlation issue
• July 2005: proposal of Basel 2
• But limited to professional protection providers
202
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
203
5. Securitization
• Banks must apply the securitisation framework to determine the capital requirements for exposures resulting from traditional, synthetic and other types of securitisations.
• As securitisation can be structured in several ways, the method how it is treated for capital adequacy purposes must be based rather on its economic substance than on its various legal forms.
• The economic substance of transactions should indicate whether or not they should be considered as securitisation.
204
5. Securitization
Traditional securitisation• A structure when the cash flow from the underlying pool of exposures relates at least to
two different exposures or tranches with different degrees of credit risk.• The payment to the investor depends on the development of the underlying exposure.• Categorized structure (in tranches) characterizing securitisation differs from regular debt
instruments in that the “junior” tranches may absorb losses without affecting more senior tranches.
Synthetic securitisations• A structure of at least two categorized (stratified) risk positions or tranches taking into
consideration a different degree of credit risk while the credit risk of the underlying pool is transferred through guarantees or credit derivatives (funded credit linked notes or unfunded credit default swap).
• The risk of investor again depends on the development of the underlying exposure.
205
5. Securitization
Originator means either of the following:• an entity which, either itself or through related entities, directly or indirectly,
was involved in the original agreement which created the obligations or potential obligations of the debtor or potential debtor giving rise to exposure being securitised;
• an entity which purchases a third party’s exposures onto its balance sheet and then securitises them;
Investor:• institution which is not the originator, sponsor or provider of services and
carries the economic risk of the securitisation exposure.
206
5. Securitization
Capital requirements:
Standardized approach (may be used in IRB)
- Banks that invest in exposures that they originate themselves that receive an external rating below BBB- must deduct them form their capital base
- For off-balance sheet exposures, CCF are used (if they are externally rated, the CCF is 100%).
LT rating (ST
rating)
AAA to AA-
(A-1/P-1)
A+ to A- (A2/P-2)
BBB+ to BBB-
(A-3/P-3)
BB+ to BB-
Other ratings and unrated
RWA 20% 50% 100% 350% Deducted
207
5. Securitization
IRB Approach
The Rating Based Approach (RBA) that must be applied when the securitisedtranche has external or internal ratings.
The Supervisory Formula (SF) is used when there are no available ratings.
The Internal Assessment Approach (IAA) can also be used when there are no available ratings but only for exposures extended to ABCP programmes.
208
5. Securitization
Rating Based Approach
• a risk weight is assigned in function of an external or internal inferred rating (that can be assigned in reference to an external rating already given to another tranche that is of equal seniority or more junior and of equal or shorter maturity)
• the granularity of the pool calculated with N=
• the seniority of the position.
∑∑
²)²(
EADEAD
209
5. Securitization
RW Rating Senior tranche, N≥6
Not senior tranches and
N≥6 N<6
AAA 7% 12% 20% AA 8% 15% 25% A+ 10% 18% A 12% 20% A- 20% 35%
35%
BBB+ 35% 50% BBB 60% 75% BBB- 100% BB+ 250% BB 425% BB- 650%
Long Term ratings
Unrated and < BB- Deduction
A1/P-1 7% 12% 20% A2/P-2 12% 20% 35% A3/P-3 60% 75% 75% Short Term
Ratings Other and unrated Deduction
210
5. Securitization
Internal Assessment Approach
• Only applies to ABCP programmes. Banks can use their internal ratings if they meet some operational requirements, mainly:
- The ABCP must be externally rated (the underlying, not the securitisedtranche).
- The internal assessment of the tranche must be based on ECAI criteria and used in the bank’s internal risk management systems.
- A credit analysis of the asset seller’s risk profile must be performed.
⇒Then, the risk-weight associated to the internal rating is the same as in the RBA
211
5. Securitization
The Supervisory Formula
-is used when there is no external rating, no inferred internal rating and no internal rating given to an ABCP programme.
-The capital requirement is a function of:
- The IRB capital charge had the underlying exposures not been securitised (KIRB)
- The tranche’s credit enhancement level (L)
-The tranche’s thickness (T)
- The pool’s effective number of exposures (N)
- The pool’s exposure weighted average loss-given-default (LGD).
212
5. Securitization
-The tranche’s IRB capital charge is the greater of 0.0056xT or S[L+T]-S[L]. S[L] is the supervisory formula defined as
213
5. Securitization
- Until the sum of the subordinated tranches and tranche for which the capital is calculated is inferior to the regulatory capital had the exposures not been securitised, the capital rate is 100%.
- Then it decreases sharply until the marginal capital rate becomes close to zero, as illustrated on the following graphs (in this example the capital had the exposures not been securitised would be 8.14 EUR, and the credit enhancement equals 5 EUR)
Securitised assets: 100 EUR
K irb= 8.14 EURFirst loss 5 EUR
Bank investment
X EUR
Senior Tranche
(100 – 3 – X) EUR
Bank buys
214
5. Securitization
0
1
2
3
4
5
6
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5
S i z e o f t h e t r a n c h e
Cap
ital
S i z e o f t h e t r a n c h e 3 . 1 4C a p i t a l 3 . 1 4
0 %
2 0 %
4 0 %
6 0 %
8 0 %
1 0 0 %
1 2 0 %
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5
T r a n c h e s i z e
Cap
ital /
tran
che
size
S i z e o f t h e t r a n c h e 3 . 1 4C a p i t a l r a t e 1 0 0 %
215
5. Securitization
Comparison between Corporate and securitised exposures
• Ratings of external agencies mainly based on EL measures
• UL may be very different, which is reflected in RWA
0%
200%
400%
600%
800%
1000%
1200%
1400%
AAA AA A+ A A- BBB+ BBB BBB- BB+ BB BB- B+ B B-
Securitisation exposure Corporate Bond exposure
216
Agenda
1. Introduction to IRB2. Risk parameters in IRB
• PD: Minimum requirements and operational implementation• LGD: Minimum requirements and operational implementation• EAD: Minimum requirements and examples• Maturity: Minimum requirements and examples
3. Risk quantification• Understanding the Risk weighting function • Detailed issues of Risk quantification
4. Credit Risk Mitigation5. Securitization6. Application for supervisory approval
217
6. Application for supervisory approval
1960 1970 1980 1990 2000 2001 2002 2003 2005 20062004
3-6-3 principle
Liberalisation
1974: G10 launch Basel Committee
1988: Basel I Accord
1990: 100 countries apply Basel I
1996: Market riskJune/1999: CP1
Jan/2001: CP2
Apr&May: QIS1,2
Nov: QIS2,5
Oct: QIS3
May: Release of CP3
July: QIS3 resultspublished
Dec: Finalised Version of the new Accord
Jan: start parallel run
Jan: Basel II comes in force
2007
218
6. Application for supervisory approval
Meetingall concerned supervisors
Local supervisors locallegal entities
Local solvency reporting
CRD local implementation
Current legal requirements
Consolidating supervisor
College of supervisors
ConsolidatedBank
Consolidated solvency reporting
Supervisory review
Single entry pointValidation & permission Act as
ONEcompany
Home-host issue
219
6. Application for supervisory approval
Key success and quiet revolution in supervisory world
Framework• Overall responsibilities (going concern & emergency situations)
• Assessment of compliance with the requirements for FIRBA, AIRBA and AMA
• Coordination of gathering & dissemination of information• Planning and coordination of supervisory activities, including Pillar 2• Other specific provisions
• Permission to go FIRBA, AIRBA and AMA• Reach a joint decision within six months• In the absence of joint decision, make its own decision• The decision of the consolidating supervisor will be recognised and
applied by the local supervisors
220
6. Application for supervisory approval
To get supervisory approval
- Regulators resources limited => regulators will rely extensively on internal validation
- More important than models is use test => key issue is communication- 4 key dimensions investigated:
Rating system (PD and LGD)
Data management system
Quantification process
Oversight and control mechanisms
Calibration
Monitor
Support
221
6. Application for supervisory approval
Statistical validation (non-availability of specific test to be justified)
• Model power statistics• Build in and out sample• Model power statistics for a 5 years’ period before default• Rank ordering comparison with external & internal rating tool • Justification of calibration
Business and Credit Experts validation• Business and credit experts blind test• Business and credit experts pilot phase
Rating system (PD and LGD)
222
6. Application for supervisory approval
- Estimation of PD: internal / external ?
- Coherence with bank portfolio ?
- Conservative bias ?
- Business cycle state at time of collection ?
- Correlation between various parameters ?
Quantification process
223
6. Application for supervisory approval
- Corporate governance issue ?
- Control of a coherent use of the models ?
- Organization for model approval / review ?
- Follow up of overrulings ?
- Reporting of model results ?
Oversight and control mechanisms
224
6. Application for supervisory approval
Example: Dexia Control of rating quality
Rating tool
Quality Control
AuditHead of analysts
Model manager Credit analysts
Rating Committee
Rating follow up group
Validation Department
Validation Committee
225
Data management system
6. Application for supervisory approval
-Are the rating tools secured ?
-Are all the data historized (bank able to apply backward model changes) ?
- Do data management systems allows to verify that guidelines arerespected ?
- Integrity of the data used for regulatory capital calculation ?
- Do data management support use test ?
226
6. Application for supervisory approval
Primary Validation responsibility = the bank NOT supervisors
AIG subgroup : 6 principles – January 2005
Assessing the predictive ability & use• historical experience, forward looking, discriminating power, reassessment when
divergence from expected results, ….RAM EXPERT Function
Iterative process• changing market and operating conditions• on-going process
No single method• statistical tools• other methods (back testing, benchmarking, …internalisation of ECAI’s)• combination of methods
Qualitative and quantitative• not only a mathematical exercise• must cover structures, procedures, controls, ...
Subject to independent review• validation ≠ audit
227
6. Application for supervisory approval
Duration 3 monthsRegulators 4 2 Quantitative Specialists
2 Process SpecialistsReview documentation, interviews ( credit management,
analytics, chief risk officer, business)Report CEO, CCO, Chief Auditor, External Auditors
Point of attention
Outliers detectionCoherency of default definitionDocumentation of methodological choices (test)Central Documentation RepositoryOverruling process
228
Agenda
Conclusions
229
7. Conclusion
• A permanently strong Credit Risk framework is the aim and key driver, Basel 2 gives the needed leverage
• Model development is not a one shot exercise but a continuous process based on input from users, refined data and new insights
• USE the models and use them respecting the rules
• A lot of work has been done but still a lot needs to be done : we know we can rely on your dedication and professionalism to succeed
230
• Management empowerment is crucial for validation
• Model validation not an exact science : a model might assess relative quality of the counterparty but it cannot capture all elements as it is based on portfolio analysis : this means : on average over time
• Expert judgement is of critical importance : for modelling and for communication
• Data issues centre around quantity not quality
• Regional difference in culture and modelling e.g. equity model versus debt model
• Use test of critical importance: do you believe your model for day to day financial decision ?
7. Conclusion
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• Hold on funds in excess of 8 %
• Reinforce arrangements and strategies
• Apply specific provisioning policy
• Restrict/limit business, operations…
• Reduce risk in activities, product, systems
7. Conclusion: not meet requirements of directive?(art. 136)
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