Importancia Da Qualidade de Dados Nas Abordagens IRB - Isabelle Thomazeau

7/28/2019 Importancia Da Qualidade de Dados Nas Abordagens IRB - Isabelle Thomazeau

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Key role of data qualityin Internal Ratings Based (IRB) approaches

10/22/2012 Isabelle Thomazeau Banque de France - ACP

International Congress of RisksSao Paulo 22-23 October 2012


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Disclaimer

The views in this presentation are those of the author and donot necessarily reflect those of the Autorit de Contrle

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.


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Preliminary remarks

Another presentation in this seminar describes the validation process tobe applied for IRB models.

The review of data is part of the validation process.

This presentation focuses on the data to be used in IRB approaches:

To estimate IRB parameters (PD and LGD) for assets which have notdefaulted on cor orate exce t S ecialized lendin soverei n banks

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and retail portfolios.

EAD/CCF will not be detailed nor other Basel portfolios

To calculate these IRB parameters on the whole perimeter Implementation


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Summary

I. Introduction1. Context2. Presentation of IRB approaches

II. PD

1. Rating1. Scoring models2. Expert given approach

2. PD estimation1. Context

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2.Default data available3. Low Default Portfolios

III. LGD1. Context2. No data available3. Recovery data available

IV. Implementation, information systemsV. Back-testingVI. Conclusion


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I.1 Introduction - Context

The Basel Committee on Banking Supervision (BCBS)introduced in April 1995 the notion of internal model to estimatethe capital adequacy of banks trading book. The risk indicatorused is called Value-at-Risk (VaR).

The use of internal models was then extended to credit risk and

operational risk in June 2004.

Main reference from the Basel Committee on BankingSupervision for IRB approaches: International Convergence of Capital Measurement and

ap ta tan ar s : ev se ramewor , ompre ens veVersion june 2006 which is a compilation of somedocuments among which the 1996 Amendments to theCapital Accord. http://www.bis.org/publ/bcbs128.htm. [1]

In Europe, Committee of European Banking Supervisors(CEBS)

Guidelines on implementation, validation and assessmentof Advanced Measurement (AMA) and Internal RatingsBased (IRB) Approaches . 04/04/2006

http://www.eba.europa.eu/Publications/Guidelines...

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I.1 Introduction - Context

In France, institutions may use Internal Ratings Based (IRB)approaches for the calculation of their minimum capitalrequirements for Credit Risk, instead of the StandardisedApproach.

French Commission Bancaire (now the Prudential ControlAuthority ACP) authorized the first institutions to use theirIRB approaches at the end of 2007.

,

models for credit risk for part or all of their banking bookportfolios. Some information on these models are given in theirannual reports.

The Risk Modeling Control Unit (CCRM) team from the ACP

is particularly in charge of the models on-site reviews.

For IRB internal models the review must be made a priori, inorder to determine whether, or not, the institution can beallowed to use its internal models for prudential purposes.

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I.2 Introduction - Presentation of IRB approaches

Under the IRB approaches, banks must categorize bankingbook exposures into 5 broad classes of assets :

Corporate

(+ 5 sub-classes of specialized lending):

project finance, object finance,

commodities finance,

income-producing real estate,

g -vo a y commerc a rea es a e

Sovereign

Bank

Retail (3 sub-classes)

exposures secured by residential properties,

qualifying revolving retail exposures,

other retail exposures

Equity

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The IRB approaches require the banks to use their owninternal estimates of some or all of the following 4 riskcomponents for a given exposure:

Probability of Default (PD) : defined per rating and classes

of assets, it represents the one year probability of default ofthe borrower

Loss Given Default (LGD) : defined by homogenous risk,

the loss given default as a percentage of the EAD

Exposure At Default (EAD)/Credit Conversion Factor (CCF):once again defined by homogenous risk classes, thesequantities measure the exposure rate when default happens

Effective Maturity (M) effective maturity of the exposurecalculated by the bank (only for Corporate portfolios)

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One approach for Retail Banks provide their own estimates of PD, LGD and EAD,

with minimum standards.

Two approaches for corporate (except specialised lending),banks and sovereign: IRB Foundation (IRBF):

Banks rovide their own estimates of PD

Supervisory estimates for other risk components IRB Advanced (IRBA):

Banks provide their own estimates of PD, LGD and EADand their own calculation of M, with minimum standards(e.g. PD: 0.03% except for sovereign).

For both IRBF and IRBA approaches, the risk-weightedassets (RWA), which depend on PD, LGD, EAD (CCF) areprovided in the Framework [1].

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II PD

Main steps in the process:

Segmentation of the population in homogeneous riskclasses in terms of default risk (i.e. rating) Construction of a notation tool at a borrower or exposure

level. Choice between: Scores

Expert given approach

Mixed method

PD estimation in each class At least 7 non defaulted grades have to be defined

(corporate, sovereign, banks)

A PD must be calibrated for each grade inside a given class.

Validation Independent periodic review of the PD modelling (score and

segmentation)

Back-testing

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II.1 PD - Rating

1. Scoring models

Statistical approaches may be applied when a significantnumber of defaults is observed:

Retail, Small and Medium size Entities (SME)

Steps:

Define the sample used to build the score

Choose the criteria to be explained (Y) :

e ect a st o qua tat ve an quant tat ve ata can ates toexplain Y

Segmentation of into several brackets Xi manually orwith optimization algorithms

Measure of the ability to explain Y as a function of Xi

using statistical indicators (Chi2, T-Tschuprov, V-

Cramer, ) Final selection of Xi and coefficients, computed using

statistical tools so that :

Y = i Xi

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II.1 PD - Rating

Three main technics to select the final variables of thescore :

Backward : Many variables are initially included in themodel. Step by step some of them are removed if it does

not really impact the discrimination of the model. Forward : Variables are added one by one to the model.

The process stops when adding one more variable doesnot impact the discrimination of the model.

Stepwise : At each step variables can be added or removed.

At the end of this process, the selected Xi have lowcorrelations between them.

Score tranching in homogeneous classes

Enough exposures or borrowers in each pool

No undue concentration

Correct risk differentiation and risk level stability

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II.1 PD - Rating

Sample

Large sample

to be split in two parts, one to build the score, and thesecond to test it.

Otherwise, bootstrapping methods can be applied.

Sample representative of the population

It would be identical to the o ulation re ardin all its

characteristics. In fact, as there are a lot of variables, the distribution of

the sample is generally studied regarding some maincriteria

For example Corporate : Region, sector, size, ,

The procedure used to build the calibration sample mustnot generate any selection bias

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II.1 PD - Rating

Data for each observation

For each observation (borrower/transaction), at thebeginning of the process, take a large range of qualitativeand quantitative data among which the Xi will be selected: General characteristics Solvability criteria:

Retail : profession, revenues, Corporate: Capital, debts,

The quality of the data is essential:

Missing values: a process to deal with missing values muste eterm ne :

Elimination of these data above a threshold of missingvalues in the sample

Replace them by the average Replace them by the 50% percentile,

The process used may have an impact on the result ofthe modelisation

Errors: a very limited number of erroneous values in thedatabase may impact significantly the calibration of themodel: erroneous data to be removed or replaced.

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II.1 PD - Rating

Example 1Simulation of two data with very low correlation (-4%)

Change of value for these two data for one observation in the sample (these newvalues are erroneous ones, in red in the following plot)

The correlation increases from -4% to 56%.

At least one of these data will be removed from the score because of its highcorrelation with the other, due to an erroneous value.

The plot represents one data as a function of the other for a set of observations.

-4

-2

0

2

4

6

8

10

-4 -2 0 2 4 6 8 10 12 14

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II.1 PD - Rating

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Example 2

Simulation of two data with very high correlation (-75%)

Change of value for one of these two data for one observation (toobtain an erroneous value).

The correlation decreases from 75% to 13%.

Perhaps these two data will be taken into account into the score,due to an erroneous value of one of them in one observation of thesample: low correlation due to one erroneous value.

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-25

-20

-15

-10

-5

0

-3 -2 -1 0 1 2 3


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II.1 PD - Rating

Definition of the criteria to be explained

Criteria : Usually default (or not default) for a given timehorizon.

Default may be defined at a counterparty or transaction level(sometimes for Retail)

This time horizon is often (but not always) of one year (butin any case the PD is a 1 year PD)

For each borrower/transaction in the sample, a photo istaken at a date T and the default is observed during the

, , . . ,

Data have to be available one year before theobservation default/no default

Sometimes, data at T (which are data in the past) haveto be reconstructed, especially qualitative ones.

All these tasks on data are time consuming but areessential for the score to be of good quality(discriminant,)

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II.1 PD - Rating

2. Expert given approach

Usually applied for Low Default Portfolios: Large Corporate,

Banks, Sovereign But sometimes scoring model by replication of (external)ratings

Notation to be objective:

Anyone could approximately reproduce it Notation grids make easier this internal rating process

Correspondence between internal and external ratings: mapping are usually defined (for the further step ofestimation of the PD in each class)

Differences between internal and external ratings have to beexplained.

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II.2 PD - Estimation

1. Context

PD estimated for each class as a Long Term average ofannual default rates.

Requirement : calculation with 1 year default rates observed

during at least a 5 years period.

PD Through The Cycle (TTC)

Define the length of a cycle

s are not ca cu ate on an ent re cyc e or on severa

entire cycles, they can be under or overestimated dependingon the position in the cycle

Finally, PD have to be estimated using an average of

observed default rates on a long period, preferably multiplierof a cycle

Prudential margins may have to be added (for data quality,models uncertainties, TTC effects, )

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Two important components in the default definition:

Materiality threshold:

If the threshold is too low, the PD are likely to go up and theLGD to decrease. Then the RWA are often underestimated.

Some European countries have already defined a threshold

Future CRR/CRD4: The supervisors will have to fix athreshold (Regulatory Technical Standards from theEuropean Banking Authority).

Contagion : The default rates will be higher when the default contagion is

applied to the whole subsidiaries in a group, than if not.

Clear rules of contagion to be defined:

For example for retail portfolios, if the default is defined at

a transaction level, contagion to all the transactions of theborrower, to clients linked to this borrower,

For Corporate, banks and sovereigns, materiality thresholdsand contagion are more judgmental

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Calculation of the1 year observed default rates times seriesfor each class:

Used for PD estimations when sufficient default data are

available for every risk pool

Used for Back-testing purposes

1 year default rate=

number of observed defaults during the 1 year period

divided by

population in the class at the beginning of the period.

Rectification techniques sometimes used in order to obtain comparable default rates in the time series

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So, a one year default rates depends on the approach usedto determine:

(a): The number of default during the one year periodconsidered,

(b): The total population in the class.

Rules have to be specified for the treatment of specificcases:

Multi defaults durin the eriod im act on a

If they are taken into account, increase of theobserved default rate, but probably decrease of theLGD

Occurrences not available on the whole period (impact on(b))

Usually removed except if a default occurred as theywere in the sample

Half of these contracts removed from the population

Technical defaults (impact on (a))

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2. Default data available

The estimation of the PDs must be based on observedinternal default rates calculated on the whole population andnot on samples.

Many factors impact the determination of the observed oneyear default rates:

,

contagion rules, multi defaults treatment,

All these factors also impact the PDs.

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Update frequency:

Yearly:

For example time series of one year defaults rateslengthened every year:

question of the maximum length

Length is not an entire number of economic cycles

If the back-testing is not acceptable.

In France, when the first IRB models have been reviewed bythe ACP, most observed defaults rates have been correctedto take into account data quality problems and additionalmargins have been included in the PD estimation.

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3. Low Default Portfolios (LDP)

Use of external rating agencies long term default rates todetermine the PD. Pay attention to:

Adequacy between the internal and external default

definitions Criteria taken into account for external and internal ratings

definitions (for example Moodys ratings represent jugementon the Expected Loss (EL), ie PD and LGD)

Re resentativit of the external a encies o ulation

More or less complex calculation tool to calculate the PDs toapply to each internal rating :

Mappings between internal and external ratings

Generally the number of classes is not the same forinternal and external ratings

Every bank applies its own methodology to calculate its PDsbased on default rates published by external agencies.

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Use of shared databases is allowed for PD (but not used forFrench banks).

Academic litterature gives techniques which could be applied

to LDP

Observation of migrations between risk classes,

Theoretical PD scale based on the rating hierarchy,

When applying these different techniques, no internalhistorical data is used to calculate the PD, prudential marginis required.

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III LGD

1. Context

LGD are defined at a transaction level.

(but LGD senior unsecured rather estimated at thecounterparty level, then the garantees are taken into account

at the transaction level)

Same steps than for PD estimations

Se mentation in homo eneous classes in terms of recover

(or losses) LGD estimation for each class

LGD apply to exposures not in default

LGD Through The Cycle,

Length of the cycle

Prudential margins to add to the LGD estimations10/22/2012 27


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III LGD

Two cases: No available data (Low Default Portfolio): Expert Given

segmentation

Recovery data available: modelling (Retail, PME)

2. No data available (Corporate, banks, sovereign)

Expert given approach for both segmentation and values of

Examples of axis for a Corporate LGD segmentation:

Guarantee (secured/unsecured), region, economic sector,sales,

LGD values fixed by experts for each class

Then, correction of the senior unsecured LGD to take intoaccount the different guarantees to estimate secured LGD.

This last step is possible if guarantees have beenregistered in the systems.

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III LGD3. Recovery Data available

Segmentation by statistical approach or expert given

LGD are estimated using recoveries observed on defaulted

transactions Importance of the default definition (like for PD)

Requirements: Historical data of at least 5 years of annualrecoveries for retail, 7 years for corporate, sovereign andbanks

LGD have to be estimated using long term weightedaverages losses (or recoveries) observed for exposures on

counterparties in default: Given at a transaction level and based on annual recoveries

1, 2, , n years after the default event,.

Recovery data have to be as exhaustive as possible:correctly registered in the information system of the bank.

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III LGD

The post default recovery process may be very long:

Problem: usually lack of data available on the long term.

The final recovery depends on the way the long termrecoveries are estimated. Several possibilities:

For each transaction, use of the whole data available Extrapolation: from the last available point, from a fixed delay

after default,

Choice of the horizon above which recoveries areextrapo ate

Fix a maximum time after which no more amount isrecovered:

Relevance of the maximum recovery horizon chosen

Modelling with defaults closed or with closed and not closeddefaults (to increase the size of the database)

Take into account the specificities of restructured debts.

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III LGD

LGD also depends on:

Discount factors applied to the recoveries

Use the nominal rate of the contract is not relevant

Costs

They have to be deducted from the recoveries

If they are partially taken into account, the LGD isunderestimated

Problem of accuracy (global estimations)

Post default recoveries

If they are not taken into account, the LGD will beconservative (which is not a problem).

As LGD depends on the recovery politics of the bank, it is

difficult to compare the banks LGD levels.

Downturn LGD:

Often not really taken into account except via additionalmargins, and difficult to calibrate.

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IV Implementation, information systems

In order to calculate the RWA and capital requirements:

For each exposure, determination of the PD (depending on

the rating), LGD (depending on some characteristics of theexposure) and EAD

For corporate the same rating and PD are assigned to each,

transfert risk ; guarantees attached to an exposure, theseone require an adjustment of the notation)

The quality of the information system is essential in theprocess.

The following part lists some major components of theinformation system (not exhaustive)

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Borrowers/transactions administration tools:

Links between transactions and clients

Corporate structures, including subsidiaries and the nature ofthe links between entities in the same group

In order to be able to apply default or ratings contagion

Exhaustivity of the clients/credits, with their main characteristics.

Default registrations: dates of entry/exit,

Defaults have to be taken into account without delay

An important delay between a default and its integrationin the system is not acceptable.

A regular update process has to be planned.

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Notation tools

Availability in the rating tools of all the data required to rate thecounterparties/transaction:

Missing values for data used in the rating process should berare

Coherence between data has to be checked before input int e system no c ent orn n , no c ent years o

having accounts in the bank for 20 years, )

Data have to be updated on a regular basis and in case ofchanges in the characteristics of the counterparty

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Client relationship officers may be located anywhere in the bank: Notation tools have to be available anywhere

Notation must be updated at least once a year

Consistency of the rating

Same rating tool for any counterparty of a given nature

Unicity of the rating for a given counterparty, even if it is.

Treatments to apply to the non rated borrowers/transactionshave to be specified

these cases must be rare.

Reliability of the ratings, which gives the PD (because of thedirect correspondence between rating and PD) depends on thequality of the data in input of the notation tool.

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IV I l t ti i f ti t


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Perimeter:

Exhaustivity: the whole IRB perimeter has to be taken intoaccount in terms of:

Foreign implentations of the bank: subsidiaries,

Borrowers/products.

Every counterparty/transaction in the IRB perimeter has to be

When different systems are implemented in different locations, datamay not be homogeneous Be careful

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IV I l t ti i f ti t


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Risk database

Identification of the Basel portfolio and sub-portfolio for eachtransaction, to include every exposure in the appropriateportfolio

Exhaustivity of data required to classify exposures in Baselportfolios, PD, LGD, EAD/CCF

Historisation of data:

, , ,

guarantees, At a transaction level: data useful for PD, LGD, EAD/CCF

attributions

Times series of default rates per rating, recoveries per classof LGD,

For transactions in default: dates of default and of exit of default,exposure at default, drawn amounts posterior to default,recoveries post default, losses amounts,

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IV Implementation information s stems


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Calculation tools for PD, LGD, EAD/CCF

Calculation tools for RWA and capital requirements

Accounting/risks reconciliation tool

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V Back testing


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V. Back-testing

Supervisors require banks to perform at least annual back-testing on PD, LGD and EAD/CCF estimates.

Back-testing :

Ex-post comparison of the 1 year default rates, the lossesand the EAD/CCF observed against the PD, LGD andEAD/CCF calibrated.

Very useful to assess the quality of PD, LGD (andEAD/CCF) calculations.

More difficult to make for LGD because of a lack ofobserved recoveries on long term horizons.

Same problem with EAD/CCF.

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V Back-testing


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V. Back-testing

Several axes (PD example):

Comparison between the average of the 1 year default ratesobserved on the historical period and the PD

Statistical validity of the estimation: determination of aconfidence interval (under normal distribution assumptionsfor example)

Comparison between the annual default rate observed (i.e.Point In Time: PIT) and the PD.

The back-testing methodology must be adapted depending

on : The update frequency of the estimators

The time series used to calculate these estimators.

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V Back testing


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V Back-testing

Example for PD:

Assume that an estimator (PD) is computed annually with anincrease of the time series (default rates)

A comparison of this estimator with the LT averages ofobserved defaults rates seems not very relevant, especially ifexactly the same data are used to compute the estimatesand the LT averages.

en s es as o e comp e e y o ers ana ys s.

A back-testing is essential to check whether the values of theBasel parameters are relevant or if a new calibration isrequired.

IRB approaches would not be validated if no back-testing isavailable.

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VI Conclusion


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VI Conclusion

The quality of the data is very important at each step of

the process:

At the modelling step, to segment the population in riskclasses (in terms of PD, LGD, and also EAD/CCF, notdeveloped in this presentation)

To calibrate PD, LGD (and EAD/CCF)

For the regular calculations of capital after the approval ofthe model.

The information system is generally complex because ithas to be able to capture data on a very large perimeter interms of subsidiaries of the bank, of portfolios and ofproducts.

The backtesting is a key test to control if the Baselestimators are correct.

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Documents

Importancia Da Qualidade de Dados Nas Abordagens IRB - Isabelle Thomazeau