+Chapter 5: PD estimation
---+Table 1: Rating and calibration philosophies

Chapter 5: PD estimation

The GL on PD estimation aim to provide, among other things, more detailed guidance on the calculation of observed default rates and on the estimation of the long run average default rate. Moreover, they clarify how risk drivers and rating criteria should be chosen, and which requirements should be fulfilled where ratings serve as input to the PD estimation. Other aspects touched upon are the rating philosophy and how the long-run average default rates relate to the final PD estimation of a grade or pool. General requirements specific to PD estimation

It is clarified that each natural or legal person that has exposures within the scope of the IRB Approach should be rated including where there is unfunded credit protection. The rationale for this is that, for the purpose of model development, risk quantification and validation the assignment to a pool or grade after the application of unfunded credit protection would bias risk differentiation and default rate calculation. Even in the case of a rating transfer from a third party to the obligor, therefore, the initial rating of the obligor without taking into account the support of a third party should be available.

Model development in PD estimation

The requirements for model development include clarifications regarding data used for this purpose, as well as requirements for risk drivers and rating criteria, to be taken into account in statistical models or other mechanical methods to assign exposures to obligor grades. These risk drivers may include in particular the rating of a third party which has certain organisational or contractual relations with the obligor.

The data requirements for building the model for assigning exposures or obligors to grades or pools clarify that the reference points in time at which risk drivers are evaluated for the purpose of developing the model should be considered taking into account the dynamics and the update frequency of the information in question. The rationale for this is to avoid unjustified burden as well as to avoid biases in analysis due to autocorrelation. For example, obligor characteristics might be fairly static over time, whereas financial data from balance sheets is usually updated annually.

Risk drivers and rating criteria

The GL clarify that the selection of certain risk drivers and rating criteria should be based not only on statistical analysis, but that the relevant business experts should be consulted on the business rationale and risk contribution of the risk drivers under consideration. The background of this requirement is to ensure that the proper risk drivers and rating criteria are taken into account in the model.

An additional characteristic that should be considered as a potential risk driver is the number of loans of the same type of facility that have been granted to an obligor. In particular, where an institution chooses for its retail portfolios to assign PDs at exposure level and to identify default at facility level, it should be ensured that the PDs are adequate for PD estimates by obligor grade or pool, as required in Article 180(1)(a) and 180(2)(a) of the CRR. The rationale is that, in the latter case, the underlying one-year default rates in a grade or pool may vary significantly if based on largely one-to-one or one-to-x relations (where one-to-x relations reflect obligors carrying multiple (x) facilities of the same type in a certain grade or pool). However, if the number of loans of the same type of facility which have been granted to one obligor does not constitute a risk driver, there may as well be no difference in risk.

Another aspect, which should be taken into account when selecting and designing risk drivers and rating criteria, relates to the loss of reliability as information ages. The rationale for this requirement is that the loss of information value over time with respect to certain risk drivers or rating criteria, and in particular information which stems from the credit application and which is usually not updated during the life time of the credit products under consideration, leads to increased uncertainty, which should be appropriately reflected in the design of grades and pools, and the corresponding PD estimates.

The last requirement specified in the GL with respect to risk drivers and rating criteria relevant for PD estimation is that risk drivers and rating criteria should be used consistently with respect to the relevant time horizon in model development, model calibration and model application. This is because any inconsistency in the time horizons could lead to significant bias in the resulting PD estimates. If, for example, an institution considers days-past-due buckets as pools in its rating model, it nevertheless has to ensure that the ranking model for the pool of obligors without any past due obligations provides PD estimates appropriate for a one-year time horizon, as this is the relevant time horizon for the application portfolio.

Treatment of ratings of third parties

Regarding the use of third party ratings in obligors’ PD estimates, the GL specify the principles for the use of third party internal or external ratings in the estimates of the PD of an obligor. It is clarified that institutions may use an internal rating of a guarantor instead of a rating of an obligor for the purposes of own funds requirements calculation where there is no difference in risk between the relevant obligor or exposure and the relevant third party, given the existence of explicit guarantees (this is referred to as a rating transfer). Furthermore, the rating of a related third party may be taken into account as a risk driver or rating criterion in the ranking method, to reflect the support from a third party to the obligor. Finally, the third party’s rating may be considered for the purpose of overriding the assignment of an obligor to a pool or grade provided by a ranking method.

Among the important aspects clarified in this chapter is the provision that the considered obligor or exposure in whose PD estimate the third party rating is considered should remain in its exposure class. Even where the PD of the obligor is fully substituted by the PD of the third party because there is no difference in risk, the exposure should remain in the exposure class applicable to the obligor. Moreover, it is required that any changes to the rating of the third party should be reflected in the PD estimate incorporating the third party rating in a timely manner.

Rating philosophy

Depending on the methods and risk drivers used to assign obligors or exposures to grades or pools, changes in the portfolio’s default rate caused by changes in economic conditions will be reflected through either, or a combination, of the following:

 migrations across risk grades or pools;
 changes in the yearly default rates of each grade or pool.

Where the rating assignment process is highly sensitive to economic conditions, grade assignment will change significantly, while default rates of each grade will re-main relatively stable. In contrast, when the assignment is less sensitive to economic conditions, the yearly default rates per grade component will capture the cyclicality of the global default rate.

The requirements in this section aim mainly at increasing institutions awareness and understanding of the relationship between the definition of risk drivers, the number of grades, migrations across risk grades, changes in the one-year default rates over time, and the dynamics and volatility of capital requirements. To achieve that objective, the GL allow institutions to decide on the philosophy underlying the grade or pool assignment and the risk drivers, but require that a number of criteria be taken into account, including, among others, that institutions need to monitor their choice of rating philosophy, to apply that philosophy consistently over time, to understand its impact on the dynamics and volatility of capital requirements, and to take the rating philosophy into account for back-testing purposes.

PD calibration

Data requirements for observed default rates calculation

For the data for calculating default rates to be complete, it has to include the criteria to identify the relevant type of exposures covered by the rating system in. The rationale for this is that the institution should take into account all defaults with respect to the relevant type of exposures, independently of the existence of a rating assignment. Moreover, data covering the risk drivers and rating criteria need to be available for the purpose of calculating default rates per grade and pool. Where relevant risk drivers or rating criteria are missing, for example because the relevant information has not been collected from the obligors in the past, institutions should apply appropriate adjustments and increase MoC. Moreover, banks should make efforts to minimise the proportion of missing data over time. The rationale for this is that the missing information increases uncertainty around the default rates per grade in the past, so institutions should ensure that obligors or exposures are appropriately assigned to grades and pools, taking into account the identified risk drivers and rating criteria.

The GL also clarify that all data relevant for identifying the non-defaulted exposures at the beginning of a one-year observation period has to be available, in addition to all relevant default information as required in Article 178 of the CRR. This clarification was considered necessary because emphasis is often put on the data collection related to defaulted exposures, but for the purpose of default rate calculation, the accurate and complete identification and collection of data for non-defaulted exposures are equally important.

Calculation of the one-year default rates

The section on the calculation of observed one-year default rates clarifies in more detail which obligors should be taken into account in the numerator and denominator for the purpose of calculating a one-year default rate.

While the general calculation of a one-year default rate is already outlined in the CRR and the RTS on IRB assessment methodology, the GL clarify this calculation for a number of specific situations. In particular, the denominator should contain the obligors of the relevant model or calibration segment, with any credit obligation at the beginning of the observation period. The rationale is to ensure accurate measurement of one-year default rates, as an obligor can also default if there is no repayment obligation during the observation period, for example because of bankruptcy filing. Moreover, it should be noted that guarantors which do not carry a credit obligation are excluded from this specification of one-year default rate calculation⁶ , as by definition they cannot be subject to the same default identification process as the institution’s obligors. However, the information stemming from defaults of guarantors or any other relevant data on external default rates should be taken into account in the estimation of the long-run average default rates if this is necessary to meet the requirements in Section 5.3.4. Where obligors whose obligations stem solely from non-credit products fall under the scope of application of the relevant model and are treated in accordance with the institution’s internal default definition, these should form a separate calibration segment in the rating system, in order not to bias the default rate of obligors with credit facilities. Similarly, with regard to obligors or facilities only with committed but undrawn credit lines, these might have to be treated in a separate calibration segment in the rating system, to avoid lowering unduly the default rate of obligors with drawn credit lines.

It is clarified that, for the purpose of calculation of the one-year default rate by grade or pool, institutions should refer to the obligors assigned to grades or pools at the beginning of the one-year observation period, where the assignment to a grade may be based on an override. However, where the assignment to a grade is the effect of a rating transfer from a provider of unfunded credit protection, the obligor and potential default should be taken into account with respect to the grade to which the obligor was assigned before the rating transfer. The rationale for this is that the default rate of lower rating grades would be biased if the defaults of those obligors that received credit protection were not taken into account for the respective default rate calculation. The same rationale holds true for the requirement that ex post conservative adjustments should not be taken into account for the purpose of one-year default rate calculations, as obligors that are downgraded for the purpose of capital requirements calculation, for example because of a missing re-rating, could unduly lower the default rate of the resulting (worse) grade.

Finally, and with respect to one-year default rate calculation, it is clarified that all obligors carrying a credit obligation at the beginning of the observation period should be included in the denominator and, if applicable, the numerator of the default rate, calculated for the grade the obligor has been assigned to at the beginning of the observation period This also holds true where obligors migrated to a different grade or pool, or to a different rating system, during the observation period, and also where the credit obligation was sold, written off, repaid or otherwise closed during the observation period. The rationale for this is to achieve a harmonised and well-defined notion of one-year default rate. However, in case of concerns that the inclusion of these obligors could lead to a biased observed average default rate, for example because of a missing information on the rating at the beginning of the observation period, appropriate adjustments may be applied and MoC should be added to the best estimate of the risk parameter. Calculation of the observed average default rate

The GL require institutions to justify their approach to calculating the average of one-year default rates taking into account, in particular, analysis of the effect of short-term contracts or specific calculation dates. The rationale for the required analysis is to ensure that institutions are aware of the impact of the chosen calculation method and of fast-growing or shrinking portfolios on the observed average default rate and that they apply appropriate adjustments and MoC where necessary. Moreover, it is clarified that the observed average of one-year default rates should be calculated as the arithmetic average of all one-year default rates, except for retail portfolios, where the observed average default rate may be calculated as a weighted average of one-year default rates if more recent data is a better predictor of losses.

Long-run average default rate

Regarding the long-run average default rate, the GL clarify that this should be calculated as the average of observed one-year default rates if the historical observation period is representative of the likely range of variability of one-year default rates and, in particular, if the historical observation period contains an appropriate mix of good and bad years. If the one-year default rates are not representative of the likely range of variability, institutions should estimate the long-run average default rate by estimating an appropriate adjustment to the average of observed one-year default rates.

For the purpose of clarity the existence, lack or prevalence of bad years should be considered with respect to economic indicators which are relevant for the considered type of exposure. In particular it is clarified that, where bad years are over-represented in the historical observation period, institutions may consider downward adjustments of the observed average of default rates, based on an appropriate method taking into account the correlation between economic indicators relevant for the considered portfolio and the underlying observed default rates.

To limit possible variability stemming from the application of downward adjustments, a benchmark is proposed, namely the maximum of the average of one-year default rates over the most recent five years and the average of one-year default rates over the whole available observation period. Institutions may still estimate long-run average default rates below this benchmark, but this should be duly justified and eventually trigger additional MoC.

Calibration to the long-run average default rate

The process of PD calibration is performed on a calibration sample, namely the sample to which the ranking or scoring method is applied to assign the long-run average default rate estimates to the grades and pools provided by the ranking or scoring method. One of the issues clarified in this context is that the calibration sample should be comparable to the current portfolio in terms of obligor and transaction characteristics, but should reflect at the same time the likely range of variability of default rates.

The choice and understanding of the rating philosophy underlying the methods and drivers used to assign obligors or exposures to grades or pools is closely related to the calibration and re-calibration process and methodology an institution has chosen in that regard. The objectives behind the chosen calibration and re-calibration process and methodology, including the design of the calibration sample, can be referred to as calibration philosophy. The extent to which capital requirements are sensitive to changes in the economic environment depends on both the rating as well as the calibration philosophy.

Institutions that have a ranking method in place which is very sensitive to macroeconomic conditions, reflecting point-in-time (PIT) rating philosophy but also aiming to obtain more stable through-the-cycle (TTC) PD estimates in their calibration and recalibration process (to ensure a certain degree of stability of capital requirements over the credit cycle), might show the same cyclicality of capital requirements as institutions that incorporate risk drivers less sensitive to the economic environment into their ranking method. The extent to which calibration influences the sensitivity of PD estimates to the economic environment depends in particular on:

 whether institutions aim to ensure that the long-run average default rate equals the PD estimates at calibration segment or portfolio level or at rating grade level; and
 the design of the calibration sample.

Table 1 outlines various combinations of rating and calibration philosophy including an indication of whether or not such combinations would be compliant with the requirements set out in these GL and other relevant regulations (i.e. the CRR and the RTS on IRB assessment methodology). For example, if the grades or pools of a model were based predominantly on risk drivers that are insensitive to economic conditions (such as the obligors jurisdiction or sector), thus constituting a TTC rating philosophy, and at the same time the PD estimates were based on the last available (‘current’) one-year default rate (‘PIT A’) these estimates would not be applicable for the purpose of own funds requirements calculation. This is because the requirements of Section 5.3.4 of these GL would not be met. For the same reason, a ranking or scoring method reflecting a PIT rating philosophy where the PD estimates by grade or pool were based on the current default rate (‘PIT B’) would not be compliant with the relevant requirements for the IRB Approach.

On the other hand, with a model based on a TTC rating philosophy where the PD estimates per grade or pool reflect long-run average default rates (‘TTC A’), the resulting PD estimates may be applicable for own funds requirements calculation if all other requirements are met, in particular those set out in Articles 170(4) and 179(1)(a) of the CRR, where the incorporation of all relevant information (including, for example, on delinquency) is required.

An institution might use a more complex combination, for example by using risk drivers that are quite sensitive to economic conditions in a statistical default prediction model providing PD estimates for individual obligors, (i.e. a PIT rating philosophy), but applying a two-step approach for the purpose of calibration, namely by evaluating these PD estimates on a more recent point in time and subsequently adjusting them such that the average of these estimates reflects the long-run average default rate at the level of the relevant calibration segment (or even portfolio – if there is only one calibration segment). This would be an example of a ‘TTC B’ calibration, as indicated in Table 1, and would be applicable for own funds requirements calculation if all other requirements are met, in particular those on the calibration sample (the chosen point in time would need to reflect a sample comparable to the current portfolio and representative of the likely range of variability of one-year default rates).

The difference between calibration approaches ‘TTC B’ and ‘TTC C’ in Table 1 is that, for the latter, the calibration sample would consist of multiple points in time covering the whole historical observation period. Another example would be if an institution estimates PDs per grade but is able to assess these grades historically for only a part of the historical observation period (‘TTC D’); for example, it might not be possible to assess retrospectively the correct grades for all obligors over the whole observation period. In this case, the ranking method would require expert-based qualitative assessments, and experts would need to historically review every rating of every obligor subject to the ranking method within the historical observation period. The PD estimates based on the available grades and pools would be adjusted to reflect a long-run average default rate of the relevant pool, covering the whole historical observation period.

Finally, the approach ‘TTC E’ reflects an example where the grades and pools are evaluated on only one or a few points in time, and the PD estimation of a grade or pool incorporates the use of migration matrices for the purpose of estimating long-run average default rates covering the full historical observation period.

⁶ And thus also from the calculation of the observed average default rate

1. Forbhreathnú

Table 1: Rating and calibration philosophies

Rating philosophy	Calibration philosophy PIT A:	Applicable for the purpose of own funds calculation
TTC: Explicit lack of sensitivity to economic conditions through selection of risk drivers	Calibrate rating grades or portfolio to ’current’ default rates TTC A: Calibrate grades or portfolio to LRA DR (*) PIT B: Use of direct PD estimates reflecting the current default rate (direct use of output or calibrate to current default rate)	No Yes, to the extent that all requirements are satisfied No Yes, to the extent that all
PIT: Explicit use of risk drivers providing high sensitivity to economic conditions	TTC B: Adjust PD on portfolio level to LRA DR; use of current average PD estimates TTC C: Adjust PD on portfolio level to LRA DR; use of average PD over historical observation period	requirements are satisfied and the current average PD estimates reflect the likely range of variability of one-year default rates Yes, to the extent that all requirements are satisfied Applicable for the purpose
Rating philosophy	Calibration philosophy TTC D: Adjust PD on rating grade level to LRA DR; use historically observed grades to the extent possible⁷ TTC E: Adjust PD on rating grade level to LRA DR; use simulated historical grades for current portfolio⁸	of own funds calculation Yes, to the extent that all requirements are satisfied Yes, to the extent that all requirements are satisfied

(*) LRA DR – long-run average default rate

For the purpose of aligning terminology, the GL define calibration in relation to PD estimation as the process of ensuring that the PDs assigned to grades or pools reflect the long-run average default rate at the level relevant to the applied calibration method.

For the avoidance of doubt, it is clarified that where banks apply scoring models and specify score intervals representative of a common level of risk, and where obligors or exposures whose scores fall into such an interval receive the same PD estimate, this process may be considered part of the calibration.

Moreover, the GL provide an overview of the calibration methods mentioned in the CRR, and state to which type of exposures, for instance retail, non-retail or purchased receivables, they are applicable. In addition, the GL clarify that each calibration method may consider the long-run average default rate at the level of the calibration segment, or at grade or pool level. Where there is only one calibration segment in a portfolio, calibration at the level of the calibration segment corresponds to calibration at portfolio level. To incentivise understanding and awareness of these different levels of calibration, and to limit RWA variability stemming from these choices, the GL require that institutions perform additional calibration tests at the level of the calibration segment where calibration is performed at the grade or pool level, and vice versa. For portfolio calibration, where the grades or pools are not available, this additional calibration test would require grouping of ranked exposures into artificial grades to allow performing the calibration test at the level of these grades. For this purpose, the grouping may be the same as for back-testing.

Regardless of the chosen level of calibration the objective is to obtain PDs at grade level that are representative of the long-run average default rate. In this sense, the portfolio level calibration is a method to obtain this long-run average default rate at a grade level, for instance where institutions do not have information at grade level for the whole historical observation period. It could therefore be seen as a two-step calibration, i.e. the first step would be to obtain the portfolio default rate

representative of the long-run

average, and the second step would

be to derive the PDs at grade

level. With direct estimates in accordance with Article 169(3) of the CRR, the risk estimates assigned to individual obligors or exposures may be seen as estimates assigned to grades on a continuous rating scale. Where calibration includes steps performed on a portfolio level, and on a grade or pool level, the additional calibration tests should be applied to the last calibration step.

Furthermore, these GL contain a definition of the calibration sample, which is defined as the data set on which the PD estimates are evaluated to perform the calibration. This notion is introduced because the GL refer to this data set and require that institutions find an appropriate balance between the calibration sample being comparable to the current portfolio, in terms of obligor and transaction characteristics, and it reflecting the likely range of variability of default rates.

Another important aspect

that is clarified with respect to calibration

is that calibration should be

performed before the application of MoC and floors on PD, as required by Articles 160(1) and 163(1) of the CRR (PD floors), and after taking overrides into account. The rationale for this is that the application of MoC or PD floors in the calibration could lead to significant underestimation of final PD estimates of a grade or pool. For example, where an institution estimates PDs as simple averages of default probability estimates in a given grade in accordance with Article 180(1)(g) of the CRR, a group of obligors with significantly different levels of default risk could be grouped into one grade or pool if MoC or PD floors were applied before calibration. It should be noted that this provision clarifies that, even where a bank has a current portfolio fully representative of the historic portfolio and of the likely range of default rates, and where the calibration sample therefore corresponds to the current portfolio, it is still expected that the final PD estimate is higher than the average of default risk probabilities due to MoC and PD floors. Moreover, overrides should be taken into account to the extent relevant and observed for the ranking method underlying the grades and pools for which the calibration is performed.

The GL acknowledge that, regarding the policy on rating philosophy and calibration outlined above, there is a wide range of practices. However, the distinction between model development (leading to risk differentiation) and calibration, including estimation of long-run average default rates (leading to risk quantification), should not prohibit institutions from using methods where some aspects of both stages are combined.

⁷ For example, where the re-calibration incorporates some amendment to a qualitative module of the rating model, it might not be possible to assess the correct grade retrospectively for all obligors, as experts would have to historically review every rating of every obligor subject to this module within the historical observation period.

⁸ Methods should be carefully assessed to ensure that they do not contain survivor bias.

1.1 Tagairtí

1.2 Ceanglais aitheanta

1.3 Caighdeáin ghaolmhara

2. Ceanglais aitheanta

Ceanglais
Foinse	Ceanglas

3. Caighdeáin ghaolmhara

Caighdeáin
Foinse	Ceanglas

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