5.3 PD calibration

For the purpose of calculating the one-year default rate defined in point (78) of Article 4(1) of Regulation (EU) No 575/2013, institutions should ensure the completeness of the quantitative and qualitative data and other information in relation to the denominator and numerator as outlined in paragraphs 73 and 74 and used for the calculation of the observed average default rate. In particular, institutions should ensure that at least the following data for the relevant observation period referred to in paragraphs 82 to 83 is properly stored and available:

• (a) the criteria for identifying the relevant type of exposures covered by the PD model under consideration;
• (b) the criteria for identifying the calibration segments;
• (c) the risk drivers used for risk differentiation; where a newly relevant risk driver has been included in the model for which no historical data is available institutions should, make efforts to minimise missing data on risk drivers over time as outlined in paragraph 51(a), and apply an appropriate adjustment and a MoC in accordance with section 4.4;
• (d) all identification numbers of obligors and exposures relevant for default rate calculation, taking into account situations where the identification number has changed over time, including changes due to restructuring of exposures.

Exclusion of observations from the one-year default rate calculation should be undertaken only in the following two situations:

• (a) obligors wrongly included in the data set of defaults, as they did not default in the meaning of the definition of default pursuant to Article 178 of Regulation (EU) No 575/2013 as further specified in the Guidelines on the application of the definition of default of an obligor under that Article should not be included in the numerator of the one-year default rate;
• (b) obligors wrongly assigned to the considered rating model, despite not falling in the range of application of that rating model, should be excluded from both the numerator and the denominator of the one-year default rate.

Institutions should document all data cleansing in accordance with Article 32(3)(b) of the RTS on IRB assessment methodology, with respect to the one-year default rate calculation and in particular:

• (a) for non-retail PD models, a list of all observations within the dataset that were excluded according to paragraph 71, with a case-by-case justification;
• (b) for retail PD models, information on the reasons and quantity of exclusions of observations made in accordance with paragraph 71.

5.3.2 Calculation of one-year default rates

For the purpose of calculating the one-year default rate referred to in point (78) of Article 4(1) of Regulation (EU) No 575/2013, institutions should ensure both of the following:

• (a) that the denominator consists of the number of non-defaulted obligors with any credit obligation observed at the beginning of the one-year observation period; in this context a credit obligation refers to both of the following:
• (i) any on balance sheet item, including any amount of principal, interest and fees;
• (ii) any off-balance sheet items, including guarantees issued by the institution as a guarantor.
• (b) that the numerator includes all those obligors considered in the denominator that had at least one default event during the one-year observation period.

When assigning the obligors or exposures to grades or pools for the purpose of the one-year default rate calculation, institutions should take overrides into account, but they should not reflect in this assignment any substitution effects due to credit risk mitigation, nor any ex post conservative adjustments introduced in accordance with section 8.1. Where the one-year default rate is calculated by rating grade or pool, the denominator should refer to all obligors assigned to a rating grade or pool at the beginning of the observation period. Where the one-year default rate is calculated at the portfolio level, the denominator should refer to all obligors assigned to the relevant calibration segment at the beginning of the observation period.

Institutions should calculate the one-year default rate also for the subset of obligors with any credit obligation that did not have a rating at the start of the relevant observation period, but which were within the range of application of the model under consideration (‘missing ratings’), even if these obligors were assigned to a rating grade or pool in a conservative manner for the purpose of calculation of own funds requirements. Obligors whose ratings are based on missing or partly missing information or where the rating is outdated but still deemed valid by the institution should not be considered as missing ratings.

For the purposes of paragraphs 73 to 75 an obligor has to be included in the denominator and, where relevant, numerator, also in the case of a migration to a different rating grade, pool or rating model, rating system or approach to calculation of capital requirements within the observation period or where the corresponding credit obligations were sold, written off, repaid or otherwise closed during the observation period. Institutions should analyse whether such migrations or sales of credit obligations bias the default rate and, if so, they should reflect this in an appropriate adjustment and consider an adequate MoC.

In any case institutions should ensure that each defaulted obligor is counted only once in the numerator and denominator of the one-year default rate calculation, even where the obligor defaulted more than once during the relevant one-year period.

In order to choose an appropriate calculation approach as required by paragraph 80, institutions should evaluate the observed one year default rates within the historical observation period at least quarterly.

5.3.3 Calculation of the observed average default rate

The observed average of one-year default rates (‘observed average default rate’) should be calculated for each rating grade or pool and additionally for the type of exposures covered by the relevant PD model as well as for any relevant calibration segment.

Institutions should choose an appropriate approach between an approach based on overlapping and an approach based on non-overlapping one-year time windows, to calculate the observed average default rate based on a documented analysis. This analysis should include at least the following:

• (a) an analysis of possible bias due to the proportion of short-term and terminated contracts that cannot be observed during the relevant one-year periods;
• (b) an analysis of possible bias due to the specific calculation dates chosen;
• (c) for institutions using overlapping one-year time windows, an analysis of potentially significant bias due to implicit over-weighting of the overlapping time period;
• (d) an analysis of potentially significant bias due to seasonal effect related to the chosen calculation dates.

For the purposes of paragraphs 79 and 80 institutions should calculate the observed average default rates as the arithmetic average of all one year default rates calculated in accordance with paragraphs 73 to 76. In the case of PD models for retail exposure class institutions may calculate the observed average default rate as a weighted average of one-year default rates where an institution does not give equal importance to historic data because more recent data is a better predictor of losses in accordance with Article 180(2)(e) of Regulation (EU) No 575/2013.

5.3.4 Long-run average default rate

For the purpose of determining the historical observation period referred to in Articles 180(1)(h) and 180(2)(e) of Regulation (EU) No 575/2013, additional observations to the most recent 5 years, at the time of model calibration, should be considered relevant when these observations are required in order for the historical observation period to reflect the likely range of variability of default rates of that type of exposures as referred to in Article 49(3) of the RTS on IRB assessment methodology.

For the purpose of assessing the representativeness of the historical observation period referred to in paragraph 82 for the likely range of variability of one-year-default rates, institutions should assess whether the historical observation period contains a representative mix of good and bad years, and they should take into account all of the following:

• (a) the variability of all observed one-year-default rates;
• (b) the existence, lack or prevalence of one-year default rates relating to bad years as reflected by economic indicators that are relevant for the considered type of exposures within the historical observation period;
• (c) significant changes in the economic, legal or business environment within the historical observation period.

Where the historical observation period referred to in paragraph 82 is representative of the likely range of variability of the default rates, the long-run average default rate should be computed as the observed average of the one-year default rates in that period.

Where the historical observation period referred to in paragraph 82 is not representative of the likely range of variability of default rates as referred to in Article 49(4) of the RTS on IRB assessment methodology, institutions should apply the following:

• (a) where no or insufficient bad years are included in the historical observation period the average of observed one year default rates should be adjusted in order to estimate a long-run average default rate;
• (b) where bad years are over-represented in the historical observation period, the average of observed one-year default rates may be adjusted to estimate a long-run average default rate where there is a significant correlation between economic indicators referred to in paragraph 83(b) and the available one-year default rates.

Institutions should ensure that, as a result of the adjustments referred to in points (a) and (b), the adjusted long-run average default rate reflects the likely range of variability of default rates.

In the exceptional case where the long-run average default rate is below the average of all observed one-year default rates due to any adjustment made in accordance with paragraph 85, institutions should compare their adjusted long-run average default rates with the higher of the following:

• (a) the observed average of the one-year default rates of the most recent 5 years;
• (b) the observed average of all available one-year default rates. Institutions should justify the direction and magnitude of the adjustment, including the adequacy of the considered MoC, in line with the requirement in Article 49(4)(b) of the RTS on IRB assessment methodology and section 4.4. In addition, where the adjusted long-run average default rate is lower than the higher of the two values referred to in points (a) and (b), they should specifically justify why these two values are not appropriate.

5.3.5 Calibration to the long-run average default rate

Institutions should have sound and well-defined processes in place which ensure sound calibration by including all of the following in their calibration process:

• (a) quantitative calibration tests by rating grade or pool;
• (b) quantitative calibration tests on calibration segment level;
• (c) supplementary qualitative analyses such as expert judgements on the shape of the resulting obligor distribution, minimum obligor numbers per grade and avoidance of undue concentration in certain grades or pools.

Institutions should store and describe in the documentation of the PD model the calibration sample associated with each calibration segment. In order to ensure compliance with Article 180(1)(a) or 180(2)(a) of Regulation (EU) No 575/2013, institutions should find an appropriate balance between the comparability of the calibration sample with the application portfolio in terms of obligor and transaction characteristics and its representativeness of the likely range of variability of default rates as referred to in section 5.3.4.

Institutions should conduct the calibration after taking into account any overrides applied in the assignment of obligors to grades or pools, and before the application of MoC or floors to PD estimates as referred to in Articles 160(1) and 163(1) of Regulation (EU) No 575/2013. Where a ranking method or overrides policy has changed over time, institutions should analyse the effects of these changes on the frequency and scope of overrides and take them into account appropriately.

The process of grouping ranked obligors or exposures to grades or pools, in particular where institutions conduct this grouping by identification of intervals of score values reflecting a predefined PD level assigned to a grade of a master scale, may be performed during the calibration.

Taking into account the availability of data, the structure of the model and portfolio as well as the business requirements, institutions should choose an appropriate method to perform the calibration in accordance with the following principles:

• (a) institutions may choose one of the following types of calibration:
• (i) a calibration in accordance with Article 180(1)(a) or 180(2)(a) of Regulation (EU) No 575/2013;
• (ii) a calibration in accordance with Article 169(3) of Regulation (EU) No 575/2013 in combination with Article 180(1)(a) or 180(2)(a) of that Regulation if a continuous rating scale is used;
• (b) for exposures to corporates, institutions, central governments and central banks and for equity exposures where an institution uses the PD/LGD approach set out in Article 155(3) of Regulation (EU) No 575/2013, institutions may choose one of the following types of calibration:
• (i) a calibration based on a mapping to the rating scale used by an external credit assessment institution (ECAI) or similar organisation in accordance with Article 180(1)(f) of Regulation (EU) No 575/2013;
• (ii) for a statistical default prediction model, in accordance with Section 4 of the RTS on IRB assessment methodology, where the PDs are estimated as simple averages of default probability estimates for individual obligors in a given grade or pool in accordance with Article 180(1)(g) of Regulation (EU) No 575/2013, a calibration at the level of appropriate calibration segments of the relevant default probability estimates;
• (c) for retail exposures institutions may choose a calibration based on total losses and LGDs in accordance with Articles 180(2)(b) and 180(2)(d) of Regulation (EU) No 575/2013;
• (d) for corporate purchased receivables institutions may choose a calibration based on expected losses and LGDs in accordance with Articles 180(1)(b) and 180(1)(c) of Regulation (EU) No 575/2013.

For the purpose of determining the PD estimates referred to in paragraph 91, the calibration should consider either:

• (a) the long-run average default rate at the level of grade or pool, in which case institutions should provide additional calibration tests at the level of the relevant calibration segment; or
• (b) the long-run average default rate at the level of the calibration segment, in which case institutions should provide additional calibration tests at the level of the relevant grades or pools or, where they use direct PD estimates in accordance with Article 169(3) of Regulation (EU) No 575/2013, at a level that is appropriate for the application of the probability model.

Irrespective of which of the approaches mentioned in paragraph 92 institutions choose, they should assess the potential effect of the chosen calibration method on the behaviour of PD estimates over time.

For the purpose of determining PD estimates based on a mapping to an external rating scale as referred to in paragraph 91(b)((i)), institutions should base the default rates observed for the external organisation’s grades on a time series representative of the likely range of variability of default rates for the grades and pools of the given portfolio.

Where institutions derive PD estimates from the estimates of losses and LGDs in accordance with Articles 161(2) and 180(2)(b) of Regulation (EU) No 575/2013 they should use a RDS that includes realised losses on all defaults identified during the historical observation period specified in accordance with section 6.3.2.1 and relevant drivers of loss.

In order to use direct PD estimates for the calculation of own funds requirements in accordance with Article 169(3) of Regulation (EU) No 575/2013, institutions should demonstrate that the theoretical assumptions of the probability model underlying the estimation methodology are met to a sufficient extent in practice and that the long-run average default rate is retained. In particular, all data and representativeness requirements should be met, including those in Article 174(c) of Regulation (EU) No 575/2013, and the definition of default should be applied in accordance with Article 178 of Regulation (EU) No 575/2013. Under no circumstances should the use of continuous PDs or any smoothening of default rates be adopted in order to overcome the lack of data, low discriminatory capacity or any other deficiencies in the rating assignment or PD estimation process, or to reduce the own funds requirements.

Institutions may split exposures covered by the same PD model into as many different calibration segments as needed where one or more subsets of these exposures carry a significantly different level of risk. For this purpose institutions should use relevant segmentation drivers and they should justify and document the use and scope of the calibration segments.

Where scoring methods are used, institutions should ensure that:

• (a) where there is a change in the scoring method used, the institutions consider whether it is necessary to recalculate scores of obligors or exposures based on the original dataset instead of using scores that were calculated based on previous versions of the scoring method, and, where such recalculation is not possible, that institutions assess potential effects and take those effects into account via an appropriate increase of the MoC to their PD estimates;
• (b) where Article 180(1)(g) of Regulation (EU) No 575/2013 applies, the PD estimates which were derived as a simple average of individual PD estimates are adequate for relevant grades, by applying calibration tests to these estimates at a grade level, on the basis of one-year default rates representative of the likely range of variability of default rates.

The calibration should not influence the rank ordering of obligors or exposures within a calibration segment other than within each grade or pool.