Commission Delegated Regulation (EU) 2024/1085 of 13 March 2024 supplementing Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to regulatory technical standards on the assessment methodology under which competent authorities verify an institution’s compliance with the requirements to use internal models for market risk

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have been assigned to an effective liquidity horizon that is the shortest liquidity horizon among the liquidity horizons provided in Table 1 of Article 325bc(1) of Regulation (EU) No 575/2013 that is greater than or equal to Mat;

• (ii) the position does not impact the calculation of

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for all j corresponding to a liquidity horizon that is greater than the shortest liquidity horizon among the liquidity horizons provided in Table 1 of Article 325bc(1) of Regulation (EU) No 575/2013 that is greater than or equal to Mat;

• (d) verify whether, where the position has a maturity of Mat days, with

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, the institution has assigned all risk factors of that position to an effective liquidity horizon corresponding to the liquidity horizon SubCatLH assigned to the risk factors;

• (e) verify whether, when computing

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, the institution keeps constant those risk factors with an effective liquidity horizon that is lower than the liquidity horizon corresponding to the index j.

For the purposes of point (a)(ii), competent authority shall assess by which margin the institution exceeded the threshold in the previous quarters.

For the purposes of point (a)(iii), competent authorities may, where they deem insufficient the testing of alternative subsets carried out by the institution, require the institution to test alternative subsets and assess whether alternative choices lead to material differences in terms of own funds requirements.

Article 43

Assessment of distributional and statistical assumption

• (a) the distributional and any other relevant statistical assumptions used in the model, including volatility and correlations, are well justified, including with regard to the tail of the distributions relevant for the expected shortfall calculation;.

• (b) the empirical correlations that the institution uses when applying scenario of future shocks to reflect the joint movement of risk factors in the calculation of the expected shortfall risk measures referred to in Article 325bb of Regulation No 575/2013 are based on historically observed data in accordance with Article 325bc(2), point (c), and Article 325bc(4), point (c), of that Regulation.

For the purposes of point (b) of the first subparagraph, competent authorities may, where appropriate, require the institution to:

• (a) provide a sample of time series;

• (b) calculate the empirical correlations among those time series;

• (c) verify whether the correlations referred to in point (b) do not materially differ from the correlations used by the institution in its internal risk-measurement model.

• (a) the volatility and other distributional properties of the scenario of future shocks applied to a given risk factor in the calculation of the partial expected shortfall measures;

• (b) the volatility and other distributional properties of the returns observed for the given risk factor.

Competent authorities shall do the assessment referred to in paragraph 1 on the basis of both the period referred to in Article 325bc(4), point (c), of Regulation (EU) No 575/2013 and the period of financial stress referred to in Article 325bc(2), point (c), of that Regulation.

Subsection 3 Assessment of aspects that are relevant for the calculation of the stress scenario risk measure

Article 44

Assessment of the stress scenario risk measure

• (a) the internal policies comply with Article 21 of Delegated Regulation (EU) 2024/397;

• (b) the internal policies require the production of an up-to-date inventory which, for each non-modellable risk factor:

• (i) describes the risk factor;

• (ii) specifies the liquidity horizon assigned to the risk factor in accordance with Article 325bd of Regulation (EU) No 575/2013;

• (iii) specifies whether the institution calculates the extreme scenario of future shock by the direct method or the stepwise method referred to in Article 2, Article 3, Article 5 and Article 6 of Delegated Regulation (EU) 2024/397 respectively, or determines a regulatory extreme scenario of future shock in accordance with Article 14 of that Delegated Regulation;

• (iv) where the institution uses the stepwise method, specifies whether the historical, asymmetrical sigma, or fallback method is used to calibrate the downward and upward shocks;

• (v) for risk factors for which the institution determines a regulatory extreme scenario of future shock in accordance with Article 14 of Delegated Regulation (EU) 2024/397, justifies that choice;

• (vi) specifies whether the risk factor is part of a bucket and, if so, which one;

• (c) internal policies specify the criteria referred to in Article 1, point (a)(i) and Article 4, point (a)(i), of Delegated Regulation (EU) 2024/397, establishing when either the direct method or the stepwise method referred to in Article 2, Article 3, Article 5 and Article 6 of that Delegated Regulation is used with reference to any non-modellable risk factor or non-modellable standardised bucket;

• (d) internal policies specify the criteria to identify business and non-business days in a way that is consistent across the calculation of the stress scenario risk measure referred to in Article 325bk of Regulation (EU) No 575/2013 and the calculation of the expected shortfall risk measure referred to in Article 325bb of that Regulation;

• (e) internal policies specify the criteria to identify risk factors for which the institution determines the stress scenario risk measure by applying a regulatory extreme scenario of future shock in accordance with Article 14 of Delegated Regulation (EU) 2024/397;

• (f) internal policies require that the institution keeps track of all pricing failures as referred to in Article 13(3) of Delegated Regulation (EU) 2024/397, the cause of the pricing failures, and the remedial actions taken under that Article;

• (g) internal policies specify the frequency of updates, in accordance with Article 12(4) of Delegated Regulation (EU) 2024/397, of the stress period used for the determination of the extreme scenario of future shock, and the other possible criteria triggering an update of such stress period.

• (a) where the institution uses the direct method referred to in Article 2 of Delegated Regulation (EU) 2024/397 in relation to non-modellable risk factors:

• (i) verify whether the institution’s processes follow the criteria referred to in Article 1, point (a)(i), of Delegated Regulation (EU) 2024/397 as laid down in the internal policies referred to in Article 325bi(1), point (e), of Regulation (EU) No 575/2013;

• (ii) verify whether, the institution documents and justifies changes in the approach used for the calculation of the stress scenario risk measure, as required by Article 1, point (a)(ii), of Delegated Regulation (EU) 2024/397;

• (iii) verify whether there is any material difference between the stress scenario risk measure resulting, on the one hand, from the direct method and, on the other hand, the stepwise method, for the period of 20 business days referred to in Article 1, point (a)(iii) of Delegated Regulation (EU) 2024/397, and investigate the reasons for any material differences;

• (b) where the institution uses the direct method referred to in Article 5 of Delegated Regulation (EU) 2024/397 in relation to non-modellable standardised buckets:

• (i) verify whether the institution’s processes follow the criteria referred to in Article 4, point (a)(i), of that Delegated Regulation, as laid down in the internal policies referred to in Article 325bi(1), point (e), of Regulation (EU) No 575/2013;

• (ii) verify whether the institution documents and justifies changes in the approach used for the calculation of the stress scenario risk measure, as required by Article 4, point (a)(ii), of Delegated Regulation (EU) 2024/397;

• (iii) verify whether there is any material difference between the stress scenario risk measure resulting, on the one hand, from the direct method and, on the other hand, the stepwise method, for the period of 20 business days referred to in Article 4, point (a)(iii), of Delegated Regulation (EU) 2024/397, and investigate the reasons for any material differences;

• (c) in relation to the determination of the time series of 10 business days returns referred to in Article 7 of Delegated Regulation (EU) 2024/397:

• (i) verify whether the institution does not include more than one observation per business day in the time series used to generate a stress scenario risk measure, and verify whether the time series includes actual market data only, as required by Article 7(1), point (a), of Delegated Regulation (EU) 2024/397;

• (ii) verify whether the criteria referred to in paragraph 1, point (d) to identify business and non-business days are used in the calculation of the 10 business days returns referred to in Article 7 of Delegated Regulation (EU) 2024/397 and in the extension of the stress period by up to 20 business days as referred to in Article 7(1), point (b), of that Regulation, and verify whether the steps to obtain the 10 business days returns, including the determination of D t' as referred to in Article 7(1), point (c), of that Delegated Regulation, are performed correctly;

• (iii) verify whether the time series of non-modellable risk factors that the institution previously assessed to be modellable in accordance with Article 325be of Regulation (EU) No 575/2013 include the observations that the institution used for calibrating the scenarios of future shocks referred to in Article 325bc of that Regulation, as required by Article 7(2) of Delegated Regulation (EU) 2024/397;

• (d) in relation to the implementation of the fallback method referred to in Article 10 of Delegated Regulation (EU) 2024/397:

• (i) verify whether institutions can justify the scarce data availability for the non-modellable risk factors or non-modellable standardised buckets for which the institution uses the fallback method;

• (ii) verify whether there is an appropriate identification of risk factors for which the approach referred to in Article 10(2) and (3) of Delegated Regulation (EU) 2024/397 is to be used;

• (iii) verify whether, when applying the method referred to in Article 10(4) of Delegated Regulation (EU) 2024/397, the approach used by the institution to select a risk factor meeting the conditions referred to in paragraph 5 of that Article leads to the determination of upward and downward shocks that are suitable for risk factor for which the fallback approach is applied;

• (e) require the institution to identify non-modellable risk factors or non-modellable standardised buckets for which the value of the non-linearity coefficient referred to in Articles 17 and 18 of Delegated Regulation (EU) 2024/397 is equal either to κ min or κ max, as referred to in those Articles, and verify whether the extreme scenario of future shock is appropriate or whether, in accordance with Article 325bk(3), point (b), of Regulation (EU) No 575/2013, the institution is to be required to apply a regulatory extreme scenario of future shock in accordance with Article 14 of Delegated Regulation (EU) 2024/397;

• (f) in relation to the determination of the stress period as required by Article 12 of Delegated Regulation (EU) 2024/397:

• (i) where the institution determines the stress period by maximising the value referred to in Article 12(1) of Delegated Regulation (EU) 2024/397 and using sensitivity-based pricing methods in accordance with Article 13(4) of that Delegated Regulation, verify the robustness of the analysis performed by the institution to demonstrate that the price changes that are not captured by the sensitivity-based pricing methods would not modify the stress period;

• (ii) where the institution determines the stress period for the non-modellable risk factors in a broad risk factor category by identifying the 12-month observation period maximising the partial expected shortfall measure PES ^{RS, i} in accordance with Article 12(2) of Delegated Regulation (EU) 2024/397, verify the robustness of the analysis performed by the institution to demonstrate that the stress period identified is a period of financial stress for its non-modellable risk factors;

• (iii) verify whether the 12-month rolling windows tested to determine the stress period starts at least from 1 January 2007 as referred to in Article 12(3) of Delegated Regulation (EU) 2024/397, and verify whether past updates of the stress period followed the frequency and criteria referred to in paragraph 1, point (g);

• (g) in relation to the computation of losses with sensitivity-based pricing methods under the conditions set out in Article 13(3) of Delegated Regulation (EU) 2024/397:

• (i) assess the robustness of the processes and methods for detecting pricing failures, identifying the financial instruments and commodities for which a pricing failure occurred, identifying the causes of the pricing failures, and determining their material sensitivities;

• (ii) verify whether, following the application of the extreme scenario of future shock to a non-modellable risk factor, the use of sensitivity-based pricing methods is applied only to financial instruments and commodity bearing that risk factor and subject to the pricing failures in accordance with Article 13(3) of Delegated Regulation (EU) 2024/397;

• (h) in relation to the determination of the regulatory extreme scenario of future shock referred to in Article 14 of Delegated Regulation (EU) 2024/397:

• (i) verify the appropriateness of the method that the institution uses to determine whether the maximum loss that may occur due to a change in a non-modellable risk factor or to a change in a non-modellable standardised bucket is finite or not;

• (ii) where the maximum loss corresponding to a non-modellable risk factor or a non-modellable bucket is finite, verify whether the institution identifies such maximum loss accurately;

• (iii) where the maximum loss that may occur due to a change in a non-modellable risk factor or to a change in a non-modellable standardised bucket is not finite, verify whether the distributional and statistical assumptions used in the expert-based approach referred to in Article 14(2), point (a), and Article 14(4) point (a) of Delegated Regulation (EU) 2024/397 are based on objective data and robust tests, and that the extreme scenario of future shock is sufficiently conservative;

• (iv) verify whether:

• (1) the information included in the inventory referred to in paragraph 1, point (b) are consistent with the criteria referred to in point (e) of that paragraph;

• (2) the criteria specified in the inventory referred to in paragraph 1, point (b) to identify those risk factors for which the stress scenario risk measure is obtained by determining a regulatory extreme scenario of future shock are sound;

• (v) verify the robustness of the methodology and the statistical tests that the institution uses to identify risk factors reflecting idiosyncratic risk only in accordance with Article 16(3) and (4) of Delegated Regulation (EU) 2024/397.

For the purposes of point (a)(ii), competent authorities shall verify whether the justification provided fits with the criteria referred to in point (a)(i) and the related changes are not driven by the fact that one method leads to a lower stress scenario risk measure than the other.

For the purposes of point (b)(ii), competent authorities shall verify whether the justification provided fits with the criteria referred to in point (b)(i) and is not driven by the fact that one method leads to a lower stress scenario risk measure than the other.

For the purposes of point (g)(ii), competent authorities shall verify that the institution calculates the losses related to other financial instruments and commodities bearing that risk factor but not subject to a pricing failure with the pricing methods used in the risk measurement model in accordance with Article 13(2) of Delegated Regulation (EU) 2024/397.

When verifying whether the two risk factors are of the same nature in accordance with Article 10(5), point (b), of Delegated Regulation (EU) 2024/397 and whether those risk factors do not differ for features leading to an underestimation of the volatility in accordance with Article 10(5), point (c), of that Delegated Regulation, competent authorities shall verify whether the risk factors share the main characteristics, and whether the selected risk factor attracts name-related specific risk if the non-modellable risk factor attracts it.

• (a) require the institution to test alternative suitable risk factors meeting the conditions referred to in Article 10(5) of Delegated Regulation (EU) 2024/397 instead of the risk factors selected by the institution;

• (b) compare the extreme scenario of future shock obtained using the risk factors selected by the institution and the extreme scenario of future shock obtained using the alternative risk factors referred to in point (a);

• (c) assess whether the risk factors selected by the institution lead to a systematic underestimation of the extreme scenario of future shock;

• (a) require the institution to estimate the volatility of those risk factors over that 1-year period;

• (b) require the institution to estimate the volatility over that 1-year period of the risk factors selected in accordance with Article 10(5) of Delegated Regulation (EU) 2024/397 for the risk factors referred to in point (a);

• (c) assess whether the volatility of the risk factors selected by the institution resulting from the estimation referred to in point (b) is systematically lower than the volatility of the risk factors in the institution risk-measurement model resulting from the estimation referred to in point (a).

• (a) assess whether the non-linearity coefficient is equal to κ min or κ max because extremely high or extremely low values characterise the numerator or denominator of the following term

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as used in the computation of κ in accordance with Articles 17 and 18 of Delegated Regulation (EU) 2024/397;

• (b) require the institution to plot the loss resulting from risk factor changes in the neighbourhood of the extreme scenario of future shock and assess whether the profile of the loss function is particularly concave or convex in that neighbourhood.

When performing such assessment, competent authorities shall choose the set of non-modellable risk factors and standardised buckets considering their materiality.

• (a) require the institution to determine the stress period by maximising the value referred to in Article 12(1) of Delegated Regulation (EU) 2024/397 on a set of non-modellable risk factors or any non-modellable standardised bucket belonging to the same broad category of risk factors, using the pricing methods that the institution uses in the risk-measurement model in accordance with Article 13(2) of that Delegated Regulation;

• (b) require the institution to determine the stress period by maximising the value referred to in Article 12(1) of Delegated Regulation (EU) 2024/397 on the set referred to in point (a) of this paragraph, using sensitivity-based pricing methods in accordance with Article 13(4) of that Delegated Regulation;

• (c) assess whether the stress periods determined in accordance with points (a) and (b) materially differ.

The set of non-modellable risk factors or non-modellable standardised buckets referred to in the first subparagraph, point (a), shall be chosen considering their materiality and the non-linear profile of the loss to changes in their values. To identify non-modellable risk factors or non-modellable standardised buckets with a non-linear loss profile, competent authorities may use as a basis the value of the non-linearity coefficient κ calculated in accordance with Article 17 or Article 18 of Delegated Regulation (EU) 2024/397.

• (a) require the institution to determine the stress period by maximising the value referred to in Article 12(1) of Delegated Regulation (EU) 2024/397 on a set of non-modellable risk factors or any non-modellable standardised bucket belonging to the same broad category of risk factors, using the pricing methods used in the risk-measurement model in accordance with Article 13(2) of that Delegated Regulation;

• (b) assess whether the stress period determined in accordance with point (a) significantly differs from the stress period identified by the institution when applying the methodology referred to in Article 12(2) of Delegated Regulation (EU) 2024/397.

• (a) require the institution to generate a time series of returns from a fat-tailed statistical distribution prescribed by the competent authority and calculate the extreme scenario of future shock with the stepwise method referred to in Article 3 and Article 6 of Delegated Regulation (EU) 2024/397 combined with the historical method referred to in Article 8 of that Delegated Regulation;

• (b) verify the conservativeness of the institution’s expert-based approach by comparing the regulatory extreme scenario of future shock resulting from that approach with the extreme scenario of future shock calculated in accordance with point (a).

• (a) the risk factors or standardised buckets for which the stress scenario risk measure are determined by applying a regulatory extreme scenario of future shock in accordance with Article 14 of Delegated Regulation (EU) 2024/397 fulfil the criteria identified by the institution to use that method;

• (b) the risk factors or standardised buckets for which the stress scenario risk measure is not determined by applying a regulatory extreme scenario of future shock in accordance with Article 14 of Delegated Regulation (EU) 2024/397 do not fulfil the criteria that the institution identified to use that method.

• (a) verify whether the nature of the risk factor is such that it reflects idiosyncratic risk only by reviewing the description of the risk factor provided in the list referred to in Article 33(1) of this Regulation, and the data inputs used to mark it, as required by Article 16(3), point (a), and Article 16(4), point (a), of Delegated Regulation (EU) 2024/397;

• (b) perform hypothesis testing to assess the significance of correlation coefficients between risk factors in the sample and compare the results of that hypothesis testing with the results that the institution obtained when performing the statistical tests referred to in Article 16(3), point (d), and Article 16(4), point (d), of Delegated Regulation (EU) 2024/397.

CHAPTER 4 ASSESSMENT OF THE INTERNAL DEFAULT RISK MODEL USED TO COMPUTE THE ADDITIONAL OWN FUNDS REQUIREMENT FOR DEFAULT RISK

SECTION 1 Overview of the assessment

Article 45

Assessment of the internal default risk model used to compute the additional own funds requirement for default risk

When assessing the institution’s compliance with the requirements applicable to the internal default risk model as referred to in Articles 325bn, 325bo and 325bp, competent authorities shall assess whether the institution complies with:

• (a) the general requirements for the internal default risk model in accordance with Section 2;

• (b) the requirements for estimates for default probabilities and losses given defaults in accordance with Section 3;

• (c) the requirements for default correlation between issuers, recognition of hedges and other particular requirements in accordance with Section 4.

SECTION 2 Assessment of general requirements

Article 46

Assessment of the scope of positions subject to default risk

• (a) verify whether the institution’s internal systems ensure that all positions containing at least one risk factor mapped to the broad categories of risk factors ‘equity’ or ‘credit spread’, as referred to in Article 325bd(1) of Regulation (EU) No 575/2013, are included in the scope of the additional own funds requirement for default risk;

• (b) obtain an overview of the default risk in the institution’s portfolio, by requiring the institution to provide an inventory of positions aggregated by one or more dimensions and the corresponding aggregated jump-to-default exposures.

For the purposes of point (a), competent authorities shall verify the consistency between the mapping and the inventories referred to in Articles 33(1), 48(1) and Article 49(1).

For the purposes of point (b), competent authorities may, depending on the portfolio, require the institution to aggregate the positions by different dimensions, including by:

• (a) positions having the same rating;

• (b) positions falling within the same exposure class;

• (c) positions sharing the same systematic risk factors as those referred to in Article 325bp(1) of Regulation (EU) No 575/2013.

• (a) require the institution to provide the list of positions assigned to trading desks for which the institution has been granted the permission to use internal models referred to in Article 325az of Regulation (EU) No 575/2013 or is in the process of being granted such permission;

• (b) require the institution to identify those positions containing a risk factor mapped to the broad category of risk factors ‘equity’ or the broad category of risk factors ‘credit spread’, as referred to in Article 325bd(1) of Regulation (EU) No 575/2013, and the corresponding traded debt or equity instrument in accordance with Article 325bi of that Regulation;

• (c) verify the accuracy of the list referred to in point (a) and of the identification referred to in point (b);

• (d) verify, on a sample of instruments identified in point (b), whether those instruments are in the scope of instruments included in the calculation of the own funds requirement for default risk.

Article 47

Assessment of accuracy and frequency of the calculation of the own fund requirement for default risk

• (a) verify whether the estimator used by the institution to estimate the value-at-risk is accurate;

• (b) where the value-at-risk calculation is based on Monte Carlo simulations, verify whether the number of simulations ensures convergence towards stable results, and the randomness properties of the sequences used to generate the simulations;

• (c) verify whether, before calculating the changes in the portfolio’s value following issuers’ defaults, the value of the positions in the institution’s portfolios refers to the value-at-risk’s reference date;

• (d) verify whether, with the exception of the positions subject to the derogation referred to in Article 325bn(3) of Regulation (EU) No 575/2013, a one-year time horizon is used in the computation of the value-at-risk;

• (e) where the default risk is computed less frequently than daily, analyse the process used by the institution to determine the frequency of the calculation of the own funds requirements for default risk, and verify whether the calculation at a reduced frequency does not lead to underestimation of risk;

• (f) verify whether for equity instruments, prices are set to zero when simulating the defaults of those equity instruments, and whether that is systematically ensured by the internal systems, and may verify whether that is the case on a sample of equity positions.

For the purposes of point (a), competent authorities shall verify how the institution chose the estimator and the analysis made to back such choice.

For the purposes of point (b), competent authorities shall review the tests performed by the institution to set the number of simulations.

For the purposes of point (d), competent authorities shall verify whether the rationale of the institution for applying that derogation is sound, in particular when the institution uses a time horizon of 60 days for some equity positions, and a one-year time horizon for some other equity positions.

For the purposes of point (e), competent authorities:

• (a) shall, where the default risk is computed weekly, analyse the process used by the institution to determine the day of the week when the own funds requirements for default risk are calculated;

• (b) shall require the institution to calculate, where not yet available, daily jump-to-default exposures over a given period, and assess whether those exposures hint at a systematically lower risk profile on those days in which the own funds requirements are calculated;

• (c) may also use additional figures that may be computed daily by the institution for internal risk-management purposes, including daily sensitivities to the most material issuers.

For the purposes of the fourth subparagraph, point (b), where there are hints of a systematically lower risk profile, competent authorities may complement their assessment by requiring the institution to calculate, on a daily basis and for a given period, its own funds requirements for default risk, and by analysing whether those measures are systematically lower on the days chosen by the institution.

• (a) require the institution to provide the Monte Carlo statistical error at 95 % confidence level, and verify whether the method employed to measure such statistical error is sound;

• (b) require the institution to calculate the value-at-risk measure with several different seeds, all other assumptions being equal, and verify that the method used to generate simulation does not create bias in the results;

• (c) assess whether the differences in the value-at-risk measures with a different seed, as calculated in accordance with point (b), are compatible with the statistical error referred to in point (a), and, where that is not the case, assess the root cause of such incompatibility and the number of simulations needed to ensure that the statistical error is below 5 %.

SECTION 3 Assessment of default probabilities and losses given default estimates

Article 48

Assessment of default probabilities

• (a) the methods that the institution uses to estimate default probabilities, including the materiality of each different method in terms of number of issuers, size of positions, and contribution to the default risk own funds requirements;

• (b) for each issuer, the default probability value, the rating, where available, and whether:

• (i) the default probability is available under the IRB approach for a non-trading book exposure of the issuer, and whether it is used for the trading book exposure as required by Article 325bp(5), point (d), of Regulation (EU) No 575/2013;

• (ii) the default probability is not available under the IRB approach for a non-trading book exposure of the issuer, and whether the institution employs the IRB approach to obtain the issuer’s default probability as required by Article 325bp(5), point (d), of Regulation (EU) No 575/2013, on the basis that the institution has the IRB approval for the exposure class to which the exposure of the issuer belongs;

• (iii) the default probability is not available under the IRB approach for a non-trading book exposure of the issuer, and whether the institution uses an internal methodology fulfilling the requirements of the IRB approach laid down in Article 1(1) of Delegated Regulation (EU) 2023/1578 to obtain that default probability;

• (iv) the default probability is not available under the IRB approach for a non-trading book exposure of the issuer, and whether the institution uses an internal methodology fulfilling the requirements laid down in Article 1(3) or (4) of Delegated Regulation (EU) 2023/1578 to obtain that default probability;

• (v) the default probability is not available under the IRB approach for a non-trading book exposure of the issuer, and whether the institution uses external sources as referred to in Article 2 of Delegated Regulation (EU) 2023/1578 to obtain that default probability;

• (c) for all issuers, the exposure class referred to in Article 147(2) of Regulation (EU) No 575/2013 to which their exposure belongs;

• (d) for issuers for which an estimate of default probability is obtained by using external sources as referred to in Article 2 of Delegated Regulation (EU) 2023/1578, whether the estimate is obtained in combination with current market prices as referred to in Article 325bp(5), point (c), of Regulation (EU) No 575/2013 and Article 2(4), point (b), of Delegated Regulation (EU) 2023/1578.

• (a) verify whether:

• (i) default probability estimates and the data inputs used to derive them are updated at a frequency that ensures that the own funds requirements for default risk are risk-sensitive;

• (ii) any new relevant information is reflected timely, as required by Article 325bp(4) of Regulation (EU) No 575/2013;

• (b) by using the inventory referred to in paragraph 1 of this Article, verify whether all estimates are floored as required by Article 325bp(5), point (a), of Regulation (EU) No 575/2013;

• (c) verify whether any method used for scaling a default probability to the applicable time horizon referred to in Article 325bp(5), point (b), or Article 325bn(3) of Regulation (EU) No 575/2013, is conceptually sound and whether such method is supported by robust analysis;

• (d) verify whether:

• (i) where the institution estimates the default probability using the method referred to in paragraph 1, points (b)(iv) and (b)(v), the definition of default used by the institution for issuers in the scope of the internal default risk model is documented in the institution’s internal policies;

• (ii) whether material differences to the definition of default used in the IRB framework are identified;

• (e) assess whether and how extreme declines in market prices as referred to in Article 325bp(5), point (c), of Regulation (EU) No 575/2013 are considered when the institution determines the estimates of default probabilities and whether and how those declines relate to the credit worthiness of an issuer;

• (f) for default probabilities that are obtained in accordance with paragraph 1, points (b)(i) to (b)(iii), of this Article verify whether those default probabilities take into account the margin of conservatism referred to in Article 179(1), point (f), and Article 180(1), point (e), of Regulation (EU) No 575/2013;

• (g) for default probabilities that are obtained in accordance with paragraph 1, point (b)(i):

• (i) verify whether any additional levels of conservatism applied to the default probabilities under the IRB approach are applied when the default-risk requirement is calculated;

• (ii) on a sample of issuers, verify whether the default probability used in the IRB approach does not differ from the one used in the calculation of the default risk requirement;

• (h) for default probabilities that are obtained in accordance with paragraph 1, point (b)(ii):

• (i) verify whether the process to estimate the default probability under the IRB approach is followed;

• (ii) on a sample of issuers, verify whether the default probability used is identical to the one that would be produced by the IT systems used under the IRB approach;

• (iii) assess input variables used in the rating process in the IRB approach and verify on a sample of issuers whether the data inputs exist and are sufficiently reliable to determine an accurate default probability;

• (i) for default probabilities that are obtained in accordance with paragraph 1, point (b)(iii), of this Article review the reports produced by the internal validation or the internal audit regarding the compliance of the internal methodology used to obtain the default probabilities with Part Three, Title II, Chapter 3, of Regulation (EU) No 575/2013;

• (j) for default probabilities that are obtained in accordance with paragraph 1, point (b)(iv):

• (i) verify whether the internal documentation supporting the compliance of the institution with the conditions laid down in Article 1(2) of Delegated Regulation (EU) 2023/1578 is complete;

• (ii) on a sample of issuers, assess the rationale for estimating the default probability by using neither the internal methodology referred to in Article 1(1) of Delegated Regulation (EU) 2023/1578, nor the external sources referred to in Article 2 of that Delegated Regulation;

• (iii) on a sample of issuers for which the rationale referred to in point (ii) relates to the lack of input data as referred to in Article 1(2), point (b)(i), of Delegated Regulation (EU) 2023/1578, verify whether the institution substantiates the fact that the input data are missing;

• (iv) verify whether, as part of its internal policies, the institution specifies the holding period referred to in Article 1(2), point (b)(ii), of Delegated Regulation (EU) 2023/1578, below which the institution deems acceptable not to use the internal methodology meeting the requirements set out for the IRB approach, and assess whether such holding period fits with the institution’s portfolio, in terms of size, complexity and trading strategy;

• (v) review the value of ‘m’ calculated in accordance with Article 1(5) of Delegated Regulation (EU) 2023/1578 and, where applicable, require the institution to explain the source of any significant changes in its value over the previous quarters;

• (vi) review the process followed by the institution to investigate whether any additional external sources are available as referred to in Article 1(2), point (c)(ii)(1), of Delegated Regulation (EU) 2023/1578;

• (vii) for a quarter where the value of ‘m’ is higher than 10 %, verify that the analysis performed in accordance with Article 1(2), point (c)(ii)(2), of Delegated Regulation (EU) 2023/1578 is robust;

• (viii) assess whether the determination of the default probability referred to in Article 1, (3) and (4) of Delegated Regulation (EU) 2023/1578, is performed correctly, by using the inventory referred to in paragraph 1 of this Article, and verify whether the institution updates the highest default probability assigned to investment grade issuers and the equally weighted average of default probabilities. as referred to Article 1(3), points (a) and (b), of Delegated Regulation (EU) 2023/1578, respectively, with the same frequency at which the default risk requirement is calculated;

• (k) for default probabilities that are obtained in accordance with paragraph 1, point (b)(v):

• (i) on a sample of issuers, verify whether the data used to estimate the default probability are representative for the issuer;

• (ii) verify whether the hierarchy of external sources referred to in Article 2(3) of Delegated Regulation (EU) 2023/1578 is well specified in the institution’s internal documentation and verify on a sample of issuers whether that hierarchy of external sources is implemented correctly;

• (iii) verify whether the methodology employed by the institution to obtain the expected range of estimation errors as referred to in Article 2(4), point (a)(i), of Delegated Regulation (EU) 2023/1578 is sound;

• (iv) assess how the institution ensures that the requirements laid down in Article 2(4), point (a), of Delegated Regulation (EU) 2023/1578 are fulfilled, and verify whether there are cases of default probabilities set at 0 before the institution applies the floor referred to in Article 325bp(5), point (a), of Regulation (EU) No 575/2013;

• (v) where applicable, verify whether the method that the institution uses to transform default probabilities that are obtained in combination with current market prices into a real-world probability is sound, and whether the analysis referred to in Article 2(4), point (b), of Delegated Regulation (EU) 2023/1578 is robust.

For the purposes of point (a), competent authorities may, where appropriate:

• (a) identify issuers for which the estimated default probability has not changed for an extensive period;

• (b) assess whether the default probability estimates are up-to-date;

• (c) verify whether the institution can explain the reasons behind the unchanged values.

For the purposes of point (b), competent authorities shall analyse the materiality and the characteristics of the positions subject to the floor, including their rating and exposure class.

For the purposes of point (c), competent authorities shall:

• (a) identify the effective time horizon that is used before applying any scaling to obtain the applicable time horizon;

• (b) assess the rationale for using, as a starting point of the scaling, a different time horizon than the time horizon that is applicable in accordance with Article 325bp(5), point (b), or Article 325bn(3) of Regulation (EU) No 575/2013.

For the purposes of point (k)(i), competent authorities shall verify whether the data used are reflective of the sector or region of the issuer.

For the purposes of point (k)(iii), competent authorities may require the institution to provide a sensitivity analysis following the principles of the sensitivity analysis referred to in Article 1(2), second subparagraph, of Delegated Regulation (EU) 2023/1578 to assess the potential impact of changes in the PD estimate.

Article 49

Assessment of losses given defaults

• (a) the methods that the institution uses to estimate the losses given default, including the materiality, in terms of size of positions and contribution to the default risk own fund requirement, of each different method;

• (b) for each position, the loss given default value, whether the position is a subordinated debt, a senior unsecured debt, a covered bond, or any other type of position, and whether:

• (i) the loss given default is available under the IRB approach for a non-trading book exposure, and whether it is used for the trading book exposure as required by Article 325bp(6), point (c), of Regulation (EU) No 575/2013;

• (ii) the loss given default is not available under the IRB approach for a non-trading book exposure, and whether the institution employs the IRB approach to obtain the position’s loss given default as required by Article 325bp(6), point (c), of Regulation (EU) No 575/2013;

• (iii) the loss given default is not available under the IRB approach for a non-trading book exposure, and whether the institution uses an internal methodology fulfilling the requirements of the IRB approach laid down in Article 3(1) of Delegated Regulation (EU) 2023/1578 to obtain it;

• (iv) the loss given default is not available under the IRB approach for a non-trading book exposure, and whether the institution uses an internal methodology fulfilling the requirements laid down in Article 3(3) or (4), of Delegated Regulation (EU) 2023/1578 to obtain it;

• (v) the loss given default is not available under the IRB approach for a non-trading book exposure, and whether the institution uses external sources as referred to in Article 4 of Delegated Regulation (EU) 2023/1578 to obtain it;

• (c) for all positions, the exposure class referred to in Article 147 of Regulation (EU) No 575/2013 to which they belong.

• (a) verify whether the granularity of the losses given default provides a meaningful differentiation of risk and, among others, whether that granularity allows to appropriately reflect the seniority of the position as referred to in Article 325bp(6), point (b), of Regulation (EU) No 575/2013, and its collateralisation;

• (b) verify whether loss given default estimates as well as the data inputs used to derive them are updated at a frequency that ensures that the own funds requirements for default risk are risk-sensitive, and whether any new relevant information is reflected timely, as required by Article 325bp(4) of Regulation (EU) No 575/2013;

• (c) for losses given default that are obtained in accordance with paragraph 1, point (b)(i), verify whether any additional layer applied to the losses given default under the IRB approach to obtain more conservative estimates is applied when the institution calculates the own funds requirements for default risk;

• (d) for losses given default that are obtained in accordance with paragraph 1, point (b)(ii):

• (i) verify whether the institution has followed the process to estimate the loss given default under the IRB approach in accordance with the institution IRB’s internal policies;

• (ii) on a sample of positions, verify whether the loss given default that the institution uses is identical to the estimate that would be produced by the IT systems used under the IRB approach;

• (iii) assess the variables used in the IRB approach, and verify on a sample of positions whether the data inputs exist and are sufficiently reliable to determine an appropriate loss given default;

• (e) for losses given default that are obtained in accordance with paragraph 1, point (b)(iii), of this Article review the reports produced by the internal validation, and the internal audit regarding the compliance of the internal methodology used to obtain the losses given default with Part Three, Title II, Chapter 3, of Regulation (EU) No 575/2013;

• (f) for losses given default that are obtained in accordance with paragraph 1, point (b)(iv):

• (i) verify whether the internal documentation supporting the compliance of the institution with the conditions referred to in Article 3(2) of Delegated Regulation (EU) 2023/1578 is complete;

• (ii) on a sample of positions, assess the rationale for estimating the loss given default by using neither the internal methodology referred to in Article 3(1) of Delegated Regulation (EU) 2023/1578, nor the external sources referred to in Article 4 of that Delegated Regulation;

• (iii) on a sample of positions for which the rationale referred to in point (ii) of this paragraph relates to the lack of input data as referred to in Article 3(2), point (b)(i), of Delegated Regulation (EU) 2023/1578, verify whether the institution substantiates the fact that the input data are missing;

• (iv) verify whether, the institution, as part of its internal policies, specified the holding period referred to in Article 3(2), point (b)(ii), of Delegated Regulation (EU) 2023/1578, below which the institution deems acceptable not to use the internal methodology meeting the requirements set out for the IRB approach, and assess whether such holding period fits with the institution’s portfolio, in terms of size, complexity and trading strategy;

• (v) review the value of ‘m’ calculated in accordance with Article 3(5) of Delegated Regulation (EU) 2023/1578 and, where applicable, require the institution to explain the source of any significant changes in its value over the previous quarters;

• (vi) review the process that the institution has followed to investigate whether any additional external sources are available as required by Article 3(2), point (c)(ii), of Delegated Regulation (EU) 2023/1578;

• (vii) by using the inventory referred to in paragraph 1 of this Article, assess whether the determination of the loss given default as referred to in Article 3(3) and (4), of Delegated Regulation (EU) 2023/1578 is performed correctly;

• (g) for losses given default that are obtained in accordance with paragraph 1, point (b):

• (i) on a sample of positions, verify whether the data used to estimate the loss given default are representative for the position;

• (ii) verify whether the hierarchy of external sources referred to in Article 4(2) of Delegated Regulation (EU) 2023/1578 is well specified in the institution’s internal documentation and verify, on a sample of positions, that that hierarchy of external sources is implemented correctly;

• (iii) verify whether the estimates of losses given default distinguish between positions that are defaulted and positions that are not.

For the purpose of point (b), competent authorities may, where appropriate, identify positions for which the estimated losses given default has not changed for an extensive period, assess whether they are up-to-date and verify that the institution can explain the reasons behind the unchanged values.

For the purposes of point (c), competent authorities shall, on a sample of positions, verify whether the loss given default estimate used in the IRB approach does not differ from the loss given default estimate used in the calculation of the default risk requirement.

For the purposes of point (g)(i), competent authorities shall verify whether the data used are reflective of the seniority of the position as referred to in Article 325bp(6), point (b), of Regulation (EU) No 575/2013, and the region or sector.

For the purposes of point (g)(iii), competent authorities may verify whether the estimates of losses given default distinguish between positions that are defaulted and positions that are not by assessing the estimate assigned by the institution to positions to the same issuer that are defaulted and that are not defaulted included in the scope of the additional own funds requirements for default risk.

SECTION 4 Assessment of correlation, hedging and particular requirements

Article 50

Assessment of the correlation structure

• (a) verify whether only listed equity and credit spreads are used as data inputs for determining the correlation between different issuers;

• (b) where the institution uses copulas to model default correlations, assess the internal validation of the copula assumptions performed by the institution and verify whether there is compatibility between the historical data used for the calibration of the correlations and the issuers included in the institution’s portfolio;

• (c) identify whether the correlation among issuers is based on absolute or relative returns, and assess whether the rationale behind the choice of the return type is:

• (i) sound;

• (ii) consistent with the choices made by the institutions in relation to other aspects of the internal risk-measurement model;

• (d) assess whether the method that the institution uses to obtain a correlation on the applicable time-horizon from returns calculated on a shorter time horizon is sound;

• (e) assess how the institution determines the calibration period referred to in Article 325bn(1), point (c), of Regulation (EU) No 575/2013.

For the purposes of point (a), competent authorities may, where appropriate, require the institution to provide data used to model the correlation between a sample of issuers selected by competent authorities, and verify whether those data only relate to listed equities and credit spreads.

For the purposes of point (d), competent authorities shall verify whether, where the institution applies the derogation referred to in Article 325bn(3) of Regulation (EU) No 575/2013, a correlation of 60 business days is used only between equity positions for which that derogation is used, and that the correlation is otherwise measured over a one-year time horizon.

For the purposes of point (e), competent authorities shall verify whether the approach that the institution uses to select the period, including its length, is:

• (a) sound;

• (b) documented in the institution’s internal policies;

• (c) reviewed to account for any changes in the stress period referred to in Article 325bc(2) of Regulation (EU) No 575/2013.

Article 51

Assessment of the hedging recognition

When assessing whether the recognition of hedges in the institution’s internal default risk model complies with Article 325bo of Regulation (EU) No 575/2013, competent authorities shall:

• (a) verify whether the institution’s internal policies:

• (i) describe how the netting is performed;

• (ii) specify:

• (1) those basis risks that are implicitly captured in the model by modelling two different positions;

• (2) those basis risk that are instead explicitly captured by introducing a basis risk factor;

• (b) review the internal policies of the institution, and verify the criteria envisaged in those internal policies to recognise netting and hedging or diversification effects;

• (c) assess whether the monitoring of potential significant basis risk that may arise in the interval between the maturity of an instrument and the one-year time horizon is robust;

• (d) require the institution to provide:

• (i) a sample of positions in the default risk model;

• (ii) the list of risk factors corresponding to the positions referred to in point (i).

When requesting the sample referred to in point (d)(i), competent authorities shall ensure that there is variety in the positions provided, and that, where applicable, both positions that are netted and positions that are not netted are included.

For the purposes of point (b), competent authorities shall verify whether the criteria in the internal policies of the institution ensure that the netting and hedging are efficient, also where a credit or any other event occurs.

For the purposes of point (d), competent authorities shall verify whether:

• (a) the institution’s mapping of positions to risk factors ensures that exposures to different obligors are not netted, and that such netting only takes place for positions that relate to the same financial instruments of the same obligor;

• (b) either exposures to different obligors are mapped to different risk factors, or there is a basis risk factor to capture the differences in those exposures, and the basis risk between obligors that are constituents of credit indices and other obligors is captured;

• (c) for positions in different financial instruments of the same obligor, the analysis performed by the institution to assess whether significant basis risk in the hedging strategies may arise due to different type of products, seniority in the capital structure, internal or external ratings, maturity, or vintage, is robust.

Article 52

Assessment of compliance with particular requirements

When assessing the internal default risk model’s compliance with the requirements laid down in Article 325bp of Regulation (EU) No 575/2013, competent authorities shall:

• (a) in relation to the modelling of the default of individual as well as multiple issuers as required by Article 325bp(1) of Regulation (EU) No 575/2013:

• (i) identify the approach that the institution uses to model the default, and verify that the two types of systematic risk factors selected by the institution capture the most relevant systematic effects;

• (ii) verify whether the granularity of the two types of systematic risk factors is sufficient to capture the characteristics of the issuers in the portfolio subject to the own funds requirement for default risk;

• (iii) verify whether for each issuer, the institution uses a separate idiosyncratic risk factor in addition to the two types of systematic risk factors referred to in Article 325bp(1) of Regulation (EU) No 575/2013;

• (iv) verify whether the mapping of issuers to the appropriate systematic risk factors is sound;

• (v) verify whether the institution analyses the explanatory power of the factor model;

• (vi) when requesting the sample for the purpose of the assessment, consider the materiality of the issuers, and ensure that the sample encompasses issuers that have been mapped to different systematic risk factors;

• (b) in relation to the requirement to reflect the economic cycle in the internal default risk model as required by Article 325bp(2) of Regulation (EU) No 575/2013, assess how the modelling of losses given defaults, including stochastic ones, is performed for such losses given defaults to reflect changes in the properties taken by the systematic risk factors;

• (c) in relation to the requirement to capture non-linearities as required by Article 325bp(3) of Regulation (EU) No 575/2013, assess:

• (i) how institutions revalue a non-linear financial instrument following the default of an issuer, including how institutions revalue a financial instrument with multiple underlying following the default of an individual issuer or of multiple issuers corresponding to the underlyings;

• (ii) whether any simplifications introduced by the institution to calculate the price of a financial instrument leads to material inaccuracies or a systematic underestimation of the risk;

• (iii) the extent to which the revaluation of a financial instrument takes into account model risk;

• (d) in relation to the requirement to have an internal default risk model that is consistent with internal risk-management as required by Article 325bp(9) of Regulation (EU) No 575/2013, verify whether the institution has documented the differences between the internal default risk model and the models that the institution uses for its internal risk management for the same scope of positions, and whether the institution is able to explain those differences.

For the purposes of point (a)(i), competent authorities shall assess the rationale provided in the institution’s internal policies for the choice of the systematic risk factors, and their economic interpretation.

For the purposes of point (a)(iii), competent authorities may, where appropriate, verify on a sample of similar issuers that the idiosyncratic risk factors differ.

For the purposes of point (a)(iv), competent authorities may, where appropriate, verify on a sample of issuers, that the mapping is correct.

For the purposes of point (a)(v), competent authorities may, where appropriate and where the analyses performed by the institution do not seem sufficient for the portfolio subject to default risk as it stands, require the institution on a sample of issuers to assess the power of the systematic risk factors chosen by the institution in explaining the drivers of the default of each issuer’s asset.

For the purposes of point (b), competent authorities may, where appropriate, perform statistical analyses on a sample of issuers, including hypothesis testing, to test the dependency of losses given defaults on the systematic risk factors.

CHAPTER 5 FINAL PROVISIONS

Article 53

Entry into force and application

This Regulation shall enter into force on the twentieth day following that of its publication in the Official Journal of the European Union.

Article 18 (1), point (a), as regards the environmental risk, Article 18(1), point (c)(vii), and Article 18(2), point (b)(v), shall apply from 1 January 2025.

Article 21 (1), point (b), shall apply from 1 January 2026.

This Regulation shall be binding in its entirety and directly applicable in all Member States.

Done at Brussels, 13 March 2024.

For the Commission

The President

Ursula VON DER LEYEN