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

(a) require an institution to provide a sample of risk factors, and the corresponding verifiable and representative prices used to assess the conditions referred to in Article 1 of Delegated Regulation (EU) 2022/2060;

(b) verify whether, where for the risk factor there are multiple verifiable prices on a given observation date, only one is considered when assessing whether the conditions referred to in Article 1 of Delegated Regulation (EU) 2022/2060 are met;

(d) for those risk factors in the sample referred to in point (a) that are systematic credit or equity risk factors capturing market-wide movements as referred to in Article 3(3) of Delegated Regulation (EU) 2022/2060, verify whether the verifiable prices used are representative of attributes of the systematic risk factors.

For the purposes of point (a), the sample of risk factors shall include, among others, risk factors that narrowly met the conditions for being assessed modellable and risk factors that changed their modellability status over the previous year. Where applicable, that sample shall contain risk factors for which verifiable prices are obtained solely by the institution, solely by third-party vendors, and by both the institution and third-party vendors.

(a) require the institution to provide a sample of buckets relating to a set of curves, surfaces or cubes, and the corresponding verifiable and representative prices;

(b) for the verifiable prices referred to in point (a), verify, for the buckets for which there are multiple verifiable prices on a given observation date, that only one verifiable price per each date is considered when assessing whether the conditions referred to in Article 1 of Delegated Regulation (EU) 2022/2060 are met;

(c) for the verifiable prices referred to in point (a), assess that the methodology employed by the institution to map a verifiable price to a given bucket is appropriate.

For the purposes of point (a), the sample of buckets shall include, among others, buckets that narrowly met the conditions for being assessed modellable and buckets that changed their modellability status over the previous year. Where applicable, that sample shall include buckets for which verifiable prices are obtained solely by the institution, solely by third-party vendors, and by both the institution and third-party vendors.

For the purposes of point (c), the competent authority shall verify whether:

(a) the points in a bucket are a strong driver of the price considered representative,

(b) the method used by the institution to conclude that there is a close relationship between any point in the bucket and that price is sound,

(c) the methodology employed by the institution to extract the value of that point in the bucket from that price is sound.

Article 33

Assessment of the risk factors’ liquidity horizon

(a) a description of the risk factor;

(b) whether the risk factor is modellable following the assessment of the modellability referred to in Article 325be of Regulation (EU) No 575/2013 and, where the risk factor is modellable, whether that risk factor is included in the subset of modellable risk factors referred to in Article 325bc(2), point (a), of that Regulation;

(c) a simple description of the data inputs used to mark the risk factor;

(d) the liquidity horizon assigned to the risk factor as required by Article 325bd(2) of Regulation (EU) No 575/2013;

(e) whether the nature of the risk factor does not correspond to any broad category of risk factors as required by Article 1(2) of Delegated Regulation (EU) 2022/2058;

(f) whether the nature of the risk captured by the risk factor and the data inputs used for that risk factor correspond to risk factors that could fall under more than one broad category of risk factors or broad sub-category of risk factors as required by Article 1(3) of Delegated Regulation (EU) 2022/2058;

(g) where used to model a homogenous index, whether the methodology referred to in Article 1 of Delegated Regulation (EU) 2022/2058 or the methodology referred to in Article 2 of that Regulation has been used to map the risk factor to the appropriate broad category and sub-category of risk factors of Table 2 of Article 325bd of Regulation (EU) No 575/2013.

(b) the institution has in place objective criteria for identifying when a credit spread risk factor refers to an investment grade or a high yield position;

(c) where the institution applies the derogation set out in Article 325bd(3) of Regulation (EU) No 575/2013 regarding the use of longer liquidity horizons in calculating the expected shortfall risk measure referred to in Article 325bb of that Regulation and the stress scenario risk measure referred to in Article 325bk of that Regulation, the institution distinguishes between positions belonging to trading desks for which the derogation is used from those trading desks for which the derogation is not used;

(e) only one currency is considered domestic for the purpose of mapping a risk factor to the broad category ‘Interest rate’ and sub-category ‘Most liquid currencies and domestic currency’ of Article 325bd, Table 2, of Regulation (EU) No 575/2013.

For the purposes of point (c), competent authorities shall focus on risk factors belonging to the sub-category subject to the derogation and that are present both in trading desks for which the derogation is used and in trading desks for which the derogation is not used.

SECTION 3

Assessment of proxies and data quality

Article 34

Assessment of proxies

(c) for non-modellable risk factors, there is a clear rationale for using a proxy approach, even though the number of returns N in the time series for the risk factor resulting from Article 7 of Delegated Regulation (EU) 2024/397 would allow for using the historical method or the asymmetrical sigma method referred to, respectively, in Articles 8 and 9 of that Delegated Regulation;

(d) the approach used to proxy the risk factor is appropriate and ensures, as required by Article 325bh(1), point (g), of Regulation (EU) No 575/2013, a conservative calibration of the scenarios of future shocks for modellable risk factors and of the extreme scenarios of future shock for non-modellable risk factors;

(e) for risk factors for which proxy data are used only for specific periods in the time series, there are no anomalous jumps between the parts of the time series that are proxied and the parts of the time series that are not proxied.

(a) the proxy approach used for those risk factors is the approach described in the internal policies as referred to in paragraph 1, point (a), and the proxy used is economically meaningful;

(b) the basis risk between that risk factor as proxied and other risk factors is duly captured, including where different risk factors are proxied by mapping them to the same risk factor;

(c) there are no cases where, as a result of the proxy, the specific risk is not duly captured.

When applying that assessment method, competent authorities shall choose a sample of risk factors reflecting a variety of proxy approaches, including, where used, factor models, beta approximations, and mapping of risk factors to benchmarks, including names representative of the sector and region or indices.

(a) require the institution to provide the time series of the proxied risk factors as used in the internal risk-measurement model and the time series of the corresponding pricing factors as used in the end-of-day valuation process;

(b) verify that the volatilities of the two time series referred to in point (a) do not substantially diverge;

(c) verify that the two time series are highly correlated.

When applying that assessment method, competent authorities shall choose a sample of risk factors reflecting a variety of proxy approaches, including, where used, factor models, beta approximations, and mapping of risk factors to benchmarks, including names representative of a given sector and region or indices.

(a) require the institution to provide the time series of a sample of risk factors that are not proxied and that, if proxied, would follow the proxy approach being assessed;

(b) require the institution to provide the time series that would be used by applying the proxy approach being assessed to the risk factors’ time series referred to in point (a);

(c) for both time series, obtain the volatilities of the risk factors in the stress period and in the last 12-month period, and verify that the volatility resulting from the proxy time series referred to in point (b) does not underestimate the volatility resulting from the time series referred to in point (a).

When applying that assessment method, competent authorities shall choose a sample of risk factors reflecting a variety of proxy approaches, including, where used, factor models, beta approximations, and mapping of risk factors to benchmarks, including names representative of a given sector and region or indices.

(a) require the institution to provide the original time series for the risk factors before any proxy approach has been used;

(b) require the institution to provide the time series used for the proxied risk factors;

(c) compare the upward and downward calibrated shocks as resulting from the application of Article 8 and 9 of Delegated Regulation (EU) 2024/397 to the time series referred to in points (a) and (b) of this paragraph, and verify that shocks resulting from the proxied time series are not systematically less conservative than the shocks obtained by using the original time series.

When applying that assessment method, competent authorities shall choose a sample of risk factors reflecting a variety of proxy approaches, including, where used, factor models, beta approximations, and mapping of risk factors to benchmarks, including names representative of the sector and region or indices.

Article 35

Assessment of the data quality

(a) the institution documents, as part of its internal policies, any methodology used to fill in time series with missing data points, and whether such documentation contains sound analysis showing that those methodologies do not affect the risk factors’ volatilities and correlations;

(b) the institution has established objective criteria setting out which methodology to fill in time series is used, where more than one methodology is available, and has documented those criteria in its internal policies;

(c) the institution has established, as part of its internal policies, the process to be followed whenever the values in a time series are changed, and whether such process includes the documentation of the performed changes;

(d) the institution does not perform filtering of data, including flooring, capping and exclusions of outliers, unless the institution is able to demonstrate that the excluded data point relates to erroneous or stale data, and the institution documents such an exclusion;

(e) the institution performs periodic quality checks on the time series used for the computation of the expected shortfall risk measure, and documents those checks and the corresponding results are documented;

(f) the institution analyses, as part of the checks referred to in point (e), the effect that missing or replaced data and the methodology used to obtain the time series have on the risk factors’ volatilities and correlations;

(g) the data quality of the time series used by the institution is appropriate.

For the purposes of point (e), competent authorities shall verify whether the institution monitors, as part of the checks referred to in that point, for each time series:

(a) the number of days for which data points were initially missing and were then filled in using a particular methodology;

(b) the number of days for which data points were initially available and have been replaced using a particular methodology;

(c) the number of days with no daily changes;

(d) the maximum number of consecutive days with no daily change.

(b) based on the overview referred to in point (a), identify those times series used for risk factors that may be affected by low data quality;

For the purposes of point (b), competent authorities may use, where appropriate, as a basis for the identification referred to in that point, the following indicators:

(a) time series with less than 10 % of initially available data points;

(b) time series with 20 consecutive business days without any daily change;

(c) time series with more than 20 % of days with no changes;

(d) time series for which more than 50 % of the initially available data have been changed.

Competent authorities shall require the institution to justify the use of those time series and, where applicable, the reason why the corresponding risk factor is included in the reduced set of risk factors as referred to in Article 325bc(2), points (a) and (b), and Article 325bc(3), points (a) and (b), of Regulation (EU) No 575/2013.

SECTION 4

Assessment of compliance with requirements relating to the back-testing and profit-loss attribution test

Article 36

Assessment of the technical elements to be included in the actual and hypothetical changes in the portfolio’s value for the back-testing requirements

(a) specify all the elements referred to in Article 5 of Delegated Regulation (EU) 2022/2059 and, where applicable, all the elements referred to in Article 1(5), point (c), of that Regulation;

(c) require the production of the report referred to in point (b) both at the level of each trading desk subject to trading desk’s back-testing requirements in accordance with Articles 1 and 3 of Delegated Regulation (EU) 2022/2059, and at the level of the portfolio subject to back-testing requirements in accordance with Articles 2 and 4 of Delegated Regulation (EU) 2022/2059;

(d) specify the rectification processes to follow in the calculation of the actual and hypothetical changes in case of contingencies, exceptions, errors, and pricing failures.

For the purposes of points (a)(vi), (b)(v)(1), (c)(v) and (d)(v)(1), competent authorities shall verify whether the institution does not derive the adjustment applicable to the trading desk from a broader scope of positions than those assigned to the trading desk.

For the purposes of point (a)(vii), competent authorities shall evaluate how the institution risk-manages those adjustments.

For the purposes of points (b)(v)(2) and (d)(v)(2), competent authorities shall verify whether the whole adjustment calculated on that scope is included in the actual changes in the portfolio’s value.

For the purposes of point (c)(vi), competent authorities shall evaluate how the institution risk-manages those adjustments.

For the purposes of point (e)(ii), competent authorities shall review the history of contingencies, exceptions, errors, and pricing failures in the calculations of the changes in the portfolios’ values, assess how they have been remediated and, where relevant, the impact of those errors on the back-testing and profit-and-loss attribution test results.

For the purposes of point (e)(iii), competent authorities shall, where, due to stale data, those positions lead to no changes in the end-of-day valuation and in the actual and hypothetical changes in the portfolio’s value, assess whether, despite the lack of data, the risk-measurement model is reasonably accurate in measuring risks of those positions as referred to in Article 325bi(1), point (f), of Regulation (EU) No 575/2013.

(a) on a sample of transactions, require the institution to calculate and reconcile the changes in the end-of-day value as resulting from the end-of-day valuation process, the actual changes, and the hypothetical changes;

(b) on a sample of transactions, require the institution to calculate the hypothetical changes and the risk-theoretical changes, and verify whether the effect of the passage of time is captured consistently;

(c) compare the profile of the cumulative hypothetical changes to the portfolio’s value over a given period of time and the corresponding cumulative actual changes over the same period to assess the plausibility of the calculations performed by the institution.

Article 37

Assessment of the analysis of overshootings

(a) identifies which portfolios or trading desks primarily caused the overshooting;

(b) analyses the differences in the hypothetical and actual changes in the portfolio’s value;

(c) analyses whether and which market movements, risk factors or parameters caused the overshooting;

(d) analyses whether any modelling issues, or missing risk factors, contributed to the overshooting, and provides an explanation of which part of the changes in the portfolio’s value can be explained by the model and which cannot;

(e) analyses whether process failures, including positions not being properly captured or missing updates of data, contributed to or caused the overshooting;

(f) describes the results of actions taken as a result of points (a) to (e) when notifying competent authorities of overshootings that emerged from their back-testing programme conducted in accordance with Article 325bf of Regulation (EU) No 575/2013.

(a) any overshooting, including those relating to the back-testing referred to in Article 325bf(5) of Regulation (EU) No 575/2013, is reported to senior management within three working days of the date the overshooting has been identified;

(b) the analyses referred to in paragraphs 1 and 2 are reported to the competent authority and to the senior management within one month of the date the overshooting has occurred.

Article 38

Assessment of compliance with the profit and loss attribution requirements

(a) ensure that the business days used in the calculation of the theoretical changes in the portfolio’s value are the same as those used in both the calculation of the expected shortfall risk measure referred to in Article 325bb of Regulation (EU) No 575/2013 and the stress scenario risk measure referred to in Article 325bk of that Regulation;

(b) specify whether the institution aligns the snapshot time for which it calculates the theoretical changes in the trading desk portfolio’s value with the snapshot time for which it calculates the hypothetical changes in the trading desk portfolio’s value, as allowed by Article 6(2) of Delegated Regulation (EU) 2022/2059;

(c) specify whether there are risk factors for which the institution, uses input data or values used in the calculation of the hypothetical changes to calculate the theoretical changes, or whether there are no risk factors for which such treatment is used, as allowed by Article 14 of Delegated Regulation (EU) 2022/2059;

(d) cover all aspects referred to in Article 15(2) and (3) of Delegated Regulation (EU) 2022/2059 in relation to risk factors for which the institution uses input data or values used in calculating the hypothetical changes to calculate the theoretical changes, as allowed by Article 14 of that Delegated Regulation;

(e) specify the rectification processes to follow in the calculation of the theoretical changes in case of contingencies, exceptions, errors, and pricing failures;

(f) cover all aspects referred to in Article 15(1) of Delegated Regulation (EU) 2022/2059.

For the purposes of point (c), where the treatment concerned is used for some, but not all, risk factors, competent authorities shall verify whether the internal policies specify objective criteria to select risk factors for which that treatment is applied.

For the purposes of point (d), competent authorities shall verify whether the institution uses quantitative criteria to assess the effect of the alignment referred to in Article 15(2), point (b), of Delegated Regulation (EU) 2022/2059.

For the purposes of point (a)(ii), competent authorities shall evaluate whether the institution’s IT systems ensure the calculation of those changes on the same positions. To that effect, competent authorities may require the institution to provide the inventory of positions captured in the actual and theoretical changes, and compare those positions.

For the purposes of point (a)(iv), competent authorities shall verify whether the institutions’ systems ensure that the pricing functions used for calculating the theoretical changes are those used in the calculation of the expected shortfall risk measure referred to in Article 325bb of Regulation (EU) No 575/2013 and the stress scenario risk measure referred to in Article 325bk of that Regulation.

For the purposes of point (a)(v), competent authorities shall verify whether the institutions’ systems ensure that the value of other risk factors is kept constant when calculating the theoretical changes. Competent authorities may complement their assessment by using the assessment method referred to in paragraph 5.

For the purposes of point (a)(vi), competent authorities shall review the history of contingencies, exceptions, errors, and pricing failures in the calculations of the changes in the portfolios’ values, assess whether and how they have been remediated and, where relevant, assess the impact of those errors on the back-testing and profit-and-loss attribution test results.

(a) to require the institution to provide the inventory, at a given day and at the subsequent day as referred to in Article 12(1) of Delegated Regulation (EU) 2022/2059, of the positions in the portfolio on which it calculates theoretical changes, and assess whether those inventories coincide;

(b) to verify that the risk theoretical changes are typically closer to the hypothetical than to the actual changes and, by using the reports referred to in Article 36, paragraph 1, points (b) and (c), identify those days in the time series where the actual and hypothetical changes differ the most due to a change in the trading desk’s portfolio composition, and verify that the theoretical changes in those days are not affected by such a change in the portfolio’s composition.

(a) when the institution calculates the excepted shortfall risk measure referred to in Article 325bb of Regulation (EU) No 575/2013 or the stress scenario risk measure referred to in Article 325bk of that Regulation, require the institution to provide a sample of financial instruments in its portfolio, the prices of which depend both on risk factors that are shocked and risk factors that are not shocked;

(b) when the institution calculates the theoretical changes related to the financial instruments referred to in point (a), verify whether, for a given reference date, the value of risk factors that are not shocked is kept constant.

(a) require the institution to provide the time series of hypothetical and theoretical changes in the trading desk’s portfolio’s value used for calculating the Spearman correlation coefficient and Kolmogorov-Smirnov test metric as referred to in Article 6 of Delegated Regulation (EU) 2022/2059;

(b) calculate the Spearman correlation coefficient in accordance with Article 7 of Delegated Regulation (EU) 2022/2059 and the Kolmogorov-Smirnov test metric in accordance with Article 8 of that Delegated Regulation;

(c) verify whether the Spearman correlation coefficient and Kolmogorov-Smirnov test metric resulting from point (b) coincide with those obtained by the institution;

(d) verify whether the classification of the trading desks to the zones referred to in Article 9 of Delegated Regulation (EU) 2022/2059 is correct.

(a) identify the most material risk factors for which the institution applied the treatment referred to in Article 14(1) of Delegated Regulation (EU) 2022/2059;

(b) verify whether the same risk factor is used in the calculation of the hypothetical and theoretical changes;

(c) verify whether the value of the risk factors referred to in point (a) differs only because of the different sources or extraction times of their input data.

The intensity at which the competent authority performs the assessment shall be proportionate to the effect that the alignment of risk factors’ input data has on the theoretical changes and on the profit and loss attribution test results as referred to in Article 15(2) of Delegated Regulation (EU) 2022/2059.

(a) identify the most material risk factors for which the institution applied the treatment referred to in Article 14(2) of Delegated Regulation (EU) 2022/2059;

(b) for the risk factors referred to in point (a), acquire a comprehensive understanding of the techniques of the valuation systems that are used to derive the value of the risk factor from the input data, as referred to in Article 14(2), point (b), of Delegated Regulation (EU) 2022/2059;

(c) on the basis of point (b) of this paragraph, assess whether the conditions referred to in Article 14(2) Delegated Regulation (EU) 2022/2059 are met, taking into account any rationale provided in accordance with Article 15(3) of that Regulation.

The intensity at which the competent authority performs the assessment shall be proportionate to the effect that the alignment of risk factors’ values has on the theoretical changes and on the profit and loss attribution test results as referred to in Articles 15(2) of Delegated Regulation (EU) 2022/2059.

SECTION 5

Assessment of compliance with requirements relating to the treatment of foreign-exchange and commodity risk in the non-trading book

Article 39

Assessment of the calculation of the own funds requirements for foreign exchange and commodity risk in the non-trading book

(a) the scope of foreign exchange positions in the non-trading book for which the institution calculates the own funds requirements with the alternative internal model approach and, where applicable, the underlying reason for excluding some positions from that scope;

(b) the scope of commodity positions in the non-trading book for which the institution calculates the own funds requirements with the alternative internal model approach, and where applicable, the underlying reason for excluding some positions from that scope;

(d) the trading desks for which the hypothetical and the actual changes in the portfolio’s value in relation to a non-trading book position which is subject to commodity risk or both to commodity and foreign exchange risk are calculated in accordance with Article 5(2), point (a), of Delegated Regulation (EU) 2023/1577, and trading desks for which the changes are calculated in accordance with Article 5(2), point (b), of that Delegated Regulation, and the reason for that choice.

(d) in relation to the calculation of own funds requirements for positions that are subject to commodity risk or both to commodity and foreign exchange risk as referred to in Article 4 of Delegated Regulation (EU) 2023/1577, verify whether scenarios of future shocks are applied only to risk factors belonging to the commodity broad risk factor category, and, where applicable, to the foreign exchange broad risk factor category;

(e) verify whether the hypothetical and actual changes related to non-trading book positions subject to foreign exchange risk or commodity risk are calculated in accordance with Article 5 of Delegated Regulation (EU) 2023/1577.

For the purposes of point (a)(iii), competent authorities shall verify how the institution includes in the internal risk-measurement model the net open positions stemming from different entities of the group.

(a) on a sample of non-trading book positions taken on a given reference date, verify whether those positions are included in the scope of positions captured in the expected shortfall risk measure or stress scenario risk measure at that reference date or in the scope of positions of the alternative standardised approach;

(b) require the institution to reconcile, on the one hand, the non-trading book positions taken at a given reference date and, on the other hand, the non-trading book positions that are in the scope of the internal risk-measurement model and in the scope of the alternative standardised approach at that reference date.

(a) assess how the institution disentangles the foreign exchange risk factors from other inputs used to determine the accounting value of a position;

(b) require the institution to provide the list of risk factors out of the foreign exchange risk factors referred to in point (a) on which the institution applies scenarios of future shocks when calculating the expected shortfall risk measure referred to in Article 325bb of Regulation (EU) No 575/2013 or the stress scenario risk measure referred to in Article 325bk of that Regulation;

(b) verify whether in the list referred to in point (a)(ii), there are only risk factors reflecting commodity risk, and foreign exchange risk where applicable.

(a) require the institution to provide a description of the valuation inputs used to determine the accounting or the fair value of the position;

(b) require the institution to provide the values of such valuation inputs at the end of the day following the calculation of the value-at-risk number referred to in Article 325bf of Regulation (EU) No 575/2013 and at the end of the previous day, as used in the calculation of the hypothetical and actual changes to the portfolio’s value;

(c) verify whether, depending on the position subject to the assessment, the values are updated or kept unchanged as required by Article 5(2) of Delegated Regulation (EU) 2023/1577.

SECTION 6

Assessment of the calculation of the expected shortfall risk measures and the stress scenario risk measure

Subsection 1

Assessment of aspects that are relevant both for the calculation of the expected shortfall risk measures and the stress scenario risk measure

Article 40

Assessment of the capability of the internal risk-measurement model to capture non-linearities

(a) the internal risk-measurement model captures at least the material first- and second-order terms of Taylor series approximations to reflect the change in the prices due to changes in relevant risk factors, including the cross-gamma risk represented by material joint-moves in risk factors;

(b) the sensitivity-based approach leads to appropriate results, including where severe shocks are applied to the risk factors.

(a) identify products for which competent authorities want to test the materiality of the order terms of a Taylor series approximation, and the appropriateness of the sensitivity-based approach under severe shock;

(b) identify a business day in the stress period where the returns observed for the risk factors in those products were particularly high, where positive, or particularly low, where negative;

(c) require the institution to calculate the hypothetical and theoretical changes in the values of those products in accordance with Delegated Regulation (EU) 2022/2059, under the scenario identified by the returns on the business day identified in accordance with point (b);

(d) based on the results of the calculation referred to in point (c), assess whether the sensitivity-based approach leads to appropriate results.

Subsection 2

Assessment of aspects that are relevant for the calculation of the expected shortfall risk measures

Article 41

Assessment of the calculation of the expected shortfall risk measure

(a) analyse the process that the institution uses to determine the day of the week when the measures are computed;

(b) verify that a reduction in the calculation frequency does not lead to an underestimation of risk.

(a) verify whether the analysis performed by the institution is adequate to demonstrate that there is no underestimation of risk;

(b) analysing whether those measures are systematically lower on the day chosen by the institution.

Article 42

Assessment of the calculation of the partial expected shortfall measures

(a) verify whether the estimator used by the institution to estimate the expected shortfall risk measures is conceptually sound and reasonably accurate;

(c) verify whether, as part of the internal policies referred to in Article 325bi(1), point (e), of Regulation (EU) No 575/2013, the institution has established objective criteria that are appropriate for choosing the risk factors forming the subset of modellable risk factors referred to in Article 325bc(2), point (a), of that Regulation;

(g) in relation to the identification of the stress period, 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 325bc(2), point (c), of Regulation (EU) No 575/2013 and that the internal policies of the institution specify the frequency of update of the stress period for the calculation of the partial expected shortfall measures, and the other applicable criteria triggering its update.

For the purposes of point (e), competent authorities shall obtain an overview of the differences in the techniques employed by the institution when calculating the partial expected shortfall measures calibrated on the recent 12-month period and on the stress period, and verify whether those differences do not go beyond what is needed to achieve compliance with the requirements set out in Regulation (EU) No 575/2013.

For the purposes of point (g), competent authorities shall verify, also on the basis of past updates, whether the stress period is updated at least with a quarterly frequency and that the institution has followed any possible criteria specified in the internal policies.

(a) shall verify how the institution choses the estimator it uses and the analysis made to support such choice;

(b) verify whether the expected shortfall estimator corresponds either to the integral of the estimator for the Value-at-Risk numbers referred to in Article 325bf of Regulation (EU) No 575/2013 understood as a function of the tail probability from zero to one minus the relevant confidence level, and dividing by one minus the relevant confidence level, or to a more conservative choice;

(d) where the calculation of the expected shortfall risk measures is based on Monte Carlo simulations, verify whether the number of simulations ensures convergence towards stable results.

For the purposes of point (d), competent authorities shall review the tests performed by the institution to set the number of simulations, and the statistical tests ensuring that the randomness properties of the sequences used to generate the simulation are appropriate. Where the competent authority deems those tests insufficient, it may use the assessment method referred to in paragraph 4.

(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 expected shortfall risk measures with several different seeds, all other assumptions being equal;

(c) assess whether the differences in the expected shortfall risk measures with a different seed resulting from the calculation in accordance with point (b) are compatible with the statistical error referred to in point (a).

(d) where competent authorities deem the results referred to in point (c) incompatible, assess the root cause of such incompatibility, and assess the number of simulations needed to ensure that the statistical error is below 5 %.

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;

(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.

(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;

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).

(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;

(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.

(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;

(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;

(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;

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;

(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;

(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;

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;

(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:

(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;

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:

(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;