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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

Type Delegated Regulation

Publication 2024-06-17

State In force

Text As published

Department European Commission, FISMA

Source EUR-Lex

articles 55

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(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;

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

For the purposes of paragraph 1, point (g), competent authorities shall:

(a) require the institution to provide an overview of their time series used in

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and

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, as referred to in Article 325bb of Regulation (EU) No 575/2013, and in the calculation of the stress scenario risk measures, as referred to in Article 7 of Commission Delegated Regulation (EU) 2024/397, and to include in that overview for each time series used:

(i) the total number of days in the historical observation period used to calculate the

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and

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, as referred to in Article 325bb of Regulation (EU) No 575/2013, and the stress scenario risk measures, as referred to in Article 7 of Commission Delegated Regulation (EU) 2024/397;

(ii) the number of days with missing data in the time series before the institution introduces any adjustment;

(iii) the number of days without any daily change in the time series before the institution introduces any adjustment;

(iv) the maximum number of consecutive days without any daily change in the time series before the institution introduces any adjustment;

(v) the number of days for which data were initially available in the time series but that the institution excluded or changed before being used in the calculation of the

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and

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, as referred to in Article 325bb of Regulation (EU) No 575/2013, and the stress scenario risk measures, as referred to in in Article 7 of Commission Delegated Regulation (EU) 2024/397;

(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;

(c) based on the overview referred to in point (a), select a sample of time series that are characterised by a high number of data points initially missing, and apply the following steps in the following order:

(i) require the institution to provide the time series with the initial data points only, and the time series after they have been filled in;

(ii) verify that the time series have been filled in in accordance with the methodologies envisaged in the internal policies as referred to in paragraph 1, points (a) and (b), and that such methodologies are appropriate for the case at matter;

(d) based on the overview referred to in point (b), select a sample of time series characterised by a high number of data points that were initially available but have been substituted by other data points, and apply the following steps in the following order:

(i) require the institution to provide the time series with the initial data points only, and the time series after data points in the time series have been substituted;

(ii) verify that the data points have been replaced in accordance with the methodologies envisaged in the internal policies as referred to in paragraph 1, points (a) and (b), and that such methodologies are appropriate for the case at matter.

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;

(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.

For risk factors for which proxy data are used, competent authorities shall perform the assessment referred to in paragraph 2 on the proxy time series as used in the calculation of the

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and

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, as referred to in Article 325bb of Regulation (EU) No 575/2013, and on the stress scenario risk measures, as referred to in Article 7 of Commission Delegated Regulation (EU) 2024/397.

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

When verifying whether an institution complies with Article 325bi(1), point (e), of Regulation (EU) No 575/2013 in relation to requirements on the technical elements to be included in the actual and hypothetical changes in the portfolio’s value, competent authorities shall verify whether the internal policies referred to in that point:

(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;

(b) require the production of a periodic report, and, where the different elements contributing to the changes in the portfolio’s value are disentangled, daily figures, including:

(i) the changes related to elements that are removed from the end-of-day value to obtain the actual and hypothetical changes in accordance with Articles 1 to 4 of Delegated Regulation (EU) 2022/2059, including those relating to intraday trading activities;

(ii) the changes related to adjustments that are included in the end-of-day of value but that are not in the calculation of the actual and hypothetical changes in accordance with Articles 1 to 4 Delegated Regulation (EU) 2022/2059;

(iii) the changes related to adjustments that are included in the end-of-day of value and in the calculation of the actual and hypothetical changes in accordance with Articles 1 to 4 Delegated Regulation (EU) 2022/2059;

(iv) the changes related to adjustments resulting from the independent price verification process referred to in Article 1(1) and 2(1) of Delegated Regulation (EU) 2022/2059;

(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.

(a) in relation to the calculation of the actual changes in the trading desk portfolio’s value as referred to in Article 1(1) of Delegated Regulation (EU) 2022/2059:

(i) by using the reports referred to in paragraph 1, points (b) and (c) of this Article and the outline of the differences referred to in Article 5, point (a), of Delegated Regulation (EU) 2022/2059:

(1) identify the elements that differ between the changes in the end-of-day portfolio values produced by the end-of-day valuation process and the actual changes;

(2) verify whether the elements identified in accordance with point (1) are limited to fees and commissions as referred to in Article 325bf(4), point (b), of Regulation (EU) No 575/2013, and are limited to those adjustments that must or may be excluded from the actual changes, as laid down in Article 1(3) and (5) of Delegated Regulation (EU) 2022/2059;

(ii) by using the reports referred to in paragraph 1, points (b) and (c) of this Article, verify whether, the adjustments resulting from the independent price verification are included in the actual changes in the trading desk portfolio’s value, as required by Article 1(1) of Delegated Regulation (EU) 2022/2059;

(iii) verify whether the passage of time as referred to in Article 1(2) of Delegated Regulation (EU) 2022/2059 is reflected in the calculation of the actual changes, and whether that passage of time is reflected in the same way as in the calculation of the end-of-day portfolio values produced by the end-of-day valuation process;

(iv) assess how the institution evaluates whether an adjustment is market-risk related, as referred to in Article 1(3) of Delegated Regulation (EU) 2022/2059 and, by using the reports referred to in paragraph 1, points (b) and (c) of this Article, verify whether those adjustments that are not market-risk related are excluded from the calculation of the actual changes;

(v) by comparing the reports referred to in paragraph 1, points (b) and (c) of this Article at different dates, verify whether, the institution reflects changes in adjustments’ values only on the dates at which the adjustment is calculated, as required by Article 1(4) of Delegated Regulation (EU) 2022/2059;

(vi) verify whether the scope of positions on which the adjustment is calculated includes only positions assigned to the trading desk, as required by Article 1(4) of Delegated Regulation (EU) 2022/2059;

(vii) verify whether the adjustments that may be excluded from the actual changes pursuant to Article 1(5) of Delegated Regulation (EU) 2022/2059 are non-additive;

(viii) verify whether the information referred to in Article 5(c) of Delegated Regulation (EU) 2022/2059 is consistent with the evidence resulting from the reports referred to in paragraph 1, points (b) and (c) of this Article;

(b) in relation to the calculation of the actual changes in the portfolio’s value as referred to in Article 2 of Delegated Regulation (EU) 2022/2059:

(i) by using the reports referred to in paragraph 1, points (b) and (c), of this Article and the outline of the differences referred to in Article 5(a) of Delegated Regulation (EU) 2022/2059:

(1) identify the elements that differ between the changes in the end-of-day portfolio values produced by the end-of-day valuation process and the actual changes;

(2) verify whether the elements referred to in point (1) are limited to fees and commissions as referred to in Article 325bf(4), point (b), of Regulation (EU) No 575/2013, and to those adjustments that must or may be excluded from the actual changes pursuant to Article 2 of Delegated Regulation (EU) 2022/2059;

(ii) by using the reports referred to in paragraph 1, points (b) and (c) of this Article, verify whether the adjustments resulting from the independent price verification are included in the actual changes in the portfolio’s value, as required by Article 2(1) of Delegated Regulation (EU) 2022/2059;

(iii) verify whether the passage of time referred to in Article 2(2) of Delegated Regulation (EU) 2022/2059 is reflected in the calculation of the actual changes, and whether that passage of time is reflected in the same way as in the calculation of the end-of-day portfolio values produced by the end-of-day valuation process;

(iv) assess how the institution evaluates whether an adjustment is market-risk related as referred to in Article 2(3) of Delegated Regulation (EU) 2022/2059 and, by using the reports referred to in paragraph 1, points (b) and (c) of this Article, verify whether those that are not market-risk related are excluded from the calculation of the actual changes;

(v) verify whether, as required by Article 2(4) of Delegated Regulation (EU) 2022/2059, the scope of positions on which an adjustment is calculated is either made of:

(1) positions assigned to trading desks for which the institution calculates its own funds requirements for market risk in accordance with Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013;

(2) all positions subject to own funds requirements for market risk;

(vi) by comparing the reports referred to in paragraph 1, points (b) and (c) of this Article at different dates, verify whether, the institution reflects changes in adjustments’ values only on the dates at which the adjustment is recomputed in accordance with Article 2(5) of Delegated Regulation (EU) 2022/2059;

(vii) verify whether the information referred to in Article 5, point (c), of Delegated Regulation (EU) 2022/2059 is consistent with the evidence resulting from the reports referred to in paragraph 1, point (b) and (c) of this Article;

(c) in relation to the calculation of the hypothetical changes in the trading desk portfolio’s value as referred to in Article 3 of Delegated Regulation (EU) 2022/2059:

(i) identify, by using the reports referred to in paragraph 1, point (b) and (c) of this Article, the elements that differ between the changes in the end-of-day portfolio values produced by the end-of-day valuation process and the hypothetical changes, and verify whether those elements are limited to:

(1) fees and commissions;

(2) those elements that are not captured due to the assumption that positions are unchanged as referred to in Article 325bf(4), point (a), of Regulation (EU) No 575/2013;

(3) those adjustments that must or may be excluded from the hypothetical changes as laid down in Article 3(3) and (5) of Delegated Regulation (EU) 2022/2059;

(ii) verify whether the effect of the passage of time is reflected in the hypothetical changes consistently with the treatment the institution applies for such effect in the calculation of the expected shortfall risk measure as referred to in Article 325bb of Regulation (EU) No 575/2013 and in the calculation of the stress scenario risk measure referred to in Article 325bk of that Regulation, as required by Article 3(2) of Delegated Regulation (EU) 2022/2059;

(iii) assess how the institution evaluates whether an adjustment is market-risk related as referred to in Article 3(3) of Delegated Regulation (EU) 2022/2059 and, by using the reports referred to in paragraph 1, point (b) and (c) of this Article, verify whether those adjustments that are not market-risk related are excluded from the calculation of the hypothetical changes;

(iv) by using the reports referred to in paragraph 1, point (b) and (c) of this Article, verify that only adjustments that are calculated daily and that are included in the institution’s risk measurement model are included as part of the hypothetical changes, as required by Article 3(3) of Delegated Regulation (EU) 2022/2059;

(v) verify that the scope of positions on which the adjustment is calculated includes only positions assigned to the trading desk, as required by Article 3(4) of Delegated Regulation (EU) 2022/2059;

(vi) verify whether the adjustments that are excluded from the hypothetical changes pursuant to Article 3(5) of Delegated Regulation (EU) 2022/2059 are non-additive;

(vii) by using the outline referred to in Article 5, point (c)(viii) of Delegated Regulation (EU) 2022/2059, verify whether the methodology used by the institution to calculate changes in the value of an adjustment assuming that positions are unchanged as referred to in Article 325bf(4), point (a), of Regulation (EU) No 575/2013 is appropriate;

(viii) verify whether the information referred to in Article 5, point (c), of Delegated Regulation (EU) 2022/2059 is consistent with the evidence resulting from the reports referred to in paragraph 1, point (b) and (c) of this Article;

(d) in relation to the calculation of the hypothetical changes in the portfolio’s value as referred to in Article 4 of Delegated Regulation (EU) 2022/2059:

(i) by using the reports referred to in paragraph 1, point (b) and (c) of this Article:

(1) identify the elements that differ between the changes in the end-of-day portfolio values produced by the end-of-day valuation process and the hypothetical changes;

(2) verify whether the elements referred to in point (1) are limited to fees and commission, to those elements that are not captured due to the assumption that positions are unchanged as referred to in Article 325bf(4), point (a), of Regulation (EU) No 575/2013, and to those adjustments that must or may be excluded from the hypothetical changes in accordance with Article 4 of Delegated Regulation (EU) 2022/2059;

(ii) verify whether, the effect of the passage of time is reflected in the hypothetical changes consistently with the treatment the institution applies for such effect in the calculation of the expected shortfall risk measure as referred to in Article 325bb of Regulation (EU) No 575/2013 and in the calculation of the stress scenario risk measure referred to in Article 325bk of that Regulation, as required by Article 4(2) of Delegated Regulation (EU) 2022/2059;

(iii) assess how the institution evaluates whether an adjustment is market-risk related as referred to in Article 4(3) of Delegated Regulation (EU) 2022/2059 and, by using the reports referred to in paragraph 1, point (b) and (c) of this Article, verify that those that are not market-risk related are excluded from the calculation of the hypothetical changes;

(iv) by using the reports referred to in paragraph 1, point (b) and (c) of this Article, verify that, only adjustments that are calculated daily and that are included in the institution’s risk measurement model are included as part of the hypothetical changes, as required by Article 4(3) of Delegated Regulation (EU) 2022/2059;

(v) verify whether, as required by Article 4(4) of Delegated Regulation (EU) 2022/2059, the scope of positions on which an adjustment is calculated is either made of:

(1) positions assigned to trading desks for which the institution calculates its own funds requirements for market risk in accordance with Part Three, Title IV, Chapter 1b of Regulation (EU) No 575/2013;

(2) all positions subject to own funds requirements for market risk;

(vi) by using the outline referred to in Article 5, point (c)(viii), of Delegated Regulation (EU) 2022/2059, verify whether the methodology used by the institution to calculate changes in the value of an adjustment assuming that positions are unchanged as referred to in Article 325bf(4), point (a), of Regulation (EU) No 575/2013 is appropriate;

(vii) verify whether the information referred to in Article 5(c) of Delegated Regulation (EU) 2022/2059 is consistent with the evidence resulting from the reports referred to in paragraph 1, point (b) and (c) of this Article;

(e) in relation to the processes followed by the institution to calculate actual and hypothetical changes:

(i) verify whether the process to map a position to one trading desk only is robust;

(ii) verify whether the rectification processes referred to in paragraph 1, point (d) are robust, and whether they are followed in practice whenever contingencies, exceptions, errors, and pricing failures occur;

(iii) verify how illiquid positions are treated in the end-of-day valuation process and in the independent price verification process.

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.

For the purposes of paragraph 2, points (a) to (d), competent authorities may apply any of the following assessment methods:

(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

Competent authorities shall verify whether an institution analyses all overshootings referred to in Article 325bf of Regulation (EU) No 575/2013 in detail, in order to determine their causes.

For the purposes of paragraph 1, competent authorities shall verify whether the institution:

(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;

(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.

Competent authorities shall verify whether, where the analysis referred to in paragraphs 1 and 2 identifies a material weakness or inaccuracy in the model or processes, the institution assesses that weakness or inaccuracy and promptly develops a plan for a timely return to compliance with the backtesting requirements to be assessed as part of the regular validation of the model.

Competent authorities shall verify whether the institution ensures both of the following:

(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

When assessing whether an institution’s internal model is implemented with integrity as required by Article 325bi(1) of Regulation (EU) No 575/2013 in relation to requirements on the technical elements to be included in the hypothetical changes in the trading desk portfolio’s value for the profit and loss attribution requirements referred to in Article 325bg of that Regulation, competent authorities shall verify whether, the time series of hypothetical changes in the trading desk portfolio’s value as used for the purpose of the back-testing requirements coincides with the time series of hypothetical changes in the trading desk portfolio’s value as used for the profit and loss attribution requirement, as required by Article 13 of Delegated Regulation (EU) 2022/2059.

When assessing an institution’s compliance with Article 325bi(1), point (e), of Regulation (EU) No 575/2013 in relation to requirements on the technical elements to be included in the theoretical changes in the portfolio’s value for the purpose of the profit and loss attribution requirements referred to in Article 325bg of that Regulation, competent authorities shall verify that the internal policies referred to in that point (e):

(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.

When assessing whether an institution’s internal model is implemented with integrity as required by Article 325bi(1) of Regulation (EU) No 575/2013 in relation to the profit and loss attribution requirements referred to in Article 325bg of that Regulation, competent authorities shall:

(a) in relation to the calculation of the theoretical changes in the portfolio’s value:

(i) verify whether the business days used in the calculation of the theoretical changes in the portfolio’s value are the same as 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;

(ii) verify whether the positions used in the calculation of the hypothetical changes are those used for calculating the theoretical changes.

(iii) verify whether when the institution calculates the theoretical changes, positions are assumed to be unchanged, as required by Article 12(1) of Delegated Regulation (EU) 2022/2059;

(iv) verify that there are no differences between the pricing methods, model parametrisations, market data and any other technique used in the internal risk-measurement model, and those used for calculating the theoretical changes, as required by Article 12(2) of Delegated Regulation (EU) 2022/2059;

(v) verify that, theoretical changes in the portfolio’s value reflect only changes in the values of risk factors that are shocked 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, as required by Article 12(3) of Delegated Regulation (EU) 2022/2059;

(vi) verify that the rectification processes referred to in paragraph 2, point (e) are robust and are followed in practice whenever contingencies, exceptions, errors, and pricing failures occur;

(b) in relation to the profit and loss attribution results:

(i) verify whether the Spearman correlation coefficient and the Kolmogorov-Smirnov test metric are calculated correctly;

(ii) verify whether the risk factors for which the institution uses input data used in calculating the hypothetical changes to calculate the theoretical changes, as allowed by Article 14(1) of Delegated Regulation (EU) 2022/2059, are only those for which the conditions referred to in that Article are met;

(iii) verify that risk factors, whose values employed in calculating the hypothetical changes are used by the institution to calculate the theoretical changes in accordance with Article 14(2) of Delegated Regulation (EU) 2022/2059, are only those for which the conditions referred to in that Article are met.

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.

For the purposes of paragraph 3, point (a)(iii), competent authorities shall use one or more of the following assessment methods:

(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.

For the purposes of paragraph 3, point (a)(v), competent authorities may:

(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.

For the purposes of paragraph 3, point (b)(i), competent authorities shall, for the most material trading desks or all trading desks:

(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.

For the purposes of paragraph 3, point (b)(ii), competent authorities shall:

(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.

For the purposes of paragraph 3, point (b)(iii), competent authorities shall:

(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

When assessing an institution’s compliance with Article 325bi(1), point (e), of Regulation (EU) No 575/2013 in relation to requirements on the calculation of own funds requirements for market risk for positions in the non-trading book, competent authorities shall verify whether the internal policies referred to in that Article specify:

(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;

(i) whether the value that is used as a basis to calculate the own funds requirements for foreign exchange risk is the last available accounting value referred to in Article 3(1) of Delegated Regulation (EU) 2023/1577, or the last available fair value referred to in Article 3(2) of that Delegated Regulation, and the frequency at which such value is recalculated;

(ii) whether there are trading desks whose non-linear positions in the exchange rate are subject to the treatment referred to in Article 3(4) and Article 5(1), second subparagraph, of Delegated Regulation (EU) 2023/1577 and, where applicable, the reason for using such derogation for some trading desks, while not for some others;

(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.

When assessing whether an institution’s internal model is implemented with integrity as required by Article 325bi(1), of Regulation (EU) No 575/2013 in relation to requirements on the calculation of own funds requirements for market risk for positions in the non-trading book, competent authorities shall:

(a) verify whether the internal processes referred to in Article 325bi(1), point (e), of Regulation (EU) No 575/2013 ensure:

(i) the traceability of non-trading book positions incorporated in the scope of the alternative internal model approach, and the correctness of the accounting values or fair values used as a basis to calculate the own funds requirements for market risk, as required by Articles 3 and 4 of Delegated Regulation (EU) 2023/1577;

(ii) that non-trading book positions attracting foreign exchange risk or commodity risk booked on a given date are included in the calculation of 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;

(iii) that any foreign exchange risk positions stemming from a change in the reporting currency at the different levels of consolidation (‘translation risk’) are included in the scope of positions subject to foreign exchange risk;

(iv) a correct identification of foreign-exchange positions meeting the conditions for using the treatment referred to in Article 3(4) and Article 5(1), second subparagraph, of Delegated Regulation (EU) 2023/1577, where the institution uses that treatment;

(v) a correct and complete identification of items meeting the conditions set out in Article 3(6) of Delegated Regulation (EU) 2023/1577;

(b) in relation to the calculation of own funds requirements for positions that are subject to foreign exchange risk as referred to in Article 3 of Delegated Regulation (EU) 2023/1577, verify whether:

(i) foreign exchange positions for which the institution uses the derogation laid down in Article 3(4) and Article 5(1), second subparagraph, of Delegated Regulation (EU) 2023/1577 are distinguished from foreign exchange positions for which the institution does not use that derogation;

(ii) only foreign-exchange risk factors of the last available accounting value or fair value are updated to determine the value of the position before the application of the scenario of future shock, unless the treatment referred to in Article 3(4) of that Regulation is used, as required by Article 3(3) of Delegated Regulation (EU) 2023/1577;

(iii) for positions for which the treatment in Article 5(1), second subparagraph of that Regulation is used, all risk factors are updated to determine the value of the position before the application of the scenario of future shock, as required by Article 3(4) of Delegated Regulation (EU) 2023/1577;

(c) in relation to items meeting the conditions referred to in Article 3(6) of Delegated Regulation (EU) 2023/1577, verify whether:

(i) the criteria established by the institution to identify events triggering an impairment are appropriate, based on historical data and historical events;

(ii) the criteria referred to in point (i) are consistent with the internal risk-management of impairment risk;

(iii) the level of impairment recognised following the events referred to in point (i) is based on objective reasoning;

(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.

For the purposes of paragraph 2, point (a)(ii), competent authorities may apply one of the two following approaches:

(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.

For the purposes of paragraph 2, point (a)(iii), competent authorities may require the institution to provide types of positions that are included in the model and that stem from assets and liabilities that do not attract market risk when the own funds requirements are calculated at the individual level, but attract it when the own funds requirements are calculated at the consolidated level because of translation risk.

For the purposes of paragraph 2, point (a)(v), competent authorities may require the institution to reconcile the items that the institution identified as meeting the conditions referred to in Article 3(6) of Delegated Regulation (EU) 2023/1577 for calculating the own funds requirements with the alternative internal model approach, with the items meeting those conditions in accordance with the applicable accounting framework.

For the purposes paragraph 2, point (b), competent authorities may, on a sample of non-trading book positions and for a reference date for the calculation of the expected shortfall risk measure as referred to in Article 325bb of Regulation (EU) No 575/2013 and the stress scenario risk measure as referred to in Article 325bk of that Regulation, apply the following assessment method:

(a) require the institution to provide the list of:

(i) risk factors used as inputs to determine the fair value constituting the basis for the calculation of the own funds requirements as required by Article 3 of Delegated Regulation (EU) 2023/1577;

(ii) out of the risk factors included in the list referred in point (i), those risk factors on which the institution applies scenarios of future shocks 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) require the institution to provide the value of the risk factors referred to in point (a) at the following dates:

(i) the date at which the last available fair value was determined;

(ii) the given reference date for the calculation of the expected shortfall risk measure or the stress scenario risk measure;

(i) for positions for which the treatment set out in Article 3(4) of Delegated Regulation (EU) 2023/1577 is not used, the value of risk factors not reflecting foreign exchange risk has not been updated between the two dates referred to in points (b)(i) and (b)(ii);

(ii) for positions for which the treatment set out in Article 3(4) of Delegated Regulation (EU) 2023/1577 is used, the value of all risk factors is updated between the two dates referred to in points (b)(i) and (b)(ii);

(iii) the risk factors referred to in point (a)(ii) relate only to foreign exchange risk, regardless of whether the treatment set out in Article 3(4) of Delegated Regulation (EU) 2023/1577 is used.

For the purposes of paragraph 2, point (b), competent authorities may, on a sample of non-trading book positions and for a reference date for the calculation of the expected shortfall risk measure as referred to in Article 325bb of Regulation (EU) No 575/2013 and the stress scenario risk measure as referred to in Article 325bk of that Regulation, apply the following assessment method:

(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;

(c) obtain the value of the foreign exchange risk factors and of other inputs used to determine the accounting value at the following dates:

(i) the date at which the last available accounting value was determined;

(ii) the given reference date for the calculation of the expected shortfall risk measure and the stress scenario risk measure;

(d) verify whether:

(i) for positions for which the treatment set out in Article 3(4) of Delegated Regulation (EU) 2023/1577 is not used, the valuation inputs not reflecting foreign exchange risk have not been updated between the two dates referred to in points (c)(i) and (c)(ii);

(ii) for positions for which the treatment set out in Article 3(4) Delegated Regulation (EU) 2023/1577 is used, the valuation inputs, including foreign exchange risk factors, have been updated between the two dates referred to in points (c)(i) and (c)(ii);

(iii) the risk factors referred to in point (b) relates only to foreign exchange risk, regardless of whether the treatment set out in Article 3(4) of Delegated Regulation (EU) 2023/1577 is used.

For the purposes of paragraph 2, point (d), competent authorities may, on a sample of non-trading book positions and for a reference date for 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, apply the following assessment method:

(a) require the institution to provide the list of:

(i) risk factors used as inputs to determine the fair value constituting the basis for the calculation of the own funds’ requirements as required by Article 4 of Delegated Regulation (EU) 2023/1577;

(ii) out of the risk factors included in the list referred to in point (a), those risk factors on which the institution applies scenario of future shock when calculating the expected shortfall risk measure referred to in Article 325bb of Regulation (EU) No 575/2013 or extreme scenario of future shock when calculating 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.

For the purposes of paragraph 2, point (e), competent authorities may, on a sample of non-trading book positions, apply the following assessment method:

(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

When assessing an institution’s compliance with Article 325bh(1), point (b), of Regulation (EU) No 575/2013 in relation to requirements on the effectiveness and capability of the internal-risk measurement model to capture non-linearities of options and other products for an institution using a sensitivity-based approach, competent authorities shall verify whether:

(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.

For the purposes of paragraph 1, competent authorities may apply the following steps in the following order:

(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

When assessing whether an institution’s internal model is implemented with integrity as required by Article 325bi(1) of Regulation (EU) No 575/2013 in relation to the calculation of the unconstrained expected shortfall measures and of the partial expected shortfall measures for all broad categories of risk factors at a reduced frequency as referred to in Article 325bb(4) of Regulation (EU) No 575/2013, competent authorities shall:

(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.

For the purposes of paragraph 1, point (b), competent authorities shall:

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

(b) verify whether the evolution of the daily figures for UES t,

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and

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calculated on all portfolio’s positions as required by Article 325bb(1) of Regulation (EU) No 575/2013, does not systematically show a lower risk profile in the day chosen by the institution.

For the purposes of paragraph 2, point (b), competent authorities may, where there are hints of a systematically lower risk profile, complement their assessment by:

(a) requiring the institution to calculate daily and for a given period the unconstrained expected shortfall measures

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and the partial expected shortfall measures

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and

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for each broad risk factor categories;

(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;

(b) verify whether, when calculating partial expected shortfall measures

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and

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as required by Article 325bc(1) of Regulation (EU) No 575/2013, the institution identifies effective liquidity horizons of the risk factors of a given position, taking into account the maturity of the position in accordance with Article 325bd(4) of that Regulation;

(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;

(d) verify whether risk factors that are not part of the subset of modellable risk factors chosen by the institution in accordance with Article 325bc(2), point (a), of Regulation (EU) No 575/2013 are kept constant when computing

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and

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;

(e) verify whether the techniques used to calculate

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and those used to calculate

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are the same, except for those deviations necessary to ensure the fulfilment of requirements set out in Article 325bc(2) to (4) of Regulation (EU) No 575/2013;

(f) verify whether, when calculating the

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, the institution uses equally weighted data in the observation period;

(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.

For the purposes of paragraph 1, point (a), competent authorities:

(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;

(c) may compare the Value-at-Risk and expected-shortfall estimators used by the institution against the estimators included in Table 1.

Table 1

Value-at-risk estimators	Expected shortfall estimators
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Image omitted; see official source	Image omitted; see official source
Where: Image omitted; see official source denotes the i-th lowest value in the sample Image omitted; see official source used for the estimation, i.e. Image omitted; see official source is the most severe loss in a profit-and-loss sample and typically a large negative number; N denotes the number of values in the sample Image omitted; see official source used for the estimation; α denotes the tail probability, i.e. one minus the confidence level; Image omitted; see official source denotes the integer part of an argument; Image omitted; see official sourceand for the expected shortfall assuming Image omitted; see official source, i.e. computing for a left tail of a sample; Image omitted; see official source Image omitted; see official sourceand for the expected shortfall assuming that Image omitted; see official source, i.e. more than one loss is in the α-tail of a profit-and-loss sample; Image omitted; see official source.	Where: Image omitted; see official source denotes the i-th lowest value in the sample Image omitted; see official source used for the estimation, i.e. Image omitted; see official source is the most severe loss in a profit-and-loss sample and typically a large negative number; N denotes the number of values in the sample Image omitted; see official source used for the estimation; α denotes the tail probability, i.e. one minus the confidence level; Image omitted; see official source denotes the integer part of an argument; Image omitted; see official sourceand for the expected shortfall assuming Image omitted; see official source, i.e. computing for a left tail of a sample; Image omitted; see official source Image omitted; see official sourceand for the expected shortfall assuming that Image omitted; see official source, i.e. more than one loss is in the α-tail of a profit-and-loss sample; Image omitted; see official source.

(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.

For the purposes of paragraph 1, point (b), competent authorities shall:

(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 paragraph 1, point (c), competent authorities shall:

(a) obtain an overview of the risk factors chosen by the institution and verify:

(i) whether the criteria ensure a sufficient level of coverage in the modellable risk factors’ types chosen compared to the full set of modellable risk factors to which the institution is exposed;

(ii) whether the criteria are such that the threshold referred to in 325bc(2), point (a), of Regulation (EU) No 575/2013 is expected to be exceeded over time;

(iii) whether the institution tests alternative subsets of modellable risk factors to ensure that its choice does not underestimate the own funds requirements;

(iv) whether the institution, in its choice, favours the selection of risk factors for which data in the stress period exist over risk factors for which proxies are used, and where that is not the case, competent authorities shall assess the reason why the institution did not implement such a criterion, and whether a different choice would improve the quality of the unconstrained and partial expected shortfall measure.

(b) verify whether, where the position has a maturity of less than 10 days, the effective liquidity horizon of all risk factors is set to 10 days, and that such position does not impact the calculation of

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for

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;

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, verify whether:

(i) all risk factors of that position with a liquidity horizon

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