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Document 32024R0397
Commission Delegated Regulation (EU) 2024/397 of 20 October 2023 supplementing Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to regulatory technical standards on the calculation of the stress scenario risk measure
Commission Delegated Regulation (EU) 2024/397 of 20 October 2023 supplementing Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to regulatory technical standards on the calculation of the stress scenario risk measure
Commission Delegated Regulation (EU) 2024/397 of 20 October 2023 supplementing Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to regulatory technical standards on the calculation of the stress scenario risk measure
C/2023/6749
OJ L, 2024/397, 29.01.2024, ELI: http://data.europa.eu/eli/reg_del/2024/397/oj (BG, ES, CS, DA, DE, ET, EL, EN, FR, GA, HR, IT, LV, LT, HU, MT, NL, PL, PT, RO, SK, SL, FI, SV)
In force
Official Journal 
EN Series L 
2024/397 
29.1.2024 
COMMISSION DELEGATED REGULATION (EU) 2024/397
of 20 October 2023
supplementing Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to regulatory technical standards on the calculation of the stress scenario risk measure
(Text with EEA relevance)
THE EUROPEAN COMMISSION,
Having regard to the Treaty on the Functioning of the European Union,
Having regard to Regulation (EU) No 575/2013 of the European Parliament and of the Council of 26 June 2013 on prudential requirements for credit institutions and amending Regulation (EU) No 648/2012 (1), and in particular Article 325bk(3), fourth subparagraph, thereof,
Whereas:
(1) 
To ensure a level playing field among institutions in the Union and to minimise regulatory arbitrage, the methodologies for developing extreme scenarios of future shock for nonmodellable risk factors should be based on the international standards agreed in January 2019 by the Basel Committee on Banking Supervision (BCBS) (Basel framework), and should take into account the materiality of the own funds requirements for nonmodellable risk factors. Therefore, specific and detailed methodologies for developing extreme scenarios of future shock for nonmodellable risk factors should be laid down. 
(2) 
The quality of data and the number of observations that are available to determine future shocks for nonmodellable risk factors may vary significantly from one nonmodellable risk factor to another. It is therefore necessary to ensure that extreme scenarios of future shock cover a wide range of cases. For that reason, it is necessary to provide for alternative sets of methodologies that institutions may use depending on the quality and the number of observations that are available for each nonmodellable risk factor. Furthermore, institutions should reflect in their calculations the fact that fewer available data leads to a higher uncertainty of the estimates or values used to determine the extreme scenarios of future shock and should therefore become more conservative. 
(3) 
Given its accuracy, one method to determine the extreme scenario of future shock for a nonmodellable risk factor should consist of directly calculating the expected shortfall measure of the losses that would occur when applying a shock to that nonmodellable risk factor with the historically observed levels during the relevant stress period. However, such method would provide reliable results only where the institution has a significant amount of data for that stress period, and would require many loss calculations per risk factor leading to a high computational effort. It is therefore necessary to provide for an alternative method that requires a significant lower number of loss calculations and applies a stepwise approach. Under that alternative method, institutions should first calculate an expected shortfall measure on the returns observed for a nonmodellable risk factor, and then calculate the loss that corresponds to the movement in the risk factor identified by that expected shortfall measure. Such stepwise approach should also address the specific case where the number of observations for a nonmodellable risk factor in the stress period concerned is insufficient to obtain accurate and prudent estimates. Since that situation can be expected to occur only in a limited number of cases, those cases should be addressed by leveraging on methodologies that institutions have implemented for other nonmodellable risk factors for which they have more observations or, where possible, on the alternative standardised approach. 
(4) 
The Basel framework requires that the market risk own funds requirements for nonmodellable risk factors have to be calibrated to a period of stress that is the same for all nonmodellable risk factors that belong to the same broad category of risk factors. To determine extreme scenarios of future shock on the basis of data observed during that identified period, institutions should collect data for nonmodellable risk factors for that identified stress period. 
(5) 
To ensure harmonisation of the calculation of the stress scenario risk measures across institutions in the Union, it is necessary to specify how institutions should identify the stress period. Those specifications should be proportionate to the purpose, and should neither require an excessive computational effort, nor the implementation of specific pricing methods. The global financial crisis of 2007–2008 has been a major stress event for the financial system. The stress period to be identified should therefore start at least from 1 January 2007. To ensure that the stress period remains relevant to an institution’s trading portfolio, institutions should periodically review that stress period. However, to limit the administrative burden on institutions, it should be only required that the frequency of such review follows at least the same quarterly frequency as the corresponding supervisory reporting. 
(6) 
The Basel framework requires that institutions determine extreme scenarios of future shock by using the pricing methods of their risk measurement model, as those methods are used in the context of the backtesting and the profit and loss attribution test. There may be scenarios of future shock for which those pricing methods cannot determine the corresponding loss for some financial instruments or commodities. Where that is the case, institutions should act in a prudentially sound manner and target only those instruments that are affected by the pricing failure. The methodologies implemented by the institution to address those cases are not to affect in any way the results of the backtesting and the profit and loss attribution requirements laid down in Commission Delegated Regulation (EU) 2022/2059 (2). 
(7) 
Article 325bk(3), second subparagraph, of Regulation (EU) No 575/2013 requires that the level of own funds requirements for market risk for a nonmodellable risk factor is to be as high as the expected shortfall measure for that risk factor referred in Article 325bb of that Regulation, i.e. an expected shortfall of losses at a 97,5 % confidence level over a period of stress. The statistical estimators and the parameters for determining that expected shortfall measure should therefore be set in such a way that that confidence level is met. 
(8) 
According to the Basel framework, the regulatory extreme scenario of future shock should be the one leading to the maximum loss that may occur due to a change in the nonmodellable risk factor. It should therefore be specified what institutions should consider as maximum loss in cases where the maximum loss is not finite. 
(9) 
To ensure consistency with the Basel framework, institutions should be able to determine the stress scenario risk measure for more than one nonmodellable risk factors where those nonmodellable risk factors are part of a curve or a surface, and where those risk factors belong to the same nonmodellable bucket among those set out in Commission Delegated Regulation (EU) 2022/2060 (3), and provided that institutions have assessed their modellability in accordance with the standardised bucketing approach referred to in that Delegated Regulation. Institutions should therefore be allowed to compute a single stress scenario risk measure for more than one nonmodellable risk factor under those conditions only. 
(10) 
To ensure the adequacy of the own funds requirements for nonmodellable risk factors with the risk profile of institutions, institutions should reflect in the aggregation of the stress scenario risk measures those risks that were not yet captured when determining the extreme scenario of future shock, including the liquidity horizons of the nonmodellable risk factors. To ensure a level playing field, the stress scenario risk measures should be aggregated by applying the aggregation formula agreed in the Basel framework. 
(11) 
This Regulation is based on the draft regulatory technical standards submitted to the Commission by the European Banking Authority. 
(12) 
The European Banking Authority has conducted open public consultations on the draft regulatory technical standards on which this Regulation is based, analysed the potential related costs and benefits, and requested the advice of the Banking Stakeholder Group established in accordance with Article 37 of Regulation (EU) No 1093/2010 of the European Parliament and of the Council (4), 
HAS ADOPTED THIS REGULATION:
CHAPTER 1
DEVELOPMENT AND APPLICATION OF THE EXTREME SCENARIOS OF FUTURE SHOCK
Article 1
Development of extreme scenarios of future shock and their application at risk factor level
Institutions shall develop the extreme scenarios of future shock for nonmodellable risk factors by applying either of the following methods:
(a) 
the direct method set out in Article 2, provided that all of the following conditions are met:

(b) 
the stepwise method set out in Article 3. 
Article 2
Direct method – nonmodellable risk factors
1. Under the direct method, institutions shall apply the following steps in the following order:
(a) 
they shall determine a time series of losses as follows:

(b) 
they shall calculate the estimate of the righttail expected shortfall in accordance with Article 11(2) for the time series of losses obtained in accordance with point (a). 2. At the end of the process set out in the first paragraph, a shock leading to the loss equal to the estimate referred to in paragraph 1, point (b), shall constitute the extreme scenario of future shock for the nonmodellable risk factor. 
Article 3
Stepwise method – nonmodellable risk factors
1. Under the stepwise method, institutions shall apply the following steps in the following order:
(a) 
they shall, in accordance with Article 7, determine the time series of 10 business days returns for the nonmodellable risk factor for the stress period determined in accordance with Article 12; 
(b) 
they shall determine an upward and a downward calibrated shock from the time series of 10 business days returns referred to in point (a) in accordance with:

(c) 
for each shock included in the following grid, institutions shall calculate the loss that occurs when that shock is applied to the nonmodellable risk factor:
where:

2. The shock which leads to the highest loss, among the shocks included in the grid referred to in paragraph 1, point (c), shall constitute the extreme scenario of future shock for the nonmodellable risk factor.
Article 4
Development and application of the extreme scenarios of future shock at standardised bucket level
Where institutions calculate a stress scenario risk measure for more than one nonmodellable risk factor, they shall determine the extreme scenario of future shock for the nonmodellable standardised bucket to which those risk factors belong in accordance with Delegated Regulation (EU) 2022/2060 by applying either of the following methods:
(a) 
the direct method set out in Article 5, provided that all of the following conditions are met:

(b) 
the stepwise method set out in Article 6. 
Article 5
Direct method – nonmodellable standardised buckets
1. When applying the direct method to nonmodellable risk factors belonging to nonmodellable standardised buckets, institutions shall apply the following steps in the following order:
(a) 
they shall determine a time series of losses as follows:

(b) 
they shall calculate the estimate of the righttail expected shortfall in accordance with Article 11(2) for the time series of the losses obtained in accordance with point (a) of this paragraph. 
2. The scenario of shocks leading to a loss equal to the estimate of the righttail expected shortfall obtained in accordance with paragraph 1, point (b), shall constitute the extreme scenario of future shock for the nonmodellable bucket.
Article 6
Stepwise method – nonmodellable standardised buckets
1. When applying the stepwise method to nonmodellable risk factors belonging to nonmodellable standardised buckets, institutions shall determine the extreme scenario of future shock by applying the following steps in the following order:
(a) 
for each nonmodellable risk factor within the nonmodellable standardised bucket they shall, in accordance with Article 7, determine the time series of 10 business days returns for the stress period determined in accordance with Article 12; 
(b) 
for each nonmodellable risk factor within the nonmodellable standardised bucket, they shall determine an upward and a downward calibrated shock from the corresponding time series of 10 business days returns referred to in point (a) in accordance with:

(c) 
they shall calculate both of the following:

For the purposes of point (c), institutions shall multiply the upward and downward calibrated shocks by the parameter β in two cases, with β = 1 and β = ⅘.
2. The scenario of shocks leading to the highest loss among those calculated in accordance with paragraph 1, point (c), shall constitute the extreme scenario of future shock for the nonmodellable standardised bucket.
Article 7
Determination of the time series of 10 business days returns
1. Institutions shall determine the time series of 10 business days returns for the stress period in relation to a given nonmodellable risk factor by applying the following steps in the following order:
(a) 
they shall determine the time series of observations for the nonmodellable risk factor for the stress period and include in that time series only one observation per business day that shall represent actual market data; 
(b) 
they shall extend the time series referred to in point (a) by including the observations available within the period of 20 business days following the stress period; where the reference date for the calculation of the stress scenario risk measure is less than 20 business days after the end of the stress period, institutions shall include those observations that are available from the end of the stress period to the reference date; 
(c) 
in relation to each date D
t
, for which there is an observation in the time series resulting from point (a) excluding the last observation, institutions shall determine, among the dates with an observation in the extended time series referred to in point (b), the date following D t that minimises the following value:
where:

(d) 
for each date D
t
, for which there is an observation in the time series resulting from point (a) excluding the last observation, they shall determine the corresponding 10 business days return by determining the return for the nonmodellable risk factor over the period between the date D
t
of the observation and the date minimising the value v in accordance with point (c), and subsequently rescaling it to obtain a return over a 10 business days period by multiplying the return with . 
shall be the date among those minimising that value that occurred later in time.
2. The time series referred to in paragraph 1, point (a), shall at least include the observations that were used for calibrating the scenarios of future shocks referred to in Article 325bc of Regulation (EU) No 575/2013, where that risk factor was previously assessed to be modellable in accordance with Article 325be of that Regulation.
Article 8
Downward and upward calibrated shock with the historical method
1. Under the historical method, institutions shall determine the downward calibrated shock from a time series of 10 business days returns for a nonmodellable risk factor in accordance with the following formula:
where:
— 
Ret denotes the time series of 10 business days returns of the nonmodellable risk factor; 
— 
is the estimate of the lefttail expected shortfall for the time series Ret calculated in accordance with Article 11(1); 
— 
N is the number of returns in the time series Ret. 
2. Institutions shall determine the upward calibrated shock from a time series of 10 business days returns for a nonmodellable risk factor with the historical method in accordance with the following formula:
where:
— 
Ret denotes the time series of 10 business days returns of the nonmodellable risk factor; 
— 
is the estimate of the righttail expected shortfall for the time series Ret calculated in accordance with Article 11(2); 
— 
N is the number of returns in the time series Ret. 
Article 9
Downward and upward calibrated shock with the asymmetrical sigma method
Under the asymmetrical sigma method, institutions shall determine the downward and upward calibrated shock from a time series of 10 business days returns for a nonmodellable risk factor by applying the following steps in the following order:
(a) 
they shall determine the median of the returns within the time series, and split the 10 business days returns comprised in that time series into the following two subsets:

(b) 
for each subset referred in point (a), they shall compute the mean of the 10 business days returns in the subset; 
(c) 
they shall determine the downward calibrated shock in accordance with the following formula: downward calibrated shock
where:

(d) 
they shall determine the upward calibrated shock in accordance with the following formula: upward calibrated shock
where:

Article 10
Downward and upward calibrated shock with the fallback method
1. Under the fallback method, institutions shall determine the downward and upward calibrated shock from the time series of 10 business days returns for a nonmodellable risk factor by applying one of the methodologies set out in this Article.
2. Where the nonmodellable risk factor is equal to one of the risk factors defined in Part Three, Title IV, Chapter 1a, Section 3, Subsection 1, of Regulation (EU) No 575/2013, institutions shall determine the downward and upward calibrated shock by applying the following steps in the following order:
(a) 
they shall identify the riskweight assigned to that risk factor in accordance with Part Three, Title IV, Chapter 1a, of Regulation (EU) No 575/2013; 
(b) 
they shall multiply that riskweight by
where:

(c) 
the downward and upward calibrated shock shall be the result of point (b). 
3. Where the nonmodellable risk factor is a point of a curve or a surface and it differs from other risk factors as defined in Part Three, Title IV, Chapter 1a, Section 3, Subsection 1, of Regulation (EU) No 575/2013 only in relation to the maturity dimension, institutions shall determine the downward and upward calibrated shocks by applying the following steps in the following order:
(a) 
from those risk factors defined in Part Three, Title IV, Chapter 1a, Section 3, Subsection 1, of Regulation (EU) No 575/2013 differing from the nonmodellable risk factor only in the maturity dimension, they shall identify the risk factor that is the closest in the maturity dimension to the nonmodellable risk factor; 
(b) 
they shall identify the riskweight assigned in accordance with Part Three, Title IV, Chapter 1a, of Regulation (EU) No 575/2013 to the risk factor identified in accordance with point (a); 
(c) 
they shall multiply that riskweight by
where:

(d) 
the downward and upward calibrated shock shall be the result of point (c). 
4. Where the nonmodellable risk factor does not meet the conditions set out in paragraphs 2 and 3, institutions shall determine the corresponding downward and upward calibrated shocks by selecting a risk factor that meets the conditions set out in paragraph 5 and apply the method set out in paragraph 6 to that selected risk factor.
5. The risk factor to be selected in accordance with paragraph 4 shall meet all of the following conditions:
(a) 
it belongs to the same broad risk factor category and broad subcategory of risk factors referred to in Article 325bd of Regulation (EU) No 575/2013 of the nonmodellable risk factor; 
(b) 
it is of the same nature as the nonmodellable risk factor; 
(c) 
it differs from the nonmodellable risk factor for features that do not lead to an underestimation of the volatility of the nonmodellable risk factor, including under stress conditions; 
(d) 
its time series of 10 business days returns referred to in paragraph 6, point (a), contains at least 12 returns. 
6. Under the method referred to in paragraph 4, institutions shall apply the following steps in the following order:
(a) 
for the selected risk factor, institutions shall, in accordance with Article 7, determine the time series of 10 business days returns for the stress period determined in accordance with Article 12; 
(b) 
institutions shall determine the downward and upward calibrated shocks for the selected risk factor with:

(c) 
institutions shall determine the downward calibrated shock for the nonmodellable risk factor by multiplying the downward shock for the selected risk factor determined in accordance with point (b) by
where:

(d) 
institutions shall determine the upward calibrated shock for the nonmodellable risk factor by multiplying the upward shock for the selected risk factor determined in accordance with point (b) by
where:

7. By way of derogation from paragraph 6, points (b)(i) and (b)(ii), where institutions apply the method referred to in paragraph 4 to all nonmodellable risk factors in a nonmodellable standardised bucket, they shall determine the upward and downward shocks for all the corresponding selected risk factors in accordance with either of the following:
(a) 
the historical method set out in Article 8, where the number of returns in the time series of 10 business days returns referred to in paragraph 6, point (a), is equal to or greater than 200 for all the selected risk factors; 
(b) 
the asymmetrical sigma method set out in Article 9, where the condition referred to in point (a) of this paragraph for applying the historical method is not met. 
Article 11
Estimators of the expected shortfall
1. Institutions shall calculate the estimate of the lefttail expected shortfall of a time series X in accordance with the following formula:
where:
— 
N is the number of observations in the time series; 
— 
α = 2,5 %; 
— 
] denotes the integer part of the product α ×N; 
— 
denotes the ith smallest observation in the time series X. 
2. Institutions shall calculate the estimate of the righttail expected shortfall of a time series X in accordance with the following formula:
where:
— 
( ) is the estimate of lefttail expected shortfall for the time series calculated in accordance with paragraph 1. 
Article 12
Determination of the stress period
1. Institutions shall determine the stress period for the nonmodellable risk factors in a broad category of risk factors by identifying the 12month observation period maximising the value obtained in accordance with following formula:
where:
— 
i denotes the broad risk factor category; 
— 
j is the index denoting the nonmodellable risk factors or the nonmodellable standardised buckets for which the institution calculates the stress scenario risk measure belonging to the broad risk factor category i; 
— 
is the rescaled stress scenario risk measure for the nonmodellable risk factor or the nonmodellable standardised bucket j calculated in accordance with Article 16. 
referred to in Article 325bb(1) of Regulation (EU) No 575/2013. Where institutions apply this derogation, they shall provide evidence that the stress period identified represents a period of financial stress for its nonmodellable risk factors. Institutions shall take into account how their portfolio is exposed to the nonmodellable risk factors in the broad category of risk factors.
3. When determining the stress period, institutions shall use an observation period starting at least from 1 January 2007, to the satisfaction of the competent authorities.
4. Institutions shall review the stress period identified at least with a quarterly frequency.
Article 13
Computation of the losses
1. Institutions shall calculate the loss corresponding to a scenario of future shock applied to one or more nonmodellable risk factors by calculating the loss on the portfolio of positions for which they calculate the own funds requirements for market risk in accordance with the alternative internal model approach set out in Part Three, Title IV, Chapter 1b, of Regulation (EU) No 575/2013, and that occurs if that scenario of future shock is applied to that nonmodellable risk factor or those nonmodellable risk factors in a standardised bucket, and all other risk factors remain unchanged.
2. Institutions shall calculate the loss corresponding to a scenario of future shock applied to one or more nonmodellable risk factors by using the pricing methods used in the risk measurement model.
3. By way of derogation from paragraph 2, where institutions cannot calculate the loss for some financial instruments or commodities included in the portfolio referred to in paragraph 1, corresponding to a scenario of future shock applied to one or several nonmodellable risk factors by using their pricing methods, they shall apply the following steps in the following order:
(a) 
they shall identify those financial instruments or commodities and the cause of the failure of the pricing calculation; 
(b) 
they shall use sensitivitybased pricing methods, including at least the material first order and material second order terms of Taylor series approximations, to reflect the change in the price of those financial instruments or commodities due to changes in the nonmodellable risk factors in this scenario of future shock. 
4. By way of derogation from paragraph 2, institutions may, only for the purpose of determining the stress period in accordance with Article 12(1), calculate the loss corresponding to a scenario of future shock applied to one or more nonmodellable risk factors using sensitivitybased pricing methods. Institutions shall demonstrate that the price changes that are not captured by the sensitivitybased pricing methods would not modify the stress period identified by the institution.
CHAPTER 2
REGULATORY EXTREME SCENARIO OF FUTURE SHOCK
Article 14
Determination of the regulatory extreme scenario of future shock
1. The regulatory extreme scenario of future shock referred to in Article 325bk(3), point (b), of Regulation (EU) No 575/2013 shall be a shock leading to the maximum loss that may occur due to a change in the nonmodellable risk factor where such maximum loss is finite.
2. Where the maximum loss referred to in paragraph 1 is not finite, institutions shall determine the regulatory extreme scenario of future shock by applying the following steps in the following order:
(a) 
they shall use an expertbased approach using qualitative and quantitative information available to identify a loss due to a change in the value taken by the nonmodellable risk factor that will not be exceeded with a level of certainty equal to 99,95 % on a 10 business day horizon in a future period of financial stress equivalent to the stress period identified for the nonmodellable risk factor. When doing so, institutions shall take into account the skewness and the excess kurtosis that may characterise the returns of the nonmodellable risk factor in a period of financial stress and shall justify any distributional or statistical assumptions taken for identifying that loss; 
(b) 
they shall multiply the loss obtained in accordance with point (a) by
where:

(c) 
they shall identify the regulatory extreme scenario of future shock as the shock leading to the loss resulting from points (a) and (b). 
3. Where institutions calculate a stress scenario risk measure for more than one nonmodellable risk factor as referred to in Article 325bk(3), point (c), of Regulation (EU) No 575/2013, the regulatory extreme scenario of future shock referred to in Article 325bk(3), point (b), of that Regulation shall be a scenario leading to the maximum loss that may occur due to a change in the values taken by those nonmodellable risk factors.
4. By way of derogation of paragraph 3, where institutions calculate a stress scenario risk measure for more than one nonmodellable risk factor as referred to in Article 325bk(3), point (c), of Regulation (EU) No 575/2013 and the maximum loss referred to in paragraph 3 of this Article is not finite, institutions shall determine the regulatory extreme scenario of future shock by applying the following steps in the following order:
(a) 
they shall use an expertbased approach using qualitative and quantitative information available to identify a loss due to a change in the values taken by the nonmodellable risk factors that will not be exceeded with a level of certainty equal to 99,95 % on a 10 business day horizon in a future period of financial stress equivalent to the stress period for the nonmodellable risk factors. When doing so, institutions shall take into account the skewness and the excess kurtosis that may characterise the returns of the nonmodellable risk factors in a period of financial stress and shall justify any distributional or statistical assumptions taken for identifying that loss; 
(b) 
they shall multiply the loss obtained in accordance with point (a) by ; where:

(c) 
they shall identify the regulatory extreme scenario of future shock as the scenario leading to the loss resulting from points (a) and (b). 
CHAPTER 3
CIRCUMSTANCES UNDER WHICH INSTITUTIONS MAY CALCULATE A STRESS SCENARIO RISK MEASURE FOR MORE THAN ONE NONMODELLABLE RISK FACTOR
Article 15
Circumstances for the calculation of a stress scenario risk measure for more than one nonmodellable risk factor
The circumstances under which institutions may calculate a stress scenario risk measure for more than one nonmodellable risk factor as referred to in Article 325bk(3), point (c), of Regulation (EU) No 575/2013 shall be the following:
(a) 
the risk factors belong to the same standardised bucket as referred to in Article 5(2) of Delegated Regulation (EU) 2022/2060; 
(b) 
institutions assessed the modellability of those risk factors, by determining the modellability of the standardised bucket to which they belong in accordance with Article 4(1) of Delegated Regulation (EU) 2022/2060. 
CHAPTER 4
AGGREGATION OF THE STRESS SCENARIO RISK MEASURES
Article 16
Aggregation of the stress scenario risk measures
1. For the purposes of aggregating the stress scenario risk measures as referred to in Article 325bk(3), point (d), of Regulation (EU) No 575/2013, institutions shall, for each stress scenario risk measure they have computed, determine the corresponding rescaled stress scenario risk measure as follows:
(a) 
where institutions determined the extreme scenario of future shock for a single risk factor in accordance with the stepwise method set out to in Article 3, the corresponding rescaled stress scenario risk measure shall be calculated in accordance with the following formula:
where:

(b) 
where institutions determined a stress scenario risk measure for more than one risk factor by determining an extreme scenario of future shock in accordance with the stepwise method set out in Article 6 for a nonmodellable standardised bucket comprising those risk factors, the corresponding rescaled stress scenario risk measure shall be calculated in accordance with the following formula:
where:

(c) 
where institutions determined the extreme scenario of future shock for a single risk factor in accordance with the direct method set out in Article 2, the corresponding rescaled stress scenario risk measure shall be calculated with the following formula:
where:

(d) 
where institutions determined a stress scenario risk measure for more than one risk factor by determining an extreme scenario of future shock in accordance with the direct method set out in Article 5 for the nonmodellable bucket comprising those risk factors, the corresponding rescaled stress scenario risk measure shall be calculated in accordance with the following formula:
where:

(e) 
where institutions determined a stress scenario risk measure by determining a regulatory extreme scenario of future shock in accordance with Article 14, the corresponding rescaled stress scenario risk measure shall be calculated in accordance with the following formula:
where:

2. Institutions shall aggregate the stress scenario risk measures in accordance with the following formula:
where:
— 
ICSR denotes the set of nonmodellable risk factors or nonmodellable standardised buckets for which institutions determined a stress scenario risk measure that was classified as reflecting idiosyncratic credit spread risk only, in accordance with paragraph 3; 
— 
k is an index denoting the nonmodellable risk factors or nonmodellable standardised buckets belonging to ICSR ; 
— 
EIR denotes the set of nonmodellable risk factors or nonmodellable standardised buckets for which institutions determine a stress scenario risk measure that was classified as reflecting idiosyncratic equity risk only, in accordance with paragraph 4; 
— 
l is an index denoting the nonmodellable risk factors or nonmodellable standardised buckets belonging to EIR ; 
— 
OR denotes a nonmodellable risk factor or nonmodellable standardised bucket for which institutions determine a stress scenario risk measure that was neither classified as reflecting idiosyncratic credit spread risk only, in accordance with paragraph 3, nor idiosyncratic equity risk only, in accordance with paragraph 4; 
— 
j is an index denoting the nonmodellable risk factors or nonmodellable standardised buckets belonging to OR; 
— 
are respectively the rescaled stress scenario risk measures for the nonmodellable risk factors or the nonmodellable standardised buckets k,l, j calculated in accordance with paragraph 1; 
— 
. 
3. The nonmodellable risk factors that institutions classify as reflecting idiosyncratic credit spread risk only shall meet all of the following conditions:
(a) 
the nature of the risk factor is such that it reflects idiosyncratic credit spread risk only; 
(b) 
the value taken by the risk factor is not driven by systematic risk components; 
(c) 
the correlation among risk factors is negligible; 
(d) 
institutions perform and document the statistical tests used to verify the condition set out in point (c). 
4. The nonmodellable risk factors that institutions classify as reflecting idiosyncratic equity risk only shall meet all of the following conditions:
(a) 
the nature of the risk factor is such that it reflects idiosyncratic equity risk only; 
(b) 
the value taken by the risk factor is not driven by systematic risk components; 
(c) 
the correlation among risk factors is negligible; 
(d) 
institutions perform and document the statistical tests used to verify the condition set out in point (c). 
Article 17
Nonlinearity coefficient for a single risk factor
Where the stress scenario risk measure for which institutions are determining the nonlinearity coefficient has been determined for a single risk factor, such nonlinearity coefficient shall be determined as follows:
(a) 
where the extreme scenario of future shock for the nonmodellable risk factor does not coincide with either the downward calibrated shock or the upward calibrated shock determined in accordance with Article 3(1), point (b), institutions shall set for that nonmodellable risk factor; 
(b) 
where the extreme scenario of future shock for the nonmodellable risk factor coincides with the downward calibrated shock determined in accordance with Article 3(1), point (b), institutions shall calculate the nonlinearity coefficient in accordance with the following formula:
where:

(c) 
where the extreme scenario of future shock for the nonmodellable risk factor coincides with the upward calibrated shock determined in accordance with Article 3(1), point (b), institutions shall calculate the nonlinearity coefficient in accordance with the following formula:
where:

Article 18
Nonlinearity coefficient for a bucket
Where the stress scenario risk measure for which institutions are determining the nonlinearity coefficient has been determined for a nonmodellable standardised bucket, the nonlinearity coefficient shall be determined as follows:
(a) 
where the extreme scenario of future shock does not correspond to a scenario identified in accordance with Article 6(1), point (b), where the value of the parameter β referred to in Article 6(1), point (c), it set equal to 1, institutions shall set the nonlinearity coefficient for that nonmodellable bucket; 
(b) 
where the extreme scenario of future shock is a scenario where the corresponding downward shock determined in accordance with Article 6(1), point (b) is applied to each risk factor in the nonmodellable bucket, institutions shall calculate the nonlinearity coefficient in accordance with the following formula:
