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Regulation (EU) No 575/2013 of the European Parliament and of the Council of 26 June 2013 on prudential requirements for credit institutions and investment firms and amending Regulation (EU) No 648/2012 Text with EEA relevance

Type Regulation

Publication 2013-06-26

Last updated 2026-06-26

State In force

Department Council of the European Union, European Parliament

Source EUR-Lex

articles 737

Reform history JSON API

(c) an external auditor of the institution has confirmed the adequacy of the third-party’s data, information or risk metrics referred to in point (b) of this paragraph and the institution’s competent authority has unrestricted access to those data, information or risk metrics upon request.

EBA shall submit those draft regulatory technical standards to the Commission by 10 January 2027.

Power is delegated to the Commission to supplement this Regulation by adopting the regulatory technical standards referred to in the first subparagraph of this paragraph in accordance with Articles 10 to 14 of Regulation (EU) No 1093/2010.

Article 325k

Underwriting positions

Institutions shall apply one of the appropriate multiplying factors listed in Table 1 to the net sensitivities of all the underwriting positions in each individual issuer, excluding the underwriting positions which are subscribed or sub-underwritten by third parties on the basis of formal agreements, and calculate the own funds requirements for market risk in accordance with the approach set out in this Chapter on the basis of the adjusted net sensitivities.

Business day 0	0 %
Business day 1	10 %
Business days 2 and 3	25 %
Business day 4	50 %
Business day 5	75 %
After business day 5	100 %

For the purposes of this Article, ‘business day 0’ means the business day on which the institution becomes unconditionally committed to accepting a known quantity of securities at an agreed price.

Section 3

Risk factor and sensitivity definitions

Subsection 1

Risk factor definitions

Article 325l

General interest rate risk factors

The delta general interest rate risk factors applicable to interest rate-sensitive instruments shall be the relevant risk-free rates per currency and per each of the following maturities: 0,25 years, 0,5 years, 1 year, 2 years, 3 years, 5 years, 10 years, 15 years, 20 years, 30 years. Institutions shall assign risk factors to the specified vertices by linear interpolation or by using a method that is most consistent with the pricing functions used by the independent risk control function of the institution to report market risk or profits and losses to senior management.

Where the data on market-implied swap curves described in paragraph 2 and the first subparagraph of this paragraph are insufficient, the risk-free rates may be derived from the most appropriate sovereign bond curve for a given currency.

Where institutions use the general interest rate risk factors derived in accordance with the procedure set out in the second subparagraph of this paragraph for sovereign debt instruments, the sovereign debt instrument shall not be exempted from the own funds requirements for credit spread risk. In those cases, where it is not possible to disentangle the risk-free rate from the credit spread component, the sensitivity to the risk factor shall be allocated both to the general interest rate risk and to credit spread risk classes.

Institutions shall apply additional risk factors for inflation risk to debt instruments whose cash flows are functionally dependent on inflation rates. Those additional risk factors shall consist of one vector of market-implied inflation rates of different maturities per currency. For each instrument, the vector shall contain as many components as there are inflation rates used as variables by the institution's pricing model for that instrument.

Each cross-currency basis risk factor shall consist of one vector of cross-currency basis of different maturities per currency. For each debt instrument, the vector shall contain as many components as there are cross-currency bases used as variables by the institution's pricing model for that instrument. Each currency shall constitute a different bucket.

Institutions shall calculate the sensitivity of the instrument to the cross-currency basis risk factor as the change in the value of the instrument, according to its pricing model, as a result of a 1 basis point shift in each of the components of the vector. Each currency shall constitute a separate bucket. Within each bucket there shall be two possible distinct risk factors: basis over euro and basis over US dollar, regardless of the number of components there are in each cross-currency basis vector. The maximum number of net sensitivities per bucket shall be two.

For netting purposes, institutions shall consider implied volatilities linked to the same risk-free rates and mapped to the same maturities to constitute the same risk factor.

Where institutions map implied volatilities to the maturities as referred to in this paragraph, the following requirements shall apply:

(a) where the maturity of the option is aligned with the maturity of the underlying, a single risk factor shall be considered, which shall be mapped to that maturity;

(b) where the maturity of the option is shorter than the maturity of the underlying, the following risk factors shall be considered as follows: (i) the first risk factor shall be mapped to the maturity of the option; (ii) the second risk factor shall be mapped to the residual maturity of the underlying of the option at the expiry date of the option.

There shall be no curvature risk own funds requirements for inflation and cross currency basis risks.

Article 325m

Credit spread risk factors for non-securitisation

Article 325n

Credit spread risk factors for securitisation

Institutions shall apply the credit spread risk factors referred to in paragraph 5 to securitisation positions that are not included in the ACTP, as referred to in Article 325(6), (7) and (8).

The buckets applicable to the credit spread risk for securitisations that are not included in the ACTP shall be specific to that risk-class category, as referred to in Section 6.

The credit spread risk factors to be applied by institutions to securitisation positions that are included in the ACTP are the following:

(a) the delta risk factors shall be all the relevant credit spread rates of the issuers of the underlying exposures of the securitisation position, inferred from the relevant debt instruments and credit default swaps, and for each of the following maturities: 0,5 years, 1 year, 3 years, 5 years, 10 years.

(b) the vega risk factors applicable to options with securitisation positions that are included in the ACTP as underlyings shall be the implied volatilities of the credit spreads of the issuers of the underlying exposures of the securitisation position, inferred as described in point (a) of this paragraph, which shall be mapped to the following maturities in accordance with the maturity of the corresponding option subject to own funds requirements: 0,5 years, 1 year, 3 years, 5 years, 10 years.

(c) the curvature risk factors shall be the relevant credit spread yield curves of the issuers of the underlying exposures of the securitisation position expressed as a vector of credit spread rates for different maturities, inferred as indicated in point (a) of this paragraph; for each instrument, the vector shall contain as many components as there are different maturities of credit spread rates that are used as variables by the institution's pricing model for that instrument.

The credit spread risk factors to be applied by institutions to securitisation positions that are not included in the ACTP shall refer to the spread of the tranche rather than the spread of the underlying instruments and shall be the following:

(a) the delta risk factors shall be the relevant tranche credit spread rates, mapped to the following maturities, in accordance with the maturity of the tranche: 0,5 years, 1 year, 3 years, 5 years, 10 years;

(b) the vega risk factors applicable to options with securitisation positions that are not included in the ACTP as underlyings shall be the implied volatilities of the credit spreads of the tranches, each of them mapped to the following maturities in accordance with the maturity of the option subject to own funds requirements: 0,5 years, 1 year, 3 years, 5 years, 10 years;

(c) the curvature risk factors shall be the same as those described in point (a) of this paragraph; to all those risk factors, a common risk weight shall be applied, as referred to in Section 6.

Article 325o

Equity risk factors

For the purposes of equity risk, a specific equity repo curve shall constitute a single risk factor, which is expressed as a vector of repo rates for different maturities. For each instrument, the vector shall contain as many components as there are different maturities of repo rates that are used as variables by the institution's pricing model for that instrument.

Institutions shall calculate the sensitivity of an instrument to an equity risk factor as the change in the value of the instrument, according to its pricing model, as a result of a 1 basis point shift in each of the components of the vector. Institutions shall offset sensitivities to the repo rate risk factor of the same equity security, regardless of the number of components of each vector.

Article 325p

Commodity risk factors

The sensitivity of the instrument to each risk factor used in the curvature risk formula shall be calculated as specified in Article 325g. For the purposes of curvature risk, institutions shall consider vectors having a different number of components to constitute the same risk factor, provided that those vectors correspond to the same commodity type.

Article 325q

Foreign exchange risk factors

By way of derogation from paragraphs 1 and 3, an institution may replace, subject to permission from its competent authority, its reporting currency by another currency (‘the base currency’) in all the spot exchange rates to express the delta and curvature foreign exchange risk factors where all of the following conditions are met:

(a) the institution uses only one base currency;

(b) the institution applies the base currency consistently to all its trading book and non-trading book positions;

(c) the institution has demonstrated to the satisfaction of its competent authority that: (i) using the chosen base currency provides an appropriate risk representation for the institution’s positions subject to foreign exchange risks; (ii) the choice of base currency is compatible with the manner in which the institution manages those foreign exchange risks internally; (iii) the choice of base currency is not driven primarily by the desire to reduce the institution’s own funds requirements;

(d) the institution takes into account the translation risk between the reporting currency and the base currency.

An institution that has been permitted to use a base currency as set out in the first subparagraph shall convert the resulting own funds requirements for foreign exchange risk into the reporting currency using the prevailing spot exchange rate between the base currency and the reporting currency.

Subsection 2

Sensitivity definitions

Article 325r

Delta risk sensitivities

Institutions shall calculate delta general interest rate risk (GIRR) sensitivities as follows:

(a) the sensitivities to risk factors consisting of risk-free rates shall be calculated as follows: where: = the sensitivities to risk factors consisting of risk-free rates; rkt = the rate of a risk-free curve k with maturity t; Vi (.) = the pricing function of instrument i; and x,y = risk factors other than rkt in the pricing function Vi;

(b) the sensitivities to risk factors consisting of inflation risk and cross-currency basis shall be calculated as follows: where: = the sensitivities to risk factors consisting of inflation risk and cross-currency basis; = a vector of m components representing the implied inflation curve or the cross-currency basis curve for a given currency j with m being equal to the number of inflation or cross-currency related variables used in the pricing model of instrument i; = the unity matrix of dimension (1 × m); Vi (.) = the pricing function of the instrument i; and y, z = other variables in the pricing model.

Institutions shall calculate the delta credit spread risk sensitivities for all securitisation and non-securitisation positions as follows:

where:

Institutions shall calculate delta equity risk sensitivities as follows:

(a) the sensitivities to risk factors consisting of equity spot prices shall be calculated as follows: where: sk = the sensitivities to risk factors consisting of equity spot prices; k = a specific equity security; EQk = the value of the spot price of that equity security; Vi (.) = the pricing function of instrument i; and x,y = risk factors other than EQk in the pricing function Vi;

(b) the sensitivities to risk factors consisting of equity repo rates shall be calculated as follows: where: = the sensitivities to risk factors consisting of equity repo rates; k = the index that denotes the equity; = a vector of m components representing the repo term structure for a specific equity k with m being equal to the number of repo rates corresponding to different maturities used in the pricing model of instrument i; = the unity matrix of dimension (1 · m); Vi (.) = the pricing function of the instrument i; and y,z = risk factors other than

in the pricing function Vi.

Institutions shall calculate the delta commodity risk sensitivities to each risk factor k as follows:

where:

Institutions shall calculate the delta foreign exchange risk sensitivities to each foreign exchange risk factor k as follows:

where:

Article 325s

Vega risk sensitivities

Institutions shall calculate the vega risk sensitivity of an option to a given risk factor k as follows:

where:

Article 325t

Requirements on sensitivity computations

By way of derogation from the first subparagraph of this paragraph, competent authorities may require an institution that has been granted permission to use the alternative internal model approach set out in Chapter 1b to use the pricing functions of the risk-measurement system of their internal model approach in the calculation of sensitivities under this Chapter for the purposes of the calculation and the reporting requirements set out in Article 325(3).

When calculating vega risk sensitivities of instruments with optionality as referred to in point (b) of Article 325e(2), the following requirements shall apply:

(a) for general interest rate risk and credit spread risk, institutions shall assume, for each currency, that the underlying of the volatility risk factors for which vega risk is calculated follows either a lognormal or normal distribution in the pricing models used for those instruments;

(b) for equity risk, commodity risk and foreign exchange risk, institutions shall assume that the underlying of the volatility risk factors for which vega risk is calculated follows a lognormal distribution in the pricing models used for those instruments.

By way of derogation from paragraph 1, subject to the permission of the competent authorities, an institution may use alternative definitions of delta risk sensitivities in the calculation of the own funds requirements of a trading book position under this Chapter, provided that the institution meets all the following conditions:

(a) those alternative definitions are used for internal risk management purposes or for the reporting of profits and losses to senior management by an independent risk control unit within the institution;

(b) the institution demonstrates that those alternative definitions are more appropriate for capturing the sensitivities for the position than are the formulas set out in this Subsection, and that the resulting sensitivities do not materially differ from those formulas.

By way of derogation from paragraph 1, subject to the permission of the competent authorities, an institution may calculate vega sensitivities on the basis of a linear transformation of alternative definitions of sensitivities in the calculation of the own funds requirements of a trading book position under this Chapter, provided that the institution meets both the following conditions:

(b) the institution demonstrates that those alternative definitions are more appropriate for capturing the sensitivities for the position than are the formulae set out in this Subsection, that the linear transformation referred to in the first subparagraph reflects a vega risk sensitivity, and that the resulting sensitivities do not materially differ from the ones applying those formulae.

Section 4

The residual risk add-on

Article 325u

Own funds requirements for residual risks

Instruments are considered to be exposed to residual risks where they meet any of the following conditions:

(a) the instrument references an exotic underlying, which, for the purposes of this Chapter, means a trading book instrument referencing an underlying exposure that is not in the scope of the delta, vega or curvature risk treatments under the sensitivities-based method laid down in Section 2 or the own funds requirements for the default risk set out in Section 5;

(b) the instrument is an instrument bearing other residual risks, which, for the purposes of this Chapter, means any of the following instruments: (i) instruments that are subject to the own funds requirements for vega and curvature risk under the sensitivities-based method set out in Section 2 and that generate pay-offs that cannot be replicated as a finite linear combination of plain-vanilla options with a single underlying equity price, commodity price, exchange rate, bond price, credit default swap price or interest rate swap; (ii) instruments that are positions that are included in the ACTP referred to in Article 325(6); hedges that are included in that ACTP, as referred to in Article 325(8), shall not be considered.

Institutions shall calculate the additional own funds requirements referred to in paragraph 1 as the sum of gross notional amounts of the instruments referred to in paragraph 2, multiplied by the following risk weights:

(a) 1,0 % in the case of instruments referred to in point (a) of paragraph 2;

(b) 0,1 % in the case of instruments referred to in point (b) of paragraph 2.

By way of derogation from paragraph 1, institution shall not apply the own funds requirement for residual risks to an instrument that meets any of the following conditions:

(a) the instrument is listed on a recognised exchange;

(b) the instrument is eligible for central clearing in accordance with Regulation (EU) No 648/2012;

(c) the instrument perfectly offsets the market risk of another position in the trading book, in which case the two perfectly matching trading book positions shall be exempted from the own funds requirement for residual risks.

The competent authority shall grant permission to apply the treatment referred to in the first subparagraph if the institution can demonstrate on an ongoing basis to the satisfaction of the competent authority that the instruments comply with the criteria to be treated as hedging positions.

The institution shall report to the competent authority the result of the calculation of the own funds requirements for the residual risks for all instruments for which the derogation referred to in the first subparagraph is applied.

When developing those draft regulatory technical standards, EBA shall examine whether longevity risk, weather, natural disasters and future realised volatility should be considered as exotic underlyings.

EBA shall submit those draft regulatory technical standards to the Commission by 28 June 2021.

Power is delegated to the Commission to supplement this Regulation by adopting the regulatory technical standards referred to in the first subparagraph in accordance with Articles 10 to 14 of Regulation (EU) No 1093/2010.

EBA shall submit those draft regulatory technical standards to the Commission by 30 June 2024.

Section 5

Own funds requirements for the default risk

Article 325v

Definitions and general provisions

For the purposes of this Section, the following definitions apply:

(a) ‘short exposure’ means that the default of an issuer or group of issuers leads to a gain for the institution, regardless of the type of instrument or transaction creating the exposure;

(b) ‘long exposure’ means that the default of an issuer or group of issuers leads to a loss for the institution, regardless of the type of instrument or transaction creating the exposure;

(c) ‘gross jump-to-default (gross JTD) amount’ means the estimated size of the loss or gain that the default of the obligor would produce for a specific exposure;

(d) ‘net jump-to-default (net JTD) amount’ means the estimated size of the loss or gain that an institution would incur due to the default of an obligor, after offsetting between gross JTD amounts has taken place,

(e) ‘loss given default’ or ‘LGD’ means the loss given default of the obligor on an instrument issued by that obligor expressed as a share of the notional amount of the instrument;

(f) ‘default risk weight’ means the percentage representing the estimated probability of the default of each obligor, according to the creditworthiness of that obligor.

Subsection 1

Own funds requirements for the default risk for non-securitisations

Article 325w

Gross jump-to-default amounts

Institutions shall calculate the gross JTD amounts for each long exposure to debt instruments as follows:

Institutions shall calculate the gross JTD amounts for each short exposure to debt instruments as follows:

For the purposes of the calculation set out in paragraphs 1 and 2, the LGD for debt instruments to be applied by institutions shall be the following:

(a) exposures to non-senior debt instruments shall be assigned an LGD of 100 %;

(b) exposures to senior debt instruments shall be assigned an LGD of 75 %;

(a) in the case of a bond, the notional amount is the face value of the bond;

(b) in the case of a sold put option on a bond, the notional amount is the notional amount of the option; in the case of a bought call option on a bond, the notional amount is 0.

For exposures to equity instruments, institutions shall calculate the gross JTD amounts as follows:

where:

EBA shall develop draft regulatory technical standards to specify:

(a) how institutions are to determine the components P&Llong, P&Lshort, Adjustmentlong and Adjustmentshort when calculating the JTD amounts for different types of instruments in accordance with this Article;

(b) which alternative methodologies institutions are to use for the purposes of the estimation of gross JTD amounts referred to in paragraph 7.

EBA shall submit those draft regulatory technical standards to the Commission by 28 June 2021.

Article 325x

Net jump-to-default amounts

Offsetting shall be either full or partial, depending on the maturities of the offsetting exposures:

(a) offsetting shall be full where all offsetting exposures have maturities of one year or more;

(b) offsetting shall be partial where at least one of the offsetting exposures has a maturity of less than one year, in which case the size of the JTD amount of each exposure with a maturity of less than one year shall be multiplied by the ratio of the exposure's maturity relative to one year.

Article 325y

Calculation of the own funds requirements for the default risk

Net JTD amounts, irrespective of the type of counterparty, shall be multiplied by the default risk weights that correspond to their credit quality, as specified in Table 2:

Credit quality category	Default risk weight
Credit quality step 1	0,5 %
Credit quality step 2	3 %
Credit quality step 3	6 %
Credit quality step 4	15 %
Credit quality step 5	30 %
Credit quality step 6	50 %
Unrated	15 %
Defaulted	100 %

Weighted net JTD amounts shall be aggregated within each bucket, in accordance with the following formula:

For the purposes of calculating the DRCb and the WtS, the long positions and short positions shall be aggregated for all positions within a bucket, regardless of the credit quality step to which those positions are allocated, to produce the bucket-specific own funds requirements for the default risk.

Subsection 2

Own funds requirements for the default risk for securitisations not included in the ACTP

Article 325z

Jump-to-default amounts

Article 325aa

Calculation of the own funds requirement for the default risk for securitisations

Risk-weighted net JTD amounts shall be assigned to the following buckets:

(a) one common bucket for all corporates, regardless of the region;

(b) 44 different buckets corresponding to one bucket per region for each of the 11 asset classes defined in the second subparagraph.

For the purposes of the first subparagraph, the 11 asset classes are ABCP, auto loans/leases, residential mortgage-backed securities (RMBS), credit cards, commercial mortgage-backed securities (CMBS), collateralised loan obligations, collateralised debt obligations squared (CDO-squared), small and medium-sized enterprises (SMEs), student loans, other retail, other wholesale. The four regions are Asia, Europe, North America, and rest of the world.

Subsection 3

Own funds requirements for the default risk for securitisations included in the ACTP

Article 325ab

Scope

Article 325ac

Jump-to-default amounts for the ACTP

For the purposes of this Article, the following definitions apply:

(a) ‘decomposition with a valuation model’ means that a single name constituent of a securitisation is valued as the difference between the unconditional value of the securitisation and the conditional value of the securitisation assuming that single name defaults with an LGD of 100 %;

(b) ‘replication’ means that the combination of individual securitisation index tranches are combined to replicate another tranche of the same index series, or to replicate an untranched position in the index series;

(c) ‘decomposition’ means replicating an index by a securitisation of which the underlying exposures in the pool are identical to the single name exposures that compose the index.

Nth-to-default products shall be treated as tranched products with the following attachment and detachment points:

(a) attachment point = (N – 1) / Total Names;

(b) detachment point = N / Total Names; where ‘Total Names’ shall be the total number of names in the underlying basket or pool.

Net JTD amounts shall be determined by offsetting long gross JTD amounts and short gross JTD amounts. Offsetting shall only be possible between exposures that are otherwise identical except for maturity. Offsetting shall only be possible as follows:

(a) for indices, index tranches and bespoke tranches, offsetting shall be possible across maturities within the same index family, series and tranche, subject to the provisions on exposures of less than one year laid down in Article 325x; long gross JTD amounts and short gross JTD amounts that perfectly replicate each other may be offset through decomposition into single name equivalent exposures using a valuation model; in such cases, the sum of the gross JTD amounts of the single name equivalent exposures obtained through decomposition shall be equal to the gross JTD amount of the undecomposed exposure;

(b) offsetting through decomposition as set out is point (a) shall not be allowed for resecuritisations or derivatives on securitisation;

(c) for indices and index tranches, offsetting shall be possible across maturities within the same index family, series and tranche by replication or by decomposition; where the long exposures and short exposures are otherwise equivalent, apart from one residual component, offsetting shall be allowed and the net JTD amount shall reflect the residual exposure;

(d) different tranches of the same index series, different series of the same index and different index families may not be used to offset each other.

Article 325ad

Calculation of the own funds requirements for the default risk for the ACTP

Net JTD amounts shall be multiplied by:

(a) for non-tranched products, the default risk weights corresponding to their credit quality as specified in Article 325y(1) and (2);

(b) for tranched products, the default risk weights referred to in Article 325aa(1).

Weighted net JTD amounts shall be aggregated within each bucket in accordance with the following formula:

Institutions shall calculate the own funds requirements for the default risk for the ACTP by using the following formula:

where:

Section 6

Risk weights and correlations

Subsection 1

Delta risk weights and correlations

Article 325ae

Risk weights for general interest rate risk

For currencies not included in the most liquid currency sub-category as referred to in point (b) Article 325bd(7), the risk weights of the sensitivities to the risk-free rate risk factors shall be the following:

Bucket	Maturity	Risk Weight
1	0,25 years	1,7 %
2	0,5 years	1,7 %
3	1 year	1,6 %
4	2 years	1,3 %
5	3 years	1,2 %
6	5 years	1,1 %
7	10 years	1,1 %
8	15 years	1,1 %
9	20 years	1,1 %
10	30 years	1,1 %

The risk weights of risk factors based on the currencies included in the most liquid currency sub-category as referred to in Article 325bd(7), point (b), and the domestic currency of the institution shall be the following:

(a) for risk-free rate risk factors, the risk weights referred to in paragraph 1, Table 3, of this Article divided by ;

(b) for inflation risk factor and cross currency basis risk factors, the risk weights referred to in paragraph 2 of this Article divided by .

Article 325af

Intra bucket correlations for general interest rate risk

Between two weighted sensitivities of general interest rate risk factors WSk and WSl within the same bucket, corresponding to the same curve, but having different maturities, correlation shall be set in accordance with the following formula:

where:

Article 325ag

Correlations across buckets for general interest rate risk

Article 325ah

Risk weights for credit spread risk for non-securitisations

Risk weights for the sensitivities to credit spread risk factors for non-securitisations shall be the same for all maturities (0,5 years, 1 year, 3 years, 5 years, 10 years) within each bucket in Table 4:

Bucket number	Credit quality	Sector	Risk weight
1	All	Central government, including central banks, of Member States	0,5 %
2	Credit quality step 1 to 3	Central government, including central banks, of a third country, multilateral development banks and international organisations referred to in Article 117(2) or Article 118	0,5 %
3	Regional or local authority and public sector entities	1,0 %
4	Financial sector entities including credit institutions incorporated or established by a central government, a regional government or a local authority and promotional lenders	5,0 %
5	Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying	3,0 %
6	Consumer goods and services, transportation and storage, administrative and support service activities	3,0 %
7	Technology, telecommunications	2,0 %
8	Health care, utilities, professional and technical activities	1,5 %
9		Covered bonds issued by credit institutions established in Member States	1,0 %
10	Credit quality step 1	Covered bonds issued by credit institutions in third countries	1,5 %
Credit quality steps 2 to 3	2,5 %
11	Credit quality step 4 to 6 and unrated	Central government, including central banks, of a third country, multilateral development banks and international organisations referred to in Article 117(2) or Article 118	2 %
12	Regional or local authority and public sector entities	4,0 %
13	Financial sector entities, including credit institutions incorporated or established by a central government, a regional government or a local authority, promotional lenders and covered bonds	12,0 %
14	Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying	7,0 %
15	Consumer goods and services, transportation and storage, administrative and support service activities	8,5 %
16	Technology, telecommunications	5,5 %
17	Health care, utilities, professional and technical activities	5,0 %
18	Other sector	12,0 %
19	Listed credit indices with a majority of its individual constituents being investment grade	1,5 %
20	Listed credit indices with a majority of its individual constituents being non-investment grade or unrated	5 %

For the purposes of this Article, an exposure shall be assigned the credit quality category corresponding to the credit quality category that it would be assigned under the standardised approach for credit risk set out in Title II, Chapter 2.

Article 325ai

Intra-bucket correlations for credit spread risk for non-securitisations

The correlation parameter ρk l between two sensitivities WSk and WSl within the same bucket shall be set as follows:

The correlation parameters referred to in paragraph 1 of this Article shall not apply to bucket 18 in Table 4 of Article 325ah(1). The capital requirement for the delta risk aggregation formula within bucket 18 shall be equal to the sum of the absolute values of the net weighted sensitivities allocated to that bucket:

Article 325aj

Correlations across buckets for credit spread risk for non-securitisations

The correlation parameter γbc that applies to the aggregation of sensitivities between different buckets shall be set as follows:

(a) 1, where buckets b and c are buckets 1 to 17 and both buckets have the same credit quality category (either credit quality step 1 to 3 or credit quality step 4 to 6); otherwise it shall be equal to 50 %; for the purposes of that calculation, bucket 1 shall be considered as belonging to the same credit quality category as buckets that have credit quality step 1 to 3;

(b) 1, where either bucket b or c is bucket 18;

(c) 1, where bucket b or c is bucket 19 and the other bucket has credit quality step 1 to 3; otherwise it shall be equal to 50 %;

(d) 1, where bucket b or c is bucket 20 and the other bucket has credit quality step 4 to 6; otherwise it shall be equal to 50 %;

Bucket	3 and 12	4 and 13	5 and 14	6 and 15	7 and 16	8 and 17	9 and 10	18	19	20
1, 2 and 11	75 %	10 %	20 %	25 %	20 %	15 %	10 %	0 %	45 %	45 %
3 and 12		5 %	15 %	20 %	15 %	10 %	10 %	0 %	45 %	45 %
4 and 13			5 %	15 %	20 %	5 %	20 %	0 %	45 %	45 %
5 and 14				20 %	25 %	5 %	5 %	0 %	45 %	45 %
6 and 15					25 %	5 %	15 %	0 %	45 %	45 %
7 and 16						5 %	20 %	0 %	45 %	45 %
8 and 17							5 %	0 %	45 %	45 %
9 and 10								0 %	45 %	45 %
18									0 %	0 %
19										75 %
20

Article 325ak

Risk weights for credit spread risk for securitisations included in the ACTP

Risk weights for the sensitivities to credit spread risk factors for securitisations included in the ACTP risk factors shall be the same for all maturities (0,5 years, 1 year, 3 years, 5 years, 10 years) within each bucket and shall be specified for each bucket in Table 6 pursuant to the delegated act referred to in Article 461a:

Bucket number	Credit quality	Sector	Risk weight
1	All	Central government, including central banks, of Member States	4,0 %
2	Credit quality step 1 to 10	Central government, including central banks, of a third country, multilateral development banks and international organisations referred to in Article 117(2) or Article 118	4,0 %
3	Regional or local authority and public sector entities	4,0 %
4	Financial sector entities including credit institutions incorporated or established by a central government, a regional government or a local authority and promotional lenders	8,0 %
5	Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying	5,0 %
6	Consumer goods and services, transportation and storage, administrative and support service activities	4,0 %
7	Technology, telecommunications	3,0 %
8	Health care, utilities, professional and technical activities	2,0 %
9	Covered bonds issued by credit institutions established in Member States	3,0 %
10	Covered bonds issued by credit institutions in third countries	6,0 %
11	Credit quality step 11 to 17	Central government, including central banks, of a third country, multilateral development banks and international organisations referred to in Article 117(2) or Article 118	13,0 %
12	Regional or local authority and public sector entities	13,0 %
13	Financial sector entities, including credit institutions incorporated or established by a central government, a regional government or a local authority, promotional lenders and covered bonds	16,0 %
14	Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying	10,0 %
15	Consumer goods and services, transportation and storage, administrative and support service activities	12,0 %
16	Technology, telecommunications	12,0 %
17	Health care, utilities, professional and technical activities	12,0 %
18	Other sector	13,0 %

By way of derogation from the second paragraph, institutions may assign a risk exposure of an unrated covered bond to bucket 4 where the institution that issues the covered bond has a credit quality step 1 to 3.

Article 325al

Correlations for credit spread risk for securitisations included in the ACTP

Article 325am

Risk weights for credit spread risk for securitisations not included in the ACTP

Risk weights for the sensitivities to credit spread risk factors for securitisation not included in the ACTP shall be the same for all maturities (0,5 years, 1 year, 3 years, 5 years, 10 years) within each bucket in Table 7 and shall be specified for each bucket in Table 7 pursuant to the delegated act referred to in Article 461a:

Bucket number	Credit quality	Sector	Risk weight
1	Senior and credit quality step 1 to 10	RMBS — Prime	0,9 %
2	RMBS — Mid-Prime	1,5 %
3	RMBS — Sub-Prime	2,0 %
4	CMBS	2,0 %
5	Asset backed securities (ABS) — Student loans	0,8 %
6	ABS — Credit cards	1,2 %
7	ABS — Auto	1,2 %
8	Collateralised loan obligations (CLO) non-ACTP	1,4 %
9	Non-senior and credit quality step 1 to 10	RMBS — Prime	1,125 %
10	RMBS — Mid-Prime	1,875 %
11	RMBS — Sub-Prime	2,5 %
12	CMBS	2,5 %
13	ABS — Student loans	1 %
14	ABS — Credit cards	1,5 %
15	ABS — Auto	1,5 %
16	CLO non-ACTP	1,75 %
17	Credit quality step 11 to 17 and unrated	RMBS — Prime	1,575 %
18	RMBS — Mid-Prime	2,625 %
19	RMBS — Sub-Prime	3,5 %
20	CMBS	3,5 %
21	ABS — Student loans	1,4 %
22	ABS — Credit cards	2,1 %
23	ABS — Auto	2,1 %
24	CLO non-ACTP	2,45 %
25	Other sector	3,5 %

Article 325an

Intra-bucket correlations for credit spread risk for securitisations not included in the ACTP

Between two sensitivities WSk and WSl within the same bucket, the correlation parameter ρk l shall be set as follows:

The correlation parameters referred to in paragraph 1 shall not apply to bucket 25 in Table 7 of Article 325am(1). The own funds requirement for the delta risk aggregation formula within bucket 25 shall be equal to the sum of the absolute values of the net weighted sensitivities allocated to that bucket:

Article 325ao

Correlations across buckets for credit spread risk for securitisations not included in the ACTP

Article 325ap

Risk weights for equity risk

Risk weights for the sensitivities to equity and equity repo rate risk factors shall be specified for each bucket in Table 8 pursuant to the delegated act referred to in Article 461a:

Bucket number	Market capitali-sation	Economy	Sector	Risk weight for equity spot price	Risk weight for equity repo rate
1	Large	Emerging market economy	Consumer goods and services, transportation and storage, administrative and support service activities, healthcare, utilities	55 %	0,55 %
2	Telecommunications, industrials	60 %	0,60 %
3	Basic materials, energy, agriculture, manufacturing, mining and quarrying	45 %	0,45 %
4	Financials including government-backed financials, real estate activities, technology	55 %	0,55 %
5	Advanced economy	Consumer goods and services, transportation and storage, administrative and support service activities, healthcare, utilities	30 %	0,30 %
6	Telecommunications, industrials	35 %	0,35 %
7	Basic materials, energy, agriculture, manufacturing, mining and quarrying	40 %	0,40 %
8	Financials including government-backed financials, real estate activities, technology	50 %	0,50 %
9	Small	Emerging market economy	All sectors described under bucket numbers 1, 2, 3 and 4	70 %	0,70 %
10	Advanced economy	All sectors described under bucket numbers 5, 6, 7 and 8	50 %	0,50 %
11	Other sector	70 %	0,70 %
12	Large market cap, advanced economy indices	15 %	0,15 %
13	Other indices	25 %	0,25 %

EBA shall submit those draft regulatory technical standards to the Commission by 28 June 2021.

Article 325aq

Intra-bucket correlations for equity risk

In other cases than the cases referred to in paragraph 1, the correlation parameter ρkl between two sensitivities WSk and WSl to equity spot price within the same bucket shall be set as follows:

(a) 15 % between two sensitivities within the same bucket that fall under the category large market capitalisation, emerging market economy (bucket number 1, 2, 3 or 4);

(b) 25 % between two sensitivities within the same bucket that fall under the category large market capitalisation, advanced economy (bucket number 5, 6, 7 or 8);

(c) 7,5 % between two sensitivities within the same bucket that fall under the category small market capitalisation, emerging market economy (bucket number 9);

(d) 12,5 % between two sensitivities within the same bucket that fall under the category small market capitalisation, advanced economy (bucket number 10);

(e) 80 % between two sensitivities within the same bucket that fall under either index bucket (bucket number 12 or 13).

The correlation parameters specified in paragraphs 1 to 4 shall not apply to bucket 11. The capital requirement for the delta risk aggregation formula within bucket 11 shall be equal to the sum of the absolute values of the net weighted sensitivities allocated to that bucket:

Article 325ar

Correlations across buckets for equity risk

The correlation parameter γbc shall apply to the aggregation of sensitivities between different buckets.

It shall be set in relation to the buckets of Table 8 in Article 325ap as follows:

(a) 15 % where the two buckets fall within bucket numbers 1 to 10;

(b) 0 % where either of the two buckets fall within bucket number 11;

(d) 45 % otherwise.

Article 325as

Risk weights for commodity risk

Risk weights for sensitivities to commodity risk factors shall be the following:

Bucket number	Bucket name	Risk weight
1	Energy — solid combustibles	30 %
2	Energy — liquid combustibles	35 %
3	Energy — electricity	60 %

3a	Energy — EU ETS carbon trading	40 %
3b	Energy — non-EU ETS carbon trading	60 %

4	Freight	80 %
5	Metals — non-precious	40 %
6	Gaseous combustibles	45 %
7	Precious metals (including gold)	20 %
8	Grains and oilseed	35 %
9	Livestock and dairy	25 %
10	Softs and other agricultural commodities	35 %
11	Other commodities	50 %

Article 325at

Intra-bucket correlations for commodity risk

The correlation parameter ρk l between two sensitivities WSk and WSl within the same bucket shall be set as follows:

The intra-bucket correlations ρkl ^(commodity) are:

Bucket number	Bucket name	Correlation ρkl (commodity)
1	Energy - solid combustibles	55 %
2	Energy - liquid combustibles	95 %
3	Energy - electricity and carbon trading	40 %
4	Freight	80 %
5	Metals – non-precious	60 %
6	Gaseous combustibles	65 %
7	Precious metals (including gold)	55 %
8	Grains and oilseed	45 %
9	Livestock and dairy	15 %
10	Softs and other agricultural commodities	40 %
11	Other commodity	15 %

Notwithstanding paragraph 1, the following provisions apply:

(a) two risk factors that are allocated to bucket 3 in Table 10 and that concern electricity which is generated in different regions or is delivered at different periods under the contractual agreement shall be considered distinct commodity risk factors;

(b) two risk factors that are allocated to bucket 4 in Table 10 and that concern freight where the freight route or week of delivery differ shall be considered distinct commodity risk factors.

Article 325au

Correlations across buckets for commodity risk

The correlation parameter γb c applying to the aggregation of sensitivities between different buckets shall be set at:

(a) 20 % where the two buckets fall within bucket numbers 1 to 10;

(b) 0 % where either of the two buckets is bucket number 11.

Article 325av

Risk weights for foreign exchange risk

The risk weight of the foreign exchange risk factors concerning currency pairs which are composed of the euro and the currency of a Member State participating in the second stage of the economic and monetary union (ERM II) shall be one of the following:

(a) the risk weight referred to in paragraph 1, divided by 3;

(b) the maximum fluctuation within the fluctuation band formally agreed by the Member State and the European Central Bank, if that fluctuation band is narrower than the fluctuation band defined under ERM II.

Article 325aw

Correlations for foreign exchange risk

A uniform correlation parameter γb c equal to 60 % shall apply to the aggregation of sensitivities to foreign exchange risk factors.

Subsection 2

Vega and curvature risk weights and correlations

Article 325ax

Vega and curvature risk weights

Risk weights for sensitivities to vega risk factors shall be assigned in accordance with the risk class of the risk factors, as follows:

Risk class	Risk weights
GIRR	100 %
CSR non-securitisations	100 %
CSR securitisations (ACTP)	100 %
CSR securitisations (non-ACTP)	100 %
Equity (large cap and indices)	77,78 %
Equity (small cap and other sector)	100 %
Commodity	100 %
Foreign exchange	100 %

Article 325ay

Vega and curvature risk correlations

Between vega risk sensitivities within the same bucket of the general interest rate risk (GIRR) class, the correlation parameter ρkl shall be set as follows:.

where:

Between vega risk sensitivities within a bucket of the other risk classes, the correlation parameter ρkl shall be set as follows:

where:

CHAPTER 1b

Alternative internal model approach

Section 1

Permission and own funds requirements

Article 325az

Alternative internal model approach and permission to use alternative internal models

After having verified institutions' compliance with the requirements set out in Articles 325bh, 325bi and 325bj, competent authorities shall grant permission to those institutions to calculate their own funds requirements for the portfolio of all positions assigned to trading desks by using their alternative internal models in accordance with Article 325ba, provided that all the following requirements are met:

(a) the trading desks were established in accordance with Article 104b;

(b) the institution has provided to the competent authority a rationale for the inclusion of the trading desks in the scope of the alternative internal model approach;

(d) the trading desks have met the profit and loss attribution (‘P&L attribution’) requirements referred to in Article 325bg;

(e) for trading desks that have been assigned at least one of those trading book positions referred to in Article 325bl, the trading desks fulfil the requirements set out in Article 325bm for the internal default risk model;

(f) no securitisation or re-securitisation positions have been assigned to the trading desks;

(g) no positions in CIUs that meet the condition set out in Article 104(8), point (b), have been assigned to the trading desks.

For the purposes of point (b) of the first subparagraph of this paragraph, not including a trading desk in the scope of the alternative internal model approach shall not be motivated by the fact that the own funds requirement calculated under the alternative standardised approach set out in point (a) of Article 325(3) would be lower than the own funds requirement calculated under the alternative internal model approach.

Institutions shall notify the competent authorities of all other extensions and changes to the use of the alternative internal models for which the institution has received permission.

EBA shall develop draft regulatory technical standards to specify:

(a) the conditions for assessing the materiality of extensions and changes to the use of alternative internal models and changes to the subset of the modellable risk factors referred to in Article 325bc;

(b) the assessment methodology under which competent authorities verify an institution’s compliance with the requirements set out in this Chapter.

EBA shall submit those draft regulatory technical standards to the Commission by 28 June 2024.

For the purpose of providing that opinion, EBA shall monitor the market conditions to assess whether extraordinary circumstances have occurred and, where that is the case, shall notify the Commission immediately.

EBA shall submit those draft regulatory technical standards to the Commission by 30 June 2024.

Article 325ba

Own funds requirements when using alternative internal models

An institution using an alternative internal model shall calculate the own funds requirements for the portfolio of all positions assigned to the trading desks for which the institution has been granted permission as referred to in Article 325az(2) as the higher of the following:

(a) the sum of the following values: (i) the institution's previous day's expected shortfall risk measure, calculated in accordance with Article 325bb (ESt-1), and (ii) the institution's previous day's stress scenario risk measure, calculated in accordance with Section 5 (SSt-1); or

(b) the sum of the following values: (i) the average of the institution's daily expected shortfall risk measure, calculated in accordance with Article 325bb for each of the preceding sixty business days (ES^avg), multiplied by the multiplication factor (mc); and (ii) the average of the institution's daily stress scenario risk measure, calculated in accordance with Section 5 for each of the preceding sixty business days (SS^avg).

Where calculating the own funds requirements for market risk using an internal model in accordance with the first subparagraph, an institution shall not include its own credit spreads in the calculation of the measures referred to in points (a) and (b) for positions in the institution’s own debt instruments.

Institutions holding positions in traded debt and equity instruments that are included in the scope of the internal default risk model and assigned to the trading desks referred to in paragraph 1 shall fulfil an additional own funds requirement, expressed as the higher of the following values:

(a) the most recent own funds requirement for default risk, calculated in accordance with Section 3;

(b) the average of the amount referred to in point (a) over the preceding 12 weeks.

By way of derogation from the first subparagraph, an institution shall not be subject to the additional own funds requirement for the holdings of its own debt instruments.

An institution using an alternative internal model shall calculate the total own funds requirements for market risk for all trading book positions and all non-trading book positions generating foreign exchange risk or commodity risk in accordance with the following formula:

where:

AIMA = the sum of the own funds requirements referred to in paragraphs 1 and 2;

PLAaddon = the additional own funds requirement referred to in Article 325bg(2);

ASAnon–aima = the own funds requirements for market risk as calculated under the alternative standardised approach referred to in Article 325(1), point (a), for the portfolio of trading book positions and non-trading book positions generating foreign exchange risk or commodity risk for which the institution uses the alternative standardised approach to calculate the own funds requirements for market risk;

ASAall portofolio = the own funds requirements for market risk as calculated under the alternative standardised approach referred to in Article 325(1), point (a), for the portfolio of all trading book positions and all non-trading book positions generating foreign exchange risk or commodity risk;

ASAaima = the own funds requirements for market risk as calculated under the alternative standardised approach referred to in Article 325(1), point (a), for the portfolio of trading book positions and non-trading book positions generating foreign exchange risk or commodity risk for which the institution uses the approach referred to in Article 325(1), point (b), to calculate the own funds requirements for market risk.

Section 2

General requirements

Article 325bb

Expected shortfall risk measure

Institutions shall calculate the expected shortfall risk measure referred to in point (a) of Article 325ba(1) for any given date ‘t’ and for any given portfolio of trading book positions and non-trading book positions that are subject to foreign exchange or commodity risk as follows:

where:

Article 325bc

Partial expected shortfall calculations

Institutions shall calculate all the partial expected shortfall measures referred to in Article 325bb(1) as follows:

(a) daily calculations of the partial expected shortfall measures;

(b) at 97,5th percentile, one tailed confidence interval;

(c) for a given portfolio of trading book positions and non-trading book positions that are subject to foreign exchange or commodity risk, institutions shall calculate the partial expected shortfall measure at time ‘t’ in accordance with the following formula: where: PESt = the partial expected shortfall measure at time t; j = the index that denotes the five liquidity horizons listed in the first column of Table 1; LHj = the length of liquidity horizons j as expressed in days in Table 1; T = the base time horizon, where T = 10 days; PESt(T) = the partial expected shortfall measure that is determined by applying scenarios of future shocks with a 10-day time horizon only to the specific set of modellable risk factors of the positions in the portfolio set out in paragraphs 2, 3 and 4 for each partial expected shortfall measure referred to in Article 325bb(1); and PESt(T, j) = the partial expected shortfall measure that is determined by applying scenarios of future shocks with a 10-day time horizon only to the specific set of modellable risk factors of the positions in the portfolio set out in paragraphs 2, 3 and 4 for each partial expected shortfall measure referred to in Article 325bb(1) and of which the effective liquidity horizon, as determined in accordance with Article 325bd(2), is equal or longer than LHj.

Table 1 Liquidity horizon j Length of liquidity horizon j (in days) 1 10 2 20 3 40 4 60 5 120

(a) An institution that no longer meets the requirement referred to in the first paragraph of this point shall immediately notify the competent authorities thereof and shall update the subset of the modellable risk factors within two weeks in order to meet that requirement; where, after two weeks, that institution has failed to meet that requirement, the institution shall revert to the approach set out in Chapter 1a to calculate the own funds requirements for market risk for some trading desks, until that institution is able to demonstrate to the competent authority that it is meeting the requirement set out in the first subparagraph of this point;

(c) the data inputs used to determine the scenarios of future shocks applied to the modellable risk factors referred to in points (a) and (b) of this paragraph shall be calibrated to historical data referred to in point (c) of paragraph 4; those data shall be updated on at least a monthly basis.

(c) the data inputs used to determine the scenarios of future shocks applied to the modellable risk factors referred to in points (a) and (b) shall be calibrated to historical data from the preceding 12-month period; where there is a significant upsurge in the price volatility of a material number of modellable risks factors of an institution's portfolio which are not in the subset of the risk factors referred to in point (a) of paragraph 2, competent authorities may require an institution to use historical data for a period shorter than the preceding 12-months, but such a shorter period shall not be shorter than the preceding six-months; competent authorities shall notify EBA of any decision to require an institution to use historical data from a shorter period than 12 months and shall substantiate that decision.

EBA shall submit those draft regulatory technical standards to the Commission by 10 January 2026.

Article 325bd

Liquidity horizons

An institution shall notify the competent authorities of the trading desks and the broad sub-categories of risk factors to which it decides to apply the treatment referred to in the first subparagraph.

For the purpose of calculating the partial expected shortfall measures in accordance with point (c) of Article 325bc(1), the effective liquidity horizon of a given modellable risk factor of a given trading book position or a non-trading book position that is subject to foreign exchange or commodity risk shall be calculated as follows:

EffectiveLH =		SubCatLH if Mat > LH5

min (SubCatLH, minj{LHj/LHj ≥ Mat}) if LH1 ≤ Mat ≤ LH5
LH1 if Mat < LH1

where:

EBA shall develop draft regulatory technical standards to specify:

(a) how institutions are to map the risk factors of the positions referred to in paragraph 1 to broad categories of risk factors and broad sub-categories of risk factors for the purposes of paragraph 1;

(b) which currencies constitute the most liquid currencies sub-category of the broad category of interest rate risk factor of Table 2;

(c) which currency pairs constitute the most liquid currency pairs sub-category of the broad category of foreign exchange risk factor of Table 2;

(d) the definitions of small market capitalisation and large market capitalisation for the purposes of the equity price and volatility sub-category of the broad category of equity risk factor of Table 2.

EBA shall submit those draft regulatory technical standards to the Commission by 28 March 2020.

Broad categories of risk factors	Broad sub-categories of risk factors	Liquidity horizons	Length of the liquidity horizon (in days)
Interest rate	Most liquid currencies and domestic currency	1	10
Other currencies (excluding most liquid currencies)	2	20
Volatility	4	60
Other types	4	60
Credit spread	Central government, including central banks, of Member States	2	20
Covered bonds issued by credit institutions in Member States (Investment Grade)	2	20
Sovereign (Investment grade)	2	20
Sovereign (High yield)	3	40
Corporate (Investment grade)	3	40
Corporate (High yield)	4	60
Volatility	5	120
Other types	5	120
Equity	Equity price (Large market capitalisation)	1	10
Equity price (Small market capitalisation)	2	20
Volatility (Large market capitalisation)	2	20
Volatility (Small market capitalisation)	4	60
Other types	4	60
Foreign exchange	Most liquid currency pairs	1	10
Other currency pairs (excluding most liquid currency pairs)	2	20
Volatility	3	40
Other types	3	40
Commodity	Energy price and carbon emissions price	2	20
Precious metal price and non-ferrous metal price	2	20
Other commodity prices (excluding energy price, carbon emissions price, precious metal price and non-ferrous metal price)	4	60
Energy volatility and carbon emissions volatility	4	60
Precious metal volatility and non-ferrous metal volatility	4	60
Other commodity volatilities (excluding energy volatility, carbon emissions volatility, precious metal volatility and non-ferrous metal volatility)	5	120
Other types	5	120

Article 325be

Assessment of the modellability of risk factors

For the purposes of the assessment referred to in first subparagraph, competent authorities may allow institutions to use market data provided by third-party vendors.

In extraordinary circumstances, occurring during periods of significant reduction in certain trading activities across financial markets, competent authorities may allow institutions using the approach set out in this Chapter to consider as modellable risk factors that have been assessed as not modellable by those institutions in accordance with paragraph 1, provided that the following conditions are met:

(a) the risk factors subject to the treatment correspond to the trading activities which are significantly reduced across financial markets;

(b) the treatment is applied temporarily, and for not more than six months within one financial year;

(c) the treatment does not significantly reduce the total own funds requirements for market risk of the institutions applying it;

(d) competent authorities immediately notify EBA of any decision to allow institutions to apply the approach set out in this Chapter to consider as modellable risk factors that have been assessed as non-modellable, as well as of the trading activities concerned, and substantiate that decision.

EBA shall submit those draft regulatory technical standards to the Commission by 10 July 2025.

Article 325bf

Regulatory back-testing requirements and multiplication factors

For the purposes of this Article, an ‘overshooting’ means a one-day change in the value of a portfolio composed of all the positions assigned to the trading desk that exceeds the related value-at-risk number calculated on the basis of the institution's alternative internal model in accordance with the following requirements:

(a) the calculation of the value at risk shall be subject to a one-day holding period;

(b) scenarios of future shocks shall apply to the risk factors of the trading desk's positions referred to in Article 325bg(3) and which are considered modellable in accordance with Article 325be;

(c) data inputs used to determine the scenarios of future shocks applied to the modellable risk factors shall be calibrated to historical data referred to in point (c) of Article 325bc(4);

(d) unless stated otherwise in this Article, the institution's alternative internal model shall be based on the same modelling assumptions as those used for the calculation of the expected shortfall risk measure referred to in point (a) of Article 325ba(1).

An institution's trading desk shall be deemed to meet the back-testing requirements where the number of overshootings for that trading desk that occurred over the most recent 250 business days does not exceed any of the following:

(a) 12 overshootings for the value-at-risk number, calculated at a 99th percentile one tailed-confidence interval on the basis of back-testing of the hypothetical changes in the value of the portfolio;

(b) 12 overshootings for the value-at-risk number, calculated at a 99th percentile one tailed-confidence interval on the basis of back-testing of the actual changes in the value of the portfolio;

(c) 30 overshootings for the value-at-risk number, calculated at a 97,5th percentile one tailed-confidence interval on the basis of back-testing of the hypothetical changes in the value of the portfolio;

(d) 30 overshootings for the value-at-risk number, calculated at a 97,5th percentile one tailed-confidence interval on the basis of back-testing of the actual changes in the value of the portfolio.

Institutions shall count daily overshootings in accordance with the following:

(a) the back-testing of hypothetical changes in the value of the portfolio shall be based on a comparison between the end-of-day value of the portfolio and, assuming unchanged positions, the value of the portfolio at the end of the subsequent day;

(b) the back-testing of actual changes in the value of the portfolio shall be based on a comparison between the end-of-day value of the portfolio and its actual value at the end of the subsequent day, excluding fees and commissions;

(c) an overshooting shall be counted for each business day for which the institution is not able to assess the value of the portfolio or is not able to calculate the value-at-risk number referred to in paragraph 3.

The multiplication factor (mc) shall be equal to at least the sum of 1,5 and an add-on determined in accordance with Table 3. For the portfolio referred to in paragraph 5, that add-on shall be calculated on the basis of the number of overshootings that occurred over the most recent 250 business days as evidenced by the institution’s back-testing of the value-at-risk number calculated in accordance with point (a) of this subparagraph. The calculation of the add-on shall be subject to the following requirements:

(a) an overshooting shall be a one-day change in the portfolio's value that exceeds the related value-at-risk number calculated by the institution's internal model in accordance with the following: (i) a one-day holding period; (ii) a 99th percentile, one tailed confidence interval; (iii) scenarios of future shocks shall apply to the risk factors of the trading desks' positions referred to in Article 325bg(3) and which are considered modellable in accordance with Article 325be; (iv) the data inputs used to determine the scenarios of future shocks applied to the modellable risk factors shall be calibrated to historical data referred to in point (c) of Article 325bc(4); (v) unless stated otherwise in this Article, the institution's internal model shall be based on the same modelling assumptions as those used for the calculation of the expected shortfall risk measure referred to in point (a) of Article 325ba(1);

(b) the number of overshootings shall be equal to the greater of the number of overshootings under hypothetical and the actual changes in the value of the portfolio. Table 3 Number of overshootings Add-on Fewer than 5 0,00 5 0,20 6 0,26 7 0,33 8 0,38 9 0,42 More than 9 0,50

In extraordinary circumstances, competent authorities may permit an institution to do one or both of the following:

(a) limit the calculation of the add-on to that resulting from overshootings under the back-testing of hypothetical changes where the number of overshootings under the back-testing of actual changes does not result from deficiencies in the institution’s alternative internal model;

(b) exclude the overshootings evidenced by the back-testing of hypothetical or actual changes from the calculation of the add-on where those overshootings do not result from deficiencies in the institution’s alternative internal model.

For the purposes of the first subparagraph, competent authorities may increase the value of mc above the sum referred to in that subparagraph, where an institution’s alternative internal model shows deficiencies preventing the appropriate measurement of the own funds requirements for market risk.

EBA shall submit those draft regulatory technical standards to the Commission by 28 March 2020.

EBA shall submit those draft regulatory technical standards to the Commission by 10 July 2026.

Article 325bg

Profit and loss attribution requirement

EBA shall develop draft regulatory technical standards to specify:

(a) the criteria specifying whether the theoretical changes in the value of a trading desk’s portfolio are either close or sufficiently close to the hypothetical changes in the value of a trading desk’s portfolio for the purposes of paragraph 1, taking into account international regulatory developments;

(b) the additional own funds requirement referred to in paragraph 2;

(d) the technical elements to be included in the theoretical and hypothetical changes in the value of a trading desk's portfolio for the purposes of this Article;

EBA shall submit those draft regulatory technical standards to the Commission by 10 July 2025.

Article 325bh

Requirements on risk measurement

Institutions using an internal risk-measurement model that is used to calculate the own funds requirements for market risk as referred to in Article 325ba shall ensure that that model meets all the following requirements:

(a) the internal risk-measurement model shall capture a sufficient number of risk factors, which shall include at least the risk factors referred to in Subsection 1 of Section 3 of Chapter 1a unless the institution demonstrates to the competent authorities that the omission of those risk factors does not have a material impact on the results of the P&L attribution requirement referred to in Article 325bg; an institution shall be able to explain to the competent authorities why it has incorporated a risk factor in its pricing model but not in its internal risk-measurement model;

(b) the internal risk-measurement model shall capture nonlinearities for options and other products as well as correlation risk and basis risk;

(c) the internal risk-measurement model shall incorporate a set of risk factors that correspond to the interest rates in each currency in which the institution has interest rate sensitive on- or off-balance-sheet positions; the institution shall model the yield curves using one of the generally accepted approaches; the yield curve shall be divided into various maturity segments to capture the variations of volatility of rates along the yield curve; for material exposures to interest-rate risk in the major currencies and markets, the yield curve shall be modelled using a minimum of six maturity segments, and the number of risk factors used to model the yield curve shall be proportionate to the nature and complexity of the institution's trading strategies, the model shall also capture the risk spread of less than perfectly correlated movements between different yield curves or different financial instruments on the same underlying issuer;

(d) the internal risk-measurement model shall incorporate risk factors corresponding to gold and to the individual foreign currencies in which the institution’s positions are denominated; for CIUs, the actual foreign exchange positions of the CIU shall be taken into account; institutions may rely on third-party reporting of the foreign exchange position of the CIU, provided that the correctness of that report is adequately ensured;

(e) the sophistication of the modelling technique shall be proportionate to the materiality of the institutions' activities in the equity markets; the internal risk-measurement model shall use a separate risk factor at least for each of the equity markets in which the institution holds significant positions and at least one risk factor that captures systemic movements in equity prices and the dependency of that risk factor on the individual risk factors for each equity market;

(f) the internal risk-measurement model shall use a separate risk factor at least for each commodity in which the institution holds significant positions, unless the institution has a small aggregate commodity position compared to all its trading activities, in which case it may use a separate risk factor for each broad commodity type; for material exposures to commodity markets, the model shall capture the risk of less than perfectly correlated movements between commodities that are similar, but not identical, the exposure to changes in forward prices arising from maturity mismatches, and the convenience yield between derivative and cash positions;

(g) the proxies used shall show a good track record for the actual position held, shall be appropriately conservative, and shall be used only where the available data are insufficient, such as during the period of stress referred to in point (c) of Article 325bc(2);

(h) for material exposures to volatility risks in instruments with optionality, the internal risk-measurement model shall capture the dependency of implied volatilities across strike prices and options' maturities;

(i) for positions in CIUs, institutions shall look through the underlying positions of the CIUs at least on a weekly basis to calculate their own funds requirements in accordance with this Chapter; where the look-through approach is carried out weekly, institutions shall be able to monitor the risks resulting from significant changes in the composition of the CIU; institutions that do not have adequate data inputs or information to calculate the own funds requirements for market risk of a CIU position in accordance with the look-through approach may rely on a third party to obtain those data inputs or information, provided that all of the following conditions are met: (i) the third party is one of the following: (1) the depository institution or the depository financial institution of the CIU, provided that the CIU exclusively invests in securities and deposits all securities at that depository institution or depository financial institution; (2) the CIU management company, provided that it meets the criteria set out in Article 132(3), point (a); (3) a third-party vendor on the condition that the data, information or risk metrics are provided or calculated by the third parties referred to in point (1) or (2) of this point or another such third-party vendor; (ii) the third party provides the institution with the data, information or risk metrics to calculate the own funds requirements for market risk of the CIU position in accordance with the look-through approach referred to in the first subparagraph; (iii) an external auditor of the institution has confirmed the adequacy of the third party data, information or risk metrics referred to in point (ii) and the competent authority has unrestricted access to those data, information or risk metrics upon request.

Article 325bi

Qualitative requirements

Any internal risk-measurement model used for the purposes of this Chapter shall be conceptually sound, shall be calculated and implemented with integrity, and shall comply with all the following qualitative requirements:

(a) any internal risk-measurement model used to calculate capital requirements for market risk shall be closely integrated into the daily risk management process of the institution and shall serve as the basis for reporting risk exposures to senior management;

(b) an institution shall have a risk control unit that is independent from business trading units and that reports directly to senior management; that unit shall: (i) be responsible for designing and implementing any internal risk-measurement model used in the alternative internal model approach for the purposes of this Chapter; (ii) be responsible for the overall risk management system; (iii) produce and analyse daily reports on the output of any internal model used to calculate own funds requirements for market risk, and on the appropriateness of measures to be taken in terms of trading limits;

(c) the management body and senior management shall be actively involved in the risk-control process, and the daily reports produced by the risk control unit shall be reviewed at a level of management with sufficient authority to require the reduction of positions taken by individual traders and to require the reduction of the institution's overall risk exposure;

(d) the institution shall have a sufficient number of staff with a level of skills that is appropriate to the sophistication of the internal risk-measurement models, and a sufficient number of staff with skills in the trading, risk control, audit and back-office areas;

(e) the institution shall have in place a documented set of internal policies, procedures and controls for monitoring and ensuring compliance with the overall operation of its internal risk-measurement models;

(f) any internal risk-measurement model, including any pricing model, shall have a proven track record of being reasonably accurate in measuring risks, and shall not differ significantly from the models that the institution uses for its internal risk management;

(g) the institution shall frequently conduct rigorous programmes of stress testing, including reverse stress tests, which shall encompass any internal risk-measurement model; the results of those stress tests shall be reviewed by senior management at least on a monthly basis and shall comply with the policies and limits approved by the management body; the institution shall take appropriate actions where the results of those stress tests show excessive losses arising from the trading's business of the institution under certain circumstances;

(h) the institution shall conduct an independent review of its internal risk-measurement models, either as part of its regular internal auditing process, or by mandating a third-party undertaking to conduct that review, which shall be conducted to the satisfaction of the competent authorities.

A validation unit, which is separate from the risk control unit referred to in the first subparagraph, point (b), shall conduct the initial and ongoing validation of any internal risk-measurement model used in the alternative internal model approach for the purposes of this Chapter.

For the purposes of point (h) of the first subparagraph, a third-party undertaking means an undertaking that provides auditing or consulting services to institutions and that has staff who have sufficient skills in the area of market risk in trading activities.

The review referred to in point (h) of paragraph 1 shall include both the activities of the business trading units and the independent risk control unit. The institution shall conduct a review of its overall risk management process at least once a year. That review shall assess the following:

(a) the adequacy of the documentation of the risk management system and process and the organisation of the risk control unit;

(b) the integration of risk measures into daily risk management and the integrity of the management information system;

(c) the processes the institution employs for approving the risk-pricing models and valuation systems that are used by front and back-office personnel;

(d) the scope of risks captured by the model, the accuracy and appropriateness of the risk-measurement system, and the validation of any significant changes to the internal risk-measurement model;

(e) the accuracy and completeness of position data, the accuracy and appropriateness of volatility and correlation assumptions, the accuracy of valuation and risk sensitivity calculations, and the accuracy and appropriateness for generating data proxies where the available data are insufficient to meet the requirement set out in this Chapter;

(f) the verification process that the institution employs to evaluate the consistency, timeliness and reliability of the data sources used to run any of its internal risk-measurement models, including the independence of those data sources;

(g) the verification process that the institution employs to evaluate back-testing requirements and P&L attribution requirements that are conducted in order to assess the accuracy of its internal risk-measurement models;

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