(90)

in Title IV of Part Three, the following Chapters are inserted: ‘ CHAPTER 1a Alternative standardised approach Section 1 General provisions Article 325c Scope and structure of the alternative standardised approach 1. The alternative standardised approach as set out in this Chapter shall be used only for the purposes of the reporting requirement laid down in Article 430b(1). 2. Institutions shall calculate the own funds requirements for market risk in accordance with the alternative standardised approach for a portfolio of trading book positions or non-trading book positions that are subject to foreign exchange or commodity risk as the sum of the following three components: Section 2 Sensitivities-based method for calculating the own funds requirement Article 325d Definitions For the purposes of this Chapter, the following definitions apply: Article 325e Components of the sensitivities-based method 1. Institutions shall calculate the own funds requirement for market risk under the sensitivities-based method by aggregating the following three own funds requirements in accordance with Article 325h: 2. For the purpose of the calculation referred to in paragraph 1, For the purposes of this Chapter, instruments with optionality include, among others: calls, puts, caps, floors, swap options, barrier options and exotic options. Embedded options, such as prepayment or behavioural options, shall be considered to be stand-alone positions in options for the purpose of calculating the own funds requirements for market risk. For the purposes of this Chapter, instruments whose cash flows can be written as a linear function of the underlying's notional amount shall be considered to be instruments without optionality. Article 325f Own funds requirements for delta and vega risks 1. Institutions shall apply the delta and vega risk factors described in Subsection 1 of Section 3 to calculate the own funds requirements for delta and vega risks. 2. Institutions shall apply the process set out in paragraphs 3 to 8 to calculate own funds requirements for delta and vega risks. 3. For each risk class, the sensitivity of all instruments in scope of the own funds requirements for delta or vega risks to each of the applicable delta or vega risk factors included in that risk class shall be calculated by using the corresponding formulas in Subsection 2 of Section 3. If the value of an instrument depends on several risk factors, the sensitivity shall be determined separately for each risk factor. 4. Sensitivities shall be assigned to one of the buckets ‘b’ within each risk class. 5. Within each bucket ‘b’, the positive and negative sensitivities to the same risk factor shall be netted, giving rise to net sensitivities (sk) to each risk factor k within a bucket. 6. The net sensitivities to each risk factor within each bucket shall be multiplied by the corresponding risk weights set out in Section 6, giving rise to weighted sensitivities to each risk factor within that bucket in accordance with the following formula: 7. The weighted sensitivities to the different risk factors within each bucket shall be aggregated in accordance with the formula below, where the quantity within the square root function is floored at zero, giving rise to the bucket-specific sensitivity. The corresponding correlations for weighted sensitivities within the same bucket (ρkl), set out in Section 6, shall be used. 8. The bucket-specific sensitivity shall be calculated for each bucket within a risk class in accordance with paragraphs 5, 6 and 7. Once the bucket-specific sensitivity has been calculated for all buckets, weighted sensitivities to all risk factors across buckets shall be aggregated in accordance with the formula below, using the corresponding correlations γbc for weighted sensitivities in different buckets set out in Section 6, giving rise to the risk-class specific own funds requirement for delta or vega risk: where: The risk-class specific own funds requirements for delta or vega risk shall be calculated for each risk class in accordance with paragraphs 1 to 8. Article 325g Own funds requirements for curvature risk Institutions shall calculate the own funds requirements for curvature risk in accordance with the delegated act referred to in Article 461a. Article 325h Aggregation of risk-class specific own funds requirements for delta, vega and curvature risks 1. Institutions shall aggregate risk-class specific own funds requirements for delta, vega and curvature risks in accordance with the process set out in paragraphs 2, 3 and 4. 2. The process to calculate the risk-class specific own funds requirements for delta, vega and curvature risks described in Articles 325f and 325g shall be performed three times per risk class, each time using a different set of correlation parameters ρkl (correlation between risk factors within a bucket) and γbc (correlation between buckets within a risk class). Each of those three sets shall correspond to a different scenario, as follows: 3. Institutions shall calculate the sum of the delta, vega and curvature risk-class specific own funds requirements for each scenario to determine three scenario-specific, own funds requirements. 4. The own funds requirement under the sensitivities-based method shall be the highest of the three scenario-specific own funds requirements referred to in paragraph 3. Article 325i Treatment of index instruments and multi-underlying options Institutions shall treat the index instruments and multi-underlying options in accordance with the delegated act referred to in Article 461a. Article 325j Treatment of collective investment undertakings Institutions shall treat the collective investment undertakings in accordance with the delegated act referred to in Article 461a. Article 325k Underwriting positions 1. Institutions may use the process set out in this Article for calculating the own funds requirements for market risk of underwriting positions of debt or equity instruments. 2. 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. Table 1 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. 3. Institutions shall notify the competent authorities of the application of the process set out in this Article. Section 3 Risk factor and sensitivity definitions Subsection 1 Risk factor definitions Article 325l General interest rate risk factors 1. For all general interest rate risk factors, including inflation risk and cross-currency basis risk, there shall be one bucket per currency, each containing different types of risk factor. 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. 2. Institutions shall obtain the risk-free rates per currency from money market instruments held in the trading book of the institution that have the lowest credit risk, such as overnight index swaps. 3. Where institutions cannot apply the approach referred to in paragraph 2, the risk-free rates shall be based on one or more market-implied swap curves used by the institution to mark positions to market, such as the interbank offered rate swap curves. 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. 4. In the case of general interest rate risk factors, each currency shall constitute a separate bucket. Institutions shall assign risk factors within the same bucket, but with different maturities, a different risk weight, in accordance with Section 6. 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. 5. Institutions shall calculate the sensitivity of the instrument to the additional risk factor for inflation risk referred to in paragraph 4 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, institutions shall treat inflation as a single risk factor, regardless of the number of components of each vector. Institutions shall offset all sensitivities to inflation within a bucket, calculated as described in this paragraph, in order to give rise to a single net sensitivity per bucket. 6. Debt instruments that involve payments in different currencies shall also be subject to cross-currency basis risk between those currencies. For the purposes of the sensitivities-based method, the risk factors to be applied by institutions shall be the cross-currency basis risk of each currency over either US dollar or euro. Institutions shall compute cross currency bases that do not relate to either basis over US dollar or basis over euro either on ‘basis over US dollar’ or ‘basis over euro’. 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. 7. The vega general interest rate risk factors applicable to options with underlyings that are sensitive to general interest rate shall be the implied volatilities of the relevant risk-free rates as described in paragraphs 2 and 3, which shall be assigned to buckets depending on the currency and mapped to the following maturities within each bucket: 0,5 years, 1 year, 3 years, 5 years, 10 years. There shall be one bucket per currency. 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: 8. The curvature general interest rate risk factors to be applied by institutions shall consist of one vector of risk-free rates, representing a specific risk-free yield curve, per currency. Each currency shall constitute a different bucket. For each instrument, the vector shall contain as many components as there are different maturities of risk-free rates used as variables by the institution's pricing model for that instrument. 9. Institutions shall calculate the sensitivity of the instrument to each risk factor used in the curvature risk formula in accordance with Article 325g. For the purposes of the curvature risk, institutions shall consider vectors corresponding to different yield curves and with a different number of components as the same risk factor, provided that those vectors correspond to the same currency. Institutions shall offset sensitivities to the same risk factor. There shall be only one net sensitivity per bucket. 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 1. The delta credit spread risk factors to be applied by institutions to non-securitisation instruments that are sensitive to credit spread shall be the issuer credit spread rates of those instruments, inferred from the relevant debt instruments and credit default swaps, and mapped to each of the following maturities: 0,5 years, 1 year, 3 years, 5 years, 10 years. Institutions shall apply one risk factor per issuer and maturity, regardless of whether those issuer credit spread rates are inferred from debt instruments or credit default swaps. The buckets shall be sector buckets, as referred to in Section 6, and each bucket shall include all the risk factors allocated to the relevant sector. 2. The vega credit spread risk factors to be applied by institutions to options with non-securitisation underlyings that are sensitive to credit spread shall be the implied volatilities of the underlying's issuer credit spread rates inferred as laid down in paragraph 1, which shall be 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. The same buckets shall be used as the buckets that were used for the delta credit spread risk for non-securitisation. 3. The curvature credit spread risk factors to be applied by institutions to non-securitisation instruments shall consist of one vector of credit spread rates, representing a credit spread curve specific to the issuer. For each instrument, the vector shall contain as many components as there are different maturities of credit spread rates used as variables in the institution's pricing model for that instrument. The same buckets shall be used as the buckets that were used for the delta credit spread risk for non-securitisation. 4. Institutions shall calculate the sensitivity of the instrument to each risk factor used in the curvature risk formula in accordance with Article 325g. For the purposes of the curvature risk, institutions shall consider vectors inferred from either relevant debt instruments or credit default swaps and with a different number of components as the same risk factor, provided that those vectors correspond to the same issuer. Article 325n Credit spread risk factors for securitisation 1. Institutions shall apply the credit spread risk factors referred to in paragraph 3 to securitisation positions that are included in the ACTP, as referred to in Article 325(6), (7) and (8), 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). 2. The buckets applicable to the credit spread risk for securitisations that are included in the ACTP shall be the same as the buckets applicable to the credit spread risk for non-securitisations, as referred to in Section 6. 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. 3. The credit spread risk factors to be applied by institutions to securitisation positions that are included in the ACTP are the following: 4. Institutions shall calculate the sensitivity of the securitisation position to each risk factor used in the curvature risk formula as specified in Article 325g. For the purposes of the curvature risk, institutions shall consider vectors inferred either from relevant debt instruments or credit default swaps and with a different number of components as the same risk factor, provided that those vectors correspond to the same issuer. 5. 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: Article 325o Equity risk factors 1. The buckets for all equity risk factors shall be the sector buckets referred to in Section 6. 2. The equity delta risk factors to be applied by institutions shall be all the equity spot prices and all equity repo rates. 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. 3. The equity vega risk factors to be applied by institutions to options with underlyings that are sensitive to equity shall be the implied volatilities of equity spot prices which shall be mapped to the following maturities in accordance with the maturities of the corresponding options subject to own funds requirements: 0,5 years, 1 year, 3 years, 5 years, 10 years. There shall be no own funds requirements for vega risk for equity repo rates. 4. The equity curvature risk factors to be applied by institutions to options with underlyings that are sensitive to equity are all the equity spot prices, regardless of the maturity of the corresponding options. There shall be no curvature risk own funds requirements for equity repo rates. Article 325p Commodity risk factors 1. The buckets for all commodity risk factors shall be the sector buckets referred to in Section 6. 2. The commodity delta risk factors to be applied by institutions to commodity sensitive instruments shall be all the commodity spot prices per commodity type 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 only consider two commodity prices of the same type of commodity, and with the same maturity to constitute the same risk factor where the set of legal terms regarding the delivery location are identical. 3. The commodity vega risk factors to be applied by institutions to options with underlyings that are sensitive to commodity shall be the implied volatilities of commodity prices per commodity type, which shall be mapped to the following maturities in accordance with the maturities of the corresponding options subject to own funds requirements: 0,5 years, 1 year, 3 years, 5 years, 10 years. Institutions shall consider sensitivities to the same commodity type and allocated to the same maturity to be a single risk factor which institutions shall then offset. 4. The commodity curvature risk factors to be applied by institutions to options with underlyings that are sensitive to commodity shall be one set of commodity prices with different maturities per commodity type, expressed as a vector. For each instrument, the vector shall contain as many components as there are prices of that commodity that are used as variables by the institution's pricing model for that instrument. Institutions shall not differentiate between commodity prices by delivery location. 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 1. The foreign exchange delta risk factors to be applied by institutions to foreign exchange sensitive instruments shall be all the spot exchange rates between the currency in which an instrument is denominated and the institution's reporting currency. There shall be one bucket per currency pair, containing a single risk factor and a single net sensitivity. 2. The foreign exchange vega risk factors to be applied by institutions to options with underlyings that are sensitive to foreign exchange shall be the implied volatilities of exchange rates between the currency pairs referred to in paragraph 1. Those implied volatilities of exchange rates shall be mapped to the following maturities in accordance with the maturities of the corresponding options subject to own funds requirements: 0,5 years, 1 year, 3 years, 5 years, 10 years. 3. The foreign exchange curvature risk factors to be applied by institutions to options with underlyings that are sensitive to foreign exchange shall be the same as those referred to in paragraph 1. 4. Institutions shall not be required to distinguish between onshore and offshore variants of a currency for all foreign exchange delta, vega and curvature risk factors. Subsection 2 Sensitivity definitions Article 325r Delta risk sensitivities 1. Institutions shall calculate delta general interest rate risk (GIRR) sensitivities as follows: 2. Institutions shall calculate the delta credit spread risk sensitivities for all securitisation and non-securitisation positions as follows: where: 3. Institutions shall calculate delta equity risk sensitivities as follows: 4. Institutions shall calculate the delta commodity risk sensitivities to each risk factor k as follows: where: 5. Institutions shall calculate the delta foreign exchange risk sensitivities to each foreign exchange risk factor k as follows: where: Article 325s Vega risk sensitivities 1. Institutions shall calculate the vega risk sensitivity of an option to a given risk factor k as follows: where: 2. In the case of risk classes where vega risk factors have a maturity dimension, but where the rules to map the risk factors are not applicable because the options do not have a maturity, institutions shall map those risk factors to the longest prescribed maturity. Those options shall be subject to the residual risks add-on. 3. In the case of options that do not have a strike or barrier and options that have multiple strikes or barriers, institutions shall apply the mapping to strikes and maturity used internally by the institution to price the option. Those options shall also be subject to the residual risks add-on. 4. Institutions shall not calculate the vega risk for securitisation tranches included in the ACTP, as referred to in Article 325(6), (7) and (8), that do not have an implied volatility. Own funds requirements for delta and curvature risk shall be computed for those securitisation tranches. Article 325t Requirements on sensitivity computations 1. Institutions shall derive sensitivities from the institution's pricing models that serve as a basis for reporting profit and loss to senior management, using the formulas set out in this Subsection. By way of derogation from the first subparagraph, 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 calculation and reporting of the own funds requirements for market risk in accordance with Article 430b(3). 2. When calculating delta risk sensitivities of instruments with optionality as referred to in point (a) of Article 325e(2), institutions may assume that the implied volatility risk factors remain constant. 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: 4. Institutions shall calculate all sensitivities except for the sensitivities to credit valuation adjustments. 5. 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: 6. 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: Section 4 The residual risk add-on Article 325u Own funds requirements for residual risks 1. In addition to the own funds requirements for market risk set out in Section 2, institutions shall apply additional own funds requirements to instruments exposed to residual risks in accordance with this Article. 2. Instruments are considered to be exposed to residual risks where they meet any of the following conditions: 3. 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: 4. 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: 5. EBA shall develop draft regulatory technical standards to specify what an exotic underlying is and which instruments are instruments bearing residual risks for the purposes of paragraph 2. 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. Section 5 Own funds requirements for the default risk Article 325v Definitions and general provisions 1. For the purposes of this Section, the following definitions apply: 2. Own funds requirements for the default risk shall apply to debt and equity instruments, to derivative instruments having those instruments as underlyings and to derivatives, the pay-offs or fair values of which are affected by the default of an obligor other than the counterparty to the derivative instrument itself. Institutions shall calculate default risk requirements separately for each of the following types of instruments: non-securitisations, securitisations that are not included in the ACTP, and securitisations that are included in the ACTP. The final own funds requirements for the default risk to be applied by institutions shall be the sum of those three components. Subsection 1 Own funds requirements for the default risk for non-securitisations Article 325w Gross jump-to-default amounts 1. Institutions shall calculate the gross JTD amounts for each long exposure to debt instruments as follows: 2. Institutions shall calculate the gross JTD amounts for each short exposure to debt instruments as follows: 3. 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: 4. For the purposes of the calculations set out in paragraphs 1 and 2, notional amounts shall be determined as follows: 5. For exposures to equity instruments, institutions shall calculate the gross JTD amounts as follows, instead of using the formulas referred to in paragraphs 1 and 2: 6. Institutions shall assign an LGD of 100 % to equity instruments for the purposes of the calculation set out in paragraph 5. 7. In the case of exposures to default risk arising from derivative instruments whose pay-offs in the event of default of the obligor are not related to the notional amount of a specific instrument issued by that obligor or to the LGD of the obligor or an instrument issued by that obligor, institutions shall use alternative methodologies to estimate the gross JTD amounts. 8. EBA shall develop draft regulatory technical standards to specify: 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. Article 325x Net jump-to-default amounts 1. Institutions shall calculate net JTD amounts by offsetting the gross JTD amounts of short exposures and long exposures. Offsetting shall only be possible between exposures to the same obligor where the short exposures have the same seniority as, or lower seniority than, the long exposures. 2. Offsetting shall be either full or partial, depending on the maturities of the offsetting exposures: 3. Where no offsetting is possible gross JTD amounts shall equal net JTD amounts in the case of exposures with maturities of one year or more. Gross JTD amounts with maturities of less than one year shall be multiplied by the ratio of the exposure's maturity relative to one year, with a floor of three months, to calculate net JTD amounts. 4. For the purposes of paragraphs 2 and 3, the maturities of the derivative contracts shall be considered, rather than those of their underlyings. Cash equity exposures shall be assigned a maturity of either one year or three months, at the institution's discretion. Article 325y Calculation of the own funds requirements for the default risk 1. 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: Table 2 2. Exposures which would receive a 0 % risk-weight under the Standardised Approach for credit risk in accordance with Chapter 2 of Title II shall receive a 0 % default risk weight for the own funds requirements for the default risk. 3. The weighted net JTD shall be allocated to the following buckets: corporates, sovereigns, and local governments/municipalities. 4. 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. 5. The final own funds requirement for the default risk for non-securitisations shall be calculated as the simple sum of the bucket-level own funds requirements. Subsection 2 Own funds requirements for the default risk for securitisations not included in the ACTP Article 325z Jump-to-default amounts 1. Gross jump-to-default amounts for securitisation exposures shall be their market value or, if their market value is not available, their fair value determined in accordance with the applicable accounting framework. 2. Net jump-to-default amounts shall be determined by offsetting long gross jump-to-default amounts and short gross jump-to-default amounts. Offsetting shall only be possible between securitisation exposures with the same underlying asset pool and belonging to the same tranche. No offsetting shall be permitted between securitisation exposures with different underlying asset pools, even where the attachment and detachment points are the same. 3. Where, by decomposing or combining existing securitisation exposures, other existing securitisation exposures can be perfectly replicated, except for the maturity dimension, the exposures resulting from that decomposition or combination may be used instead of the existing securitisation exposures for the purposes of offsetting. 4. Where, by decomposing or combining existing exposures in underlying names, the entire tranche structure of an existing securitisation exposure can be perfectly replicated, the exposures resulting from that decomposition or combination may be used instead of the existing securitisation exposures for the purposes of offsetting. Where underlying names are used in that manner, they shall be removed from the non-securitisation default risk treatment. 5. Article 325x shall apply to both existing securitisation exposures and to securitisation exposures used in accordance with paragraph 3 or 4 of this Article. The relevant maturities shall be those of the securitisation tranches. Article 325aa Calculation of the own funds requirement for the default risk for securitisations 1. Net JTD amounts of securitisation exposures shall be multiplied by 8 % of the risk weight that applies to the relevant securitisation exposure, including STS securitisations, in the non-trading book in accordance with the hierarchy of approaches set out in Section 3 of Chapter 5 of Title II and irrespective of the type of counterparty. 2. A maturity of one year shall be applied to all tranches, where risk weights are calculated in accordance with the SEC-IRBA and SEC-ERBA. 3. The risk-weighted JTD amounts for individual cash securitisation exposures shall be capped at the fair value of the position. 4. Risk-weighted net JTD amounts shall be assigned to the following buckets: 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. 5. In order to assign a securitisation exposure to a bucket, institutions shall rely on a classification commonly used in the market. Institutions shall assign each securitisation exposure to only one of the buckets referred to in paragraph 4. Any securitisation exposure that an institution cannot assign to a bucket for an asset class or region shall be assigned to the asset class ‘other retail’ or ‘other wholesale’ or to the region ‘rest of the world’, respectively. 6. Weighted net JTD amounts shall be aggregated within each bucket in the same manner as for default risk of non-securitisation exposures, using the formula in Article 325y(4), resulting in the own funds requirement for the default risk for each bucket. 7. The final own funds requirement for the default risk for securitisations not included in the ACTP shall be calculated as the simple sum of the bucket-level own funds requirements. Subsection 3 Own funds requirements for the default risk for securitisations included in the ACTP Article 325ab Scope 1. For the ACTP, the own funds requirements shall include the default risk for securitisation exposures and for non-securitisation hedges. Those hedges shall be removed from the default risk calculations for non-securitisation. There shall be no diversification benefit between the own funds requirements for the default risk for non-securitisations, the own funds requirements for the default risk for securitisations not included in the ACTP and own funds requirements for the default risk for securitisations included in the ACTP. 2. For traded non-securitisation credit and equity derivatives, JTD amounts by individual constituents shall be determined by applying a look-through approach. Article 325ac Jump-to-default amounts for the ACTP 1. For the purposes of this Article, the following definitions apply: 2. The gross JTD amounts for securitisation exposures and non-securitisation exposures in the ACTP shall be their market value or, if their market value is not available, their fair value determined in accordance with the applicable accounting framework. 3. Nth-to-default products shall be treated as tranched products with the following attachment and detachment points: 4. 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: Article 325ad Calculation of the own funds requirements for the default risk for the ACTP 1. Net JTD amounts shall be multiplied by: 2. Risk-weighted net JTD amounts shall be assigned to buckets that correspond to an index. 3. Weighted net JTD amounts shall be aggregated within each bucket in accordance with the following formula: 4. 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 1. For currencies not included in the most liquid currency sub-category as referred to in point (b) of Article 325bd(7), the risk weights of the sensitivities to the risk-free rate risk factors for each bucket in Table 3 shall be specified pursuant to the delegated act referred to in Article 461a. Table 3 2. A common risk weight both for all the sensitivities to inflation and for cross currency basis risk factors shall be specified in the delegated act referred to in Article 461a. 3. For the currencies included in the most liquid currency sub-category as referred to in point (b) of 325bd(7) and the domestic currency of the institution, the risk weights of the risk-free rate risk factors shall be the risk weights referred to in Table 3 divided by √2. Article 325af Intra bucket correlations for general interest rate risk 1. Between two weighted sensitivities of general interest rate risk factors WSk and WSl within the same bucket, and with the same assigned maturity but corresponding to different curves, correlation ρkl shall be set at 99,90 %. 2. 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: 3. Between two weighted sensitivities of general interest rate risk factors WSk and WSl within the same bucket, corresponding to different curves and having different maturities, the correlation ρkl shall be equal to the correlation parameter specified in paragraph 2, multiplied by 99,90 %. 4. Between any given weighted sensitivity of general interest rate risk factors WSk and any given weighted sensitivity of inflation risk factors WSl, the correlation shall be set at 40 %. 5. Between any given weighted sensitivity of cross-currency basis risk factors WSk and any given weighted sensitivity of general interest rate risk factors WSl, including another cross-currency basis risk factor, the correlation shall be set at 0 %. Article 325ag Correlations across buckets for general interest rate risk 1. The parameter γbc = 50 % shall be used to aggregate risk factors belonging to different buckets. 2. The parameter γbc = 80 % shall be used to aggregate an interest rate risk factor based on a currency as referred to in Article 325av(3) and an interest rate risk factor based on the euro. Article 325ah Risk weights for credit spread risk for non-securitisations 1. 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: Table 4 2. To assign a risk exposure to a sector, institutions shall rely on a classification that is commonly used in the market for grouping issuers by sector. Institutions shall assign each issuer to only one of the sector buckets in Table 4. Risk exposures from any issuer that an institution cannot assign to a sector in such a manner shall be assigned to bucket 18 in Table 4. Article 325ai Intra-bucket correlations for credit spread risk for non-securitisations 1. The correlation parameter ρk l between two sensitivities WS k and WS l within the same bucket shall be set as follows: 2. 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: 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: Table 6 Article 325al Correlations for credit spread risk for securitisations included in the ACTP 1. The delta risk correlation ρk l shall be derived in accordance with Article 325ai, except that, for the purposes of this paragraph, ρk l (basis) shall be equal to 1 where the two sensitivities are related to the same curves, otherwise it shall be equal to 99,00 %. 2. The correlation γb c shall be derived in accordance with Article 325aj. Article 325am Risk weights for credit spread risk for securitisations not included in the ACTP 1. 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: Table 7 2. To assign a risk exposure to a sector, institutions shall rely on a classification that is commonly used in the market for grouping issuers by sector. Institutions shall assign each tranche to one of the sector buckets in Table 7. Risk exposures from any tranche that an institution cannot assign to a sector in such a manner shall be assigned to bucket 25. Article 325an Intra-bucket correlations for credit spread risk for securitisations not included in the ACTP 1. Between two sensitivities WS k and WS l within the same bucket, the correlation parameter ρk l shall be set as follows: 2. 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 1. The correlation parameter γb c shall apply to the aggregation of sensitivities between different buckets and shall be set at 0 %. 2. The own funds requirement for bucket 25 shall be added to the overall risk class level capital, with no diversification or hedging effects recognised with any other bucket. Article 325ap Risk weights for equity risk 1. 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: Table 8 2. For the purposes of this Article, what constitutes a small and a large market capitalisation shall be specified in the regulatory technical standards referred to in Article 325bd(7). 3. For the purposes of this Article, EBA shall develop draft regulatory technical standards to specify what constitutes an emerging market and to specify what constitutes an advanced economy. 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. 4. When assigning a risk exposure to a sector, institutions shall rely on a classification that is commonly used in the market for grouping issuers by sector. Institutions shall assign each issuer to one of the sector buckets in Table 8 and shall assign all issuers from the same industry to the same sector. Risk exposures from any issuer that an institution cannot assign to a sector in such a manner shall be assigned to bucket 11 in Table 8. Multinational or multi-sector equity issuers shall be assigned to a particular bucket on the basis of the most material region and sector in which the equity issuer operates. Article 325aq Intra-bucket correlations for equity risk 1. The delta risk correlation parameter ρkl between two sensitivities WS k and WS l within the same bucket shall be set at 99,90 % where one is a sensitivity to an equity spot price and the other a sensitivity to an equity repo rate, where both are related to the same equity issuer name. 2. In other cases than the cases referred to in paragraph 1, the correlation parameter ρkl between two sensitivities WS k and WS l to equity spot price within the same bucket shall be set as follows: 3. The correlation parameter ρkl between two sensitivities WS k and WS l to equity repo rate within the same bucket shall be set in accordance with paragraph 2. 4. Between two sensitivities WS k and WS l within the same bucket where one is a sensitivity to an equity spot price and the other a sensitivity to an equity repo rate and both sensitivities relate to a different equity issuer name, the correlation parameter ρkl shall be set to the correlation parameters specified in paragraph 2, multiplied by 99,90 %. 5. 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 γb c shall apply to the aggregation of sensitivities between different buckets. It shall be set at 15 % where the two buckets fall within buckets 1 to 10. Article 325as Risk weights for commodity risk Risk weights for sensitivities to commodity risk factors shall be specified for each bucket in Table 9 pursuant to the delegated act referred to in Article 461a: Table 9 Article 325at Intra-bucket correlations for commodity risk 1. For the purposes of this Article, any two commodities shall be considered distinct commodities where there exist in the market two contracts that are differentiated only by the underlying commodity to be delivered against each contract. 2. The correlation parameter ρk l between two sensitivities WS k and WS l within the same bucket shall be set as follows: 3. The intra-bucket correlations ρkl (commodity) are: Table 10 4. Notwithstanding paragraph 1, the following provisions apply: 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: Article 325av Risk weights for foreign exchange risk 1. Risk weight for all sensitivities to foreign exchange risk factors shall be specified in the delegated act referred to in Article 461a. 2. 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: 3. Notwithstanding paragraph 2, the risk weight of the foreign exchange risk factors concerning currencies referred to in paragraph 2 which participate in the ERM II with a formally agreed fluctuation band narrower than the standard band of plus or minus 15 % shall equal the maximum percentage fluctuation within that narrower band. 4. The risk weight of the foreign exchange risk factors included in the most liquid currency pairs sub-category as referred to in point (c) of 325bd(7) shall be the risk weight referred to in paragraph 1 of this Article divided by √2. 5. Where the daily exchange-rate data for the preceding three years show that a currency pair composed of euro and a non-euro currency of a Member State is constant and that the institution is always able to face a zero bid/ask spread on the respective trades related to that currency pair, the institution may apply the risk weight referred to in paragraph 1 divided by 2, provided that it has the express permission of its competent authority to do so. 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 1. Vega risk factors shall use the delta buckets referred to in Subsection 1. 2. The risk weight for a given vega risk factor k shall be determined as a share of the current value of that risk factor k which represents the implied volatility of an underlying, as described in Section 3. 3. The share referred to in paragraph 2 shall be made dependent on the presumed liquidity of each type of risk factor in accordance with the following formula: where: 4. Buckets used in the context of delta risk in Subsection 1 shall be used in the curvature risk context unless specified otherwise in this Chapter. 5. For foreign exchange and equity curvature risk factors, the curvature risk weights shall be relative shifts equal to the delta risk weights referred to in Subsection 1. 6. For general interest rate, credit spread and commodity curvature risk factors, the curvature risk weight shall be the parallel shift of all the vertices for each curve on the basis of the highest prescribed delta risk weight referred to in Subsection 1 for the relevant risk class. Article 325ay Vega and curvature risk correlations 1. Between vega risk sensitivities within the same bucket of the general interest rate risk (GIRR) class, the correlation parameter rkl shall be set as follows: where: 2. Between vega risk sensitivities within a bucket of the other risk classes, the correlation parameter ρkl shall be set as follows: where: 3. With regard to vega risk sensitivities between buckets within a risk class (GIRR and non-GIRR), the same correlation parameters for γbc, as specified for delta correlations for each risk class in Section 4, shall be used in the vega risk context. 4. There shall be no diversification or hedging benefit recognised in the standardised approach between vega risk factors and delta risk factors. Vega risk charges and delta risk charges shall be aggregated by simple summation. 5. The curvature risk correlations shall be the square of corresponding delta risk correlations ρkl and γbc referred to in Subsection 1. 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 1. The alternative internal model approach as set out in this Chapter shall be used only for the purposes of the reporting requirement laid down in Article 430b(3). 2. 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: 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. 3. Institutions that have received the permission to use the alternative internal model approach shall report to the competent authorities in accordance with Article 430b(3). 4. An institution that has been granted the permission referred to in paragraph 2 shall immediately notify its competent authorities that one of its trading desks no longer meets at least one of the requirements set out in that paragraph. That institution shall no longer be permitted to apply this Chapter to any of the positions assigned to that trading desk and shall calculate the own funds requirements for market risk in accordance with the approach set out in Chapter 1a for all the positions assigned to that trading desk from the earliest reporting date and until the institution demonstrates to the competent authorities that the trading desk again fulfils all the requirements set out in paragraph 2. 5. By way of derogation from paragraph 4, in extraordinary circumstances, competent authorities may permit an institution to continue using its alternative internal models for the purpose of calculating the own funds requirements for the market risk of a trading desk that no longer meets the conditions referred to in point (c) of paragraph 2 of this Article and in Article 325bg(1). When competent authorities exercise that discretion, they shall notify EBA and substantiate their decision. 6. For positions assigned to the trading desks for which an institution has not been granted permission as referred to in paragraph 2, the own funds requirements for market risk shall be calculated by that institution in accordance with Chapter 1a of this Title. For the purposes of that calculation, all those positions shall be considered on a stand-alone basis as a separate portfolio. 7. Material changes to the use of alternative internal models that an institution has received permission to use, the extension of the use of alternative internal models that the institution has received permission to use, and material changes to the institution's choice of the subset of the modellable risk factors referred to in Article 325bc(2), shall require separate permission from its competent authorities. 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. 8. EBA shall develop draft regulatory technical standards to specify: EBA shall submit those draft regulatory technical standards to the Commission by 28 June 2024. 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. 9. EBA shall develop draft regulatory technical standards to specify the extraordinary circumstances under which competent authorities may permit an institution: EBA shall submit those draft regulatory technical standards to the Commission by 28 June 2024. 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. Article 325ba Own funds requirements when using alternative internal models 1. 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: 2. 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: Section 2 General requirements Article 325bb Expected shortfall risk measure 1. 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 as follows: where: 2. Institutions shall only apply scenarios of future shocks to the specific set of modellable risk factors applicable to each partial expected shortfall measure, as set out in Article 325bc, when determining each partial expected shortfall measure for the calculation of the expected shortfall risk measure in accordance with paragraph 1. 3. Where at least one transaction of the portfolio has at least one modellable risk factor which has been mapped to the broad risk factor category i in accordance with Article 325bd, institutions shall calculate the unconstrained expected shortfall measure for the broad risk factor category i and include it in the formula for the expected shortfall risk measure referred to in paragraph 1 of this Article. 4. By way of derogation from paragraph 1, an institution may reduce the frequency of the calculation of the unconstrained expected shortfall measures and of the partial expected shortfall measures , and for all broad risk factor categories i from daily to weekly, provided that both of the following conditions are met: Article 325bc Partial expected shortfall calculations 1. Institutions shall calculate all the partial expected shortfall measures referred to in Article 325bb(1) as follows: 2. For the purpose of calculating the partial expected shortfall measures and referred to in Article 325bb(1), in addition to the requirements set out in paragraph 1 of this Article, institutions shall meet the following requirements: 3. For the purpose of calculating the partial expected shortfall measures and referred to in Article 325bb(1), institutions shall, in addition to the requirements set out in paragraph 1 of this Article, meet the following requirements: 4. For the purpose of calculating the partial expected shortfall measures and referred to in Article 325bb(1), institutions shall, in addition to the requirements set out in paragraph 1 of this Article, meet the following requirements: 5. In calculating a given partial expected shortfall measure as referred to in Article 325bb(1), institutions shall maintain the values of the modellable risks factors for which they have not been required to apply scenarios of future shocks for that partial expected shortfall measure under paragraphs 2, 3 and 4 of this Article. Article 325bd Liquidity horizons 1. Institutions shall map each risk factor of positions assigned to the trading desks for which they have been granted permission as referred to in Article 325az(2), or for which they are in the process of being granted such permission, to one of the broad categories of risk factors listed in Table 2 and to one of the broad sub-categories of risk factors listed in that Table. 2. The liquidity horizon of a risk factor of the positions referred to in paragraph 1 shall be the liquidity horizon of the corresponding broad sub-category of risk factors to which it has been mapped. 3. By way of derogation from paragraph 1 of this Article, for a given trading desk, an institution may decide to replace the liquidity horizon of a broad sub-category of risk factors listed in Table 2 of this Article with one of the longer liquidity horizons listed in Table 1 of Article 325bc. Where an institution takes such a decision, the longer liquidity horizon shall apply to all the modellable risk factors of the positions assigned to that trading desk that have been mapped to that broad sub-category of risk factors for the purpose of calculating the partial expected shortfall measures in accordance with point (c) of Article 325bc(1). 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. 4. 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 shall be calculated as follows: where: 5. Currency pairs that are composed of the euro and the currency of a Member State participating in ERM II shall be included in the most liquid currency pairs sub-category within the broad category of foreign exchange risk factor of Table 2. 6. An institution shall verify the appropriateness of the mapping referred to in paragraph 1 on at least a monthly basis. 7. EBA shall develop draft regulatory technical standards to specify: EBA shall submit those draft regulatory technical standards to the Commission by 28 March 2020. 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. Table 2 Article 325be Assessment of the modellability of risk factors 1. Institutions shall assess the modellability of all the risk factors of the positions assigned to the trading desks for which they have been granted permission as referred to in Article 325az(2) or are in the process of being granted such permission. 2. As part of the assessment referred to in paragraph 1 of this Article, institutions shall calculate the own funds requirements for market risk in accordance with Article 325bk for those risk factors that are not modellable. 3. EBA shall develop draft regulatory technical standards to specify the criteria to assess the modellability of risk factors in accordance with paragraph 1 and to specify the frequency of that assessment. EBA shall submit those draft regulatory technical standards to the Commission by 28 March 2020. 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. Article 325bf Regulatory back-testing requirements and multiplication factors 1. 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: 2. Institutions shall count daily overshootings on the basis of back-testing of the hypothetical and actual changes in the value of the portfolio composed of all the positions assigned to the trading desk. 3. 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: 4. Institutions shall count daily overshootings in accordance with the following: 5. An institution shall calculate, in accordance with paragraphs 6 and 7 of this Article, the multiplication factor (mc) referred to in Article 325ba for the portfolio of all the positions assigned to the trading desks for which it has been granted permission to use alternative internal models as referred to in Article 325az(2). 6. The multiplication factor (mc) shall be the sum of the value of 1,5 and an add-on between 0 and 0,5 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: In extraordinary circumstances, competent authorities may limit the add-on to that resulting from overshootings under back-testing hypothetical changes where the number of overshootings under back-testing actual changes does not result from deficiencies in the internal model. 7. Competent authorities shall monitor the appropriateness of the multiplication factor referred to in paragraph 5 and the compliance of trading desks with the back-testing requirements referred to in paragraph 3. Institutions shall promptly notify, the competent authorities of overshootings that result from their back-testing programme and provide an explanation for those overshootings, and in any case shall notify the competent authorities thereof no later than within five business days after the occurrence of an overshooting. 8. By way of derogation from paragraphs 2 and 6 of this Article, competent authorities may permit an institution not to count an overshooting where a one-day change in the value of its portfolio that exceeds the related value-at-risk number calculated by that institution's internal model is attributable to a non-modellable risk factor. To do so, the institution shall demonstrate to its competent authority that the stress scenario risk measure calculated in accordance with Article 325bk for that non-modellable risk factor is higher than the positive difference between the change in the value of the institution's portfolio and the related value-at-risk number. 9. EBA shall develop draft regulatory technical standards to specify the technical elements to be included in the actual and hypothetical changes to the value of the portfolio of an institution for the purposes of this Article. EBA shall submit those draft regulatory technical standards to the Commission by 28 March 2020. 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. Article 325bg Profit and loss attribution requirement 1. An institution's trading desk meets the P&L attribution requirements where that trading desk complies with the requirements set out in this Article. 2. The P&L attribution requirement shall ensure that the theoretical changes in the value of a trading desk's portfolio, based on the institution's risk-measurement model, are sufficiently close to the hypothetical changes in the value of the trading desk's portfolio, based on the institution's pricing model. 3. For each position of a given trading desk, an institution's compliance with the P&L attribution requirement shall lead to the identification of a precise list of risk factors that are deemed appropriate for verifying the institution's compliance with the back-testing requirement set out in Article 325bf. 4. EBA shall develop draft regulatory technical standards to specify: EBA shall submit those draft regulatory technical standards to the Commission by 28 March 2020. 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. Article 325bh Requirements on risk measurement 1. 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: 2. Institutions may use empirical correlations within broad categories of risk factors and, for the purpose of calculating the unconstrained expected shortfall measure UESt as referred to in Article 325bb(1), across broad categories of risk factors only where the institution's approach for measuring those correlations is sound, consistent with the applicable liquidity horizons, and implemented with integrity. 3. By 28 September 2020, EBA shall issue guidelines, in accordance with Article 16 of Regulation (EU) No 1093/2010, specifying criteria for the use of data inputs in the risk-measurement model referred to in Article 325bc. Article 325bi Qualitative requirements 1. 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: 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. 2. 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: 3. Institutions shall update the techniques and practices they use for any of the internal risk-measurement models used for the purposes of this Chapter to take into account the evolution of new techniques and best practices that develop in respect of those internal risk-measurement models. Article 325bj Internal validation 1. Institutions shall have processes in place to ensure that any internal risk-measurement models used for the purposes of this Chapter have been adequately validated by suitably qualified parties that are independent of the development process, in order to ensure that any such models are conceptually sound and adequately capture all material risks. 2. Institutions shall conduct the validation referred to in paragraph 1 in the following circumstances: 3. The validation of the internal risk-measurement models of an institution shall not be limited to back-testing and P&L attribution requirements, but shall, at a minimum, include the following: Article 325bk Calculation of stress scenario risk measure 1. The ‘stress scenario risk measure’ of a given non-modellable risk factor means the loss that is incurred in all trading book positions or non-trading book positions that are subject to foreign exchange or commodity risk of the portfolio which includes that non-modellable risk factor when an extreme scenario of future shock is applied to that risk factor. 2. Institutions shall develop appropriate extreme scenarios of future shock for all non-modellable risk factors, to the satisfaction of their competent authorities. 3. EBA shall develop draft regulatory technical standards to specify: In developing those draft regulatory technical standards, EBA shall take into consideration the requirement that the level of own funds requirements for market risk of a non-modellable risk factor as set out in this Article shall be as high as the level of own funds requirements for market risk that would have been calculated under this Chapter if that risk factor were modellable. EBA shall submit those draft regulatory technical standards to the Commission by 28 September 2020. 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. Section 3 Internal default risk model Article 325bl Scope of the internal default risk model 1. All the positions of an institution that have been assigned to the trading desks for which the institution has been granted permission as referred to in Article 325az(2) shall be subject to an own funds requirement for default risk where those positions contain at least one risk factor that has been mapped to the broad categories of ‘equity’ or ‘credit spread’ risk factors in accordance with Article 325bd(1). That own funds requirement, which is incremental to the risks captured by the own funds requirements referred to in Article 325ba(1), shall be calculated using the institution's internal default risk model. That model which shall comply with the requirements laid down in this Section. 2. For each of the positions referred to in paragraph 1, an institution shall identify one issuer of traded debt or equity instruments related to at least one risk factor. Article 325bm Permission to use an internal default risk model 1. Competent authorities shall grant an institution permission to use an internal default risk model to calculate the own funds requirements referred to in Article 325ba(2) for all the trading book positions referred to in Article 325bl that are assigned to a trading desk for which the internal default risk model complies with the requirements set out in Articles 325bi, 325bj, 325bn, 325bo and 325bp. 2. Where the trading desk of an institution, to which at least one of the trading book positions referred to in Article 325bl has been assigned, does not meet the requirements set out in paragraph 1 of this Article, the own funds requirements for market risk of all positions in that trading desk shall be calculated in accordance with the approach set out in Chapter 1a. Article 325bn Own funds requirements for default risk using an internal default risk model 1. Institutions shall calculate the own funds requirements for default risk using an internal default risk model for the portfolio of all trading book positions as referred to in Article 325bl as follows: 2. Institutions shall calculate the own funds requirement for default risk using an internal default risk model as referred to in paragraph 1 on at least a weekly basis. 3. By way of derogation from points (a) and (c) of paragraph 1, an institution may replace the one-year time horizon with a time horizon of sixty days for the purpose of calculating the default risk of some or all of the equity positions, where appropriate. In such case, the calculation of default correlations between equity prices and default probabilities shall be consistent with a time horizon of sixty days and the calculation of default correlations between equity prices and bond prices shall be consistent with a one-year time horizon. Article 325bo Recognition of hedges in an internal default risk model 1. Institutions may incorporate hedges in their internal default risk model and may net positions where the long positions and short positions relate to the same financial instrument. 2. In their internal default risk models, institutions may only recognise hedging or diversification effects associated with long and short positions involving different instruments or different securities of the same obligor, as well as long and short positions in different issuers by explicitly modelling the gross long and short positions in the different instruments, including modelling of basis risks between different issuers. 3. In their internal default risk models, institutions shall capture material risks between a hedging instrument and the hedged instrument that could occur during the interval between the maturity of a hedging instrument and the one-year time horizon, as well as the potential for significant basis risks in hedging strategies that arise from differences in the type of product, seniority in the capital structure, internal or external ratings, maturity, vintage and other differences. Institutions shall recognise a hedging instrument only to the extent that it can be maintained even as the obligor approaches a credit event or other event. Article 325bp Particular requirements for an internal default risk model 1. The internal default risk model referred to in Article 325bm(1) shall be capable of modelling the default of individual issuers as well as the simultaneous default of multiple issuers, and shall take into account the impact of those defaults in the market values of the positions that are included in the scope of that model. For that purpose, the default of each individual issuer shall be modelled using two types of systematic risk factors. 2. The internal default risk model shall reflect the economic cycle, including the dependency between recovery rates and the systematic risk factors referred to in paragraph 1. 3. The internal default risk model shall reflect the nonlinear impact of options and other positions with material nonlinear behaviour with respect to price changes. Institutions shall also have due regard to the amount of model risk inherent in the valuation and estimation of price risks associated with those products. 4. The internal default risk model shall be based on data that are objective and up-to-date. 5. To simulate the default of issuers in the internal default risk model, the institution's estimates of default probabilities shall meet the following requirements: 6. To simulate the default of issuers in the internal default risk model, the institution's estimates of loss given default shall meet the following requirements: 7. As part of the independent review and validation of the internal models that they use for the purposes of this Chapter, including for the risk-measurement system, institutions shall: The tests referred to in point (b) shall not be limited to the range of past events experienced. 8. The internal default risk model shall appropriately reflect issuer concentrations and concentrations that can arise within and across product classes under stressed conditions. 9. The internal default risk model shall be consistent with the institution's internal risk management methodologies for identifying, measuring, and managing trading risks. 10. Institutions shall have clearly defined policies and procedures for determining the default assumptions for correlations between different issuers in accordance with point (c) of Article 325bn(1) and the preferred choice of method for estimating the default probabilities in point (e) of paragraph 5 of this Article and the loss given default in point (d) of paragraph 6 of this Article. 11. Institutions shall document their internal models so that their correlation assumptions and other modelling assumptions are transparent to the competent authorities. 12. EBA shall develop draft regulatory technical standards to specify the requirements that an institution's internal methodology or external sources are to fulfil for estimating default probabilities and losses given default in accordance with point (e) of paragraph 5 and point (d) of paragraph 6. EBA shall submit those draft regulatory technical standards to the Commission by 28 September 2020. 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.’; the own funds requirement under the sensitivities-based method set out in Section 2; the own funds requirement for the default risk set out in Section 5 which is only applicable to the trading book positions referred to in that Section; the own funds requirement for residual risks set out in Section 4 which is only applicable to the trading book positions referred to in that Section. ‘risk class’ means one of the following seven categories: general interest rate risk; credit spread risk (CSR) for non-securitisation; credit spread risk for securitisation not included in the alternative correlation trading portfolio (non-ACTP CSR); credit spread risk for securitisation included in the alternative correlation trading portfolio (ACTP CSR); equity risk; commodity risk; foreign exchange risk; ‘sensitivity’ means the relative change in the value of a position, as a result of a change in the value of one of the relevant risk factors of the position, calculated with the institution's pricing model in accordance with Subsection 2 of Section 3; ‘bucket’ means a sub-category of positions within one risk class with a similar risk profile to which a risk weight as defined in Subsection 1 of Section 3 is assigned. own funds requirements for delta risk which capture the risk of changes in the value of an instrument due to movements in its non-volatility related risk factors; own funds requirements for vega risk which capture the risk of changes in the value of an instrument due to movements in its volatility-related risk factors; own funds requirements for curvature risk which capture the risk of changes in the value of an instrument due to movements in the main non-volatility related risk factors not captured by the own funds requirements for delta risk. all the positions of instruments with optionality shall be subject to the own funds requirements referred to in points (a), (b) and (c) of paragraph 1; all the positions of instruments without optionality shall only be subject to the own funds requirements referred to in point (a) of paragraph 1. | WSk = RWk · sk where: WSk = the weighted sensitivities; RWk = the risk weights; and sk = the risk factor. | where: Kb = the bucket-specific sensitivity; and WS = the weighted sensitivities. Sb | = | Σk WSk for all risk factors in bucket b and Sc = Σk WSk in bucket c; where those values for Sb and Sc produce a negative number for the overall sum of , the institution shall calculate the risk-class specific own funds requirements for delta or vega risk using an alternative specification whereby Sb | = | max [min (Σk WSk, Kb), – Kb] for all risk factors in bucket b and Sc | = | max [min (Σk WSk, Kc), – Kc] for all risk factors in bucket c. the medium correlations scenario, whereby the correlation parameters ρkl and γbc remain unchanged from those specified in Section 6; the high correlations scenario, whereby the correlation parameters ρkl and γbc that are specified in Section 6 shall be uniformly multiplied by 1,25, with ρkl and γbc subject to a cap at 100 %; the low correlations scenario shall be specified in the delegated act referred to in Article 461a. 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 % 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; where the maturity of the option is shorter than the maturity of the underlying, the following risk factors shall be considered as follows: the first risk factor shall be mapped to the maturity of the option; the second risk factor shall be mapped to the residual maturity of the underlying of the option at the expiry date of the option. 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. 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. 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 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; 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; 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. 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; 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. | = | the delta credit spread risk sensitivities for all securitisation and non-securitisation positions; cskt | = | the value of the credit spread rate of an issuer j at maturity t; Vi (.) | = | the pricing function of instrument i; and x,y | = | risk factors other than cskt in the pricing function Vi. 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; 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. sk | = | the delta commodity risk sensitivities; k | = | a given commodity risk factor; CTYk | = | the value of risk factor k; Vi (.) | = | the market value of instrument i as a function of risk factor k; and y, z | = | risk factors other than CTYk in the pricing model of instrument i. sk | = | the delta foreign exchange risk sensitivities; k | = | a given foreign exchange risk factor; FXk | = | the value of the risk factor; Vi (.) | = | the market value of instrument i as a function of the risk factor k; and y, z | = | risk factors other than FXk in the pricing model of instrument i. sk | = | the vega risk sensitivity of an option; k | = | a specific vega risk factor, consisting of an implied volatility; volk | = | the value of that risk factor, which should be expressed as a percentage; and x,y | = | risk factors other than volk in the pricing function Vi. 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; 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. those alternative definitions are used for internal risk management purposes and for the reporting of profits and losses to senior management by an independent risk control unit within the institution; 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. those alternative definitions are used for internal risk management purposes and for the reporting of profits and losses to senior management by an independent risk control unit within the institution; 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 linear transformation referred to in the first subparagraph reflects a vega risk sensitivity. 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; the instrument is an instrument bearing other residual risks, which, for the purposes of this Chapter, means any of the following instruments: 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; 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. 1,0 % in the case of instruments referred to in point (a) of paragraph 2; 0,1 % in the case of instruments referred to in point (b) of paragraph 2. the instrument is listed on a recognised exchange; the instrument is eligible for central clearing in accordance with Regulation (EU) No 648/2012; 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. ‘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; ‘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; ‘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; ‘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, ‘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; ‘default risk weight’ means the percentage representing the estimated probability of the default of each obligor, according to the creditworthiness of that obligor. | JTDlong = max {LGD Vnotional + P&Llong + Adjustmentlong; 0} where: JTDlong = the gross JTD amount for the long exposure; Vnotional = the notional amount of the instrument; P&Llong = a term which adjusts for gains or losses already accounted for by the institution due to changes in the fair value of the instrument creating the long exposure; gains shall enter the formula with a positive sign and losses with a negative; and Adjustmentlong = the amount by which, due to the structure of the derivative instrument, the institution's loss in the event of default would be increased or reduced relative to the full loss on the underlying instrument; increases shall enter the Adjustmentlong term with a positive sign and decreases with a negative sign. | JTDshort = min {LGD Vnotional + P&Lshort + Adjustmentshort; 0} where: JTDshort = the gross JTD amount for the short exposure; Vnotional = the notional amount of the instrument that shall enter into the formula with a negative sign; P&Lshort = a term which adjusts for gains or losses already accounted for by the institution due to changes in the fair value of the instrument creating the short exposure; gains shall enter into the formula with a positive sign and losses shall enter into the formula with a negative sign; and Adjustmentshort = the amount by which, due to the structure of the derivative instrument, the institution's gain in the event of default would be increased or reduced relative to the full loss on the underlying instrument; decreases shall enter the Adjustmentshort term with a positive sign and increases shall enter the Adjustmentshort term with a negative sign. exposures to non-senior debt instruments shall be assigned an LGD of 100 %; exposures to senior debt instruments shall be assigned an LGD of 75 %; exposures to covered bonds, as referred to in Article 129, shall be assigned an LGD of 25 %. in the case of debt instruments, the notional amount is the face value of the debt instrument; in the case of derivative instruments with debt security underlyings, the notional amount is the notional amount of the derivative instrument. | JTDlong = max {LGD · V + P&Llong + Adjustmentlong; 0} | JTDshort = min {LGD · V + P&Lshort + Adjustmentshort; 0} where: JTDlong = the gross JTD amount for the long exposure; JTDshort = the gross JTD amount for the short exposure; and V = the fair value of the equity or, in the case of derivative instruments with equity underlyings, the fair value of the equity underlying. how institutions are to calculate JTD amounts for different types of instruments in accordance with this Article; which alternative methodologies institutions are to use for the purposes of the estimation of gross JTD amounts referred to in paragraph 7. the notional amounts of instruments other than the ones referred to in points (a) and (b) of paragraph 4. offsetting shall be full where all offsetting exposures have maturities of one year or more; 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. 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 % | DRCb = max {(Σi ∈ long RWi · net JTDi) – WtS · (Σi ∈ short RWi · |net JTDi|); 0} where: DRCb = the own funds requirement for the default risk for bucket b; i = the index that denotes an instrument belonging to bucket b; RWi = the risk weight; and WtS = a ratio recognising a benefit for hedging relationships within a bucket, which shall be calculated as follows: one common bucket for all corporates, regardless of the region; 44 different buckets corresponding to one bucket per region for each of the 11 asset classes defined in the second subparagraph. ‘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 %; ‘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; ‘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. attachment point = (N – 1) / Total Names; detachment point = N / Total Names; where ‘Total Names’ shall be the total number of names in the underlying basket or pool. 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; offsetting through decomposition as set out is point (a) shall not be allowed for resecuritisations or derivatives on securitisation; 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; 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. for tranched products, the default risk weights corresponding to their credit quality as specified in Article 325y(1) and (2); for non-tranched products, the default risk weights referred to in Article 325aa(1). | DRCb = max {(Σi ∈ long RWi · net JTDi) – WtSACTP · (Σi ∈ short RWi · |net JTDi|); 0} where: DRCb = the own funds requirement for the default risk for bucket b; i = an instrument belonging to bucket b; and WtSACTP = the ratio recognising a benefit for hedging relationships within a bucket, which shall be calculated in accordance with the WtS formula set out in Article 325y(4), but using long positions and short positions across the entire ACTP and not just the positions in the particular bucket. DRCACTP | = | the own funds requirement for the default risk for the ACTP; and DRCb | = | the own funds requirement for the default risk for bucket b. Maturity 0,25 years 0,5 years 1 year 2 years 3 years 5 years 10 years 15 years 20 years 30 years Tk (respectivelyTl) | = | the maturity that relates to the risk free rate; θ | = | 3 % Bucket number | Credit quality | Sector | Risk weight (percentage points) 1 | All | Central government, including central banks, of a Member State | 0,50 % 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 in Member States | 1,0 % 11 | Credit quality step 4 to 6 | Central government, including central banks, of a third country, multilateral development banks and international organisations referred to in Article 117(2) or Article 118 | 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 and promotional lenders | 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 % | ρkl = ρkl (name) · ρkl (tenor) · ρkl (basis) where: ρkl (name) shall be equal to 1 where the two names of sensitivities k and l are identical, otherwise it shall be equal to 35 %; ρkl (tenor) shall be equal to 1 where the two vertices of the sensitivities k and l are identical, otherwise it shall be equal to 65 %; and ρkl (basis) shall be equal to 1 where the two sensitivities are related to the same curves, otherwise it shall be equal to 99,90 %. | γbc = γbc (rating) · γbc (sector) where: γbc (rating) shall be equal to 1 where the two 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; and γbc (sector) shall be equal to 1 where the two buckets belong to the same sector, and otherwise shall be equal to the corresponding percentage set out in Table 5: Table 5 Bucket 1, 2 and 11 3 and 12 4 and 13 5 and 14 6 and 15 7 and 16 8 and 17 9 1, 2 and 11 75 % 10 % 20 % 25 % 20 % 15 % 10 % 3 and 12 5 % 15 % 20 % 15 % 10 % 10 % 4 and 13 5 % 15 % 20 % 5 % 20 % 5 and 14 20 % 25 % 5 % 5 % 6 and 15 25 % 5 % 15 % 7 and 16 5 % 20 % 8 and 17 5 % 9 — Bucket number | Credit quality | Sector 1 | All | Central government, including central banks, of Member States 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 3 | Regional or local authority and public sector entities 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 | Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying 6 | Consumer goods and services, transportation and storage, administrative and support service activities 7 | Technology, telecommunications 8 | Health care, utilities, professional and technical activities 9 | Covered bonds issued by credit institutions in Member States 10 | Covered bonds issued by credit institutions in third countries 11 | Credit quality step 4 to 6 | Central government, including central banks, of a third country, multilateral development banks and international organisations referred to in Article 117(2) or Article 118 12 | Regional or local authority and public sector entities 13 | Financial sector entities including credit institutions incorporated or established by a central government, a regional government or a local authority and promotional lenders 14 | Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying 15 | | Consumer goods and services, transportation and storage, administrative and support service activities 16 | Technology, telecommunications 17 | Health care, utilities, professional and technical activities 18 | Other sector Bucket number | Credit quality | Sector 1 | Senior and Credit quality step 1 to 3 | RMBS - Prime 2 | RMBS - Mid-Prime 3 | RMBS - Sub-Prime 4 | CMBS 5 | Asset backed securities (ABS) - Student loans 6 | ABS - Credit cards 7 | ABS - Auto 8 | Collateralised loan obligations (CLO) non-ACTP 9 | Non-senior and credit quality step 1 to 3 | RMBS - Prime 10 | RMBS - Mid-Prime 11 | RMBS - Sub-Prime 12 | | CMBS 13 | ABS - Student loans 14 | ABS - Credit cards 15 | ABS - Auto 16 | CLO non-ACTP 17 | Credit quality step 4 to 6 | RMBS - Prime 18 | RMBS - Mid-Prime 19 | RMBS - Sub-Prime 20 | CMBS 21 | ABS - Student loans 22 | ABS - Credit cards 23 | ABS - Auto 24 | CLO non-ACTP 25 | Other sector | ρkl = ρkl (tranche) · ρkl (tenor) · ρkl (basis) where: ρkl (thranche) shall be equal to 1 where the two names of sensitivities k and l are within the same bucket and are related to the same securitisation tranche (more than 80 % overlap in notional terms), otherwise it shall be equal to 40 %; ρkl (tenor) shall be equal to 1 where the two vertices of the sensitivities k and l are identical, otherwise it shall be equal to 80 %; and ρkl (basis) shall be equal to 1 where the two sensitivities are related to the same curves, otherwise it shall be equal to 99,90 %. Bucket number | Market capitalisation | Economy | Sector 1 | Large | Emerging market economy | Consumer goods and services, transportation and storage, administrative and support service activities, healthcare, utilities 2 | Telecommunications, industrials 3 | Basic materials, energy, agriculture, manufacturing, mining and quarrying 4 | Financials including government-backed financials, real estate activities, technology 5 | Advanced economy | Consumer goods and services, transportation and storage, administrative and support service activities, healthcare, utilities 6 | Telecommunications, industrials 7 | Basic materials, energy, agriculture, manufacturing, mining and quarrying 8 | Financials including government-backed financials, real estate activities, technology 9 | Small | Emerging market economy | All sectors described under bucket numbers 1, 2, 3 and 4 10 | Advanced economy | All sectors described under bucket numbers 5, 6, 7 and 8 11 | Other sector 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); 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); 7,5 % between two sensitivities within the same bucket that fall under the category small market capitalisation, emerging market economy (bucket number 9); 12,5 % between two sensitivities within the same bucket that fall under the category small market capitalisation, advanced economy (bucket number 10). Bucket number | Bucket name 1 | Energy - solid combustibles 2 | Energy - liquid combustibles 3 | Energy - electricity and carbon trading 4 | Freight 5 | Metals – non-precious 6 | Gaseous combustibles 7 | Precious metals (including gold) 8 | Grains and oilseed 9 | Livestock and dairy 10 | Softs and other agricultural commodities 11 | Other commodity | ρkl = ρkl (commodity) · ρkl (tenor) · ρkl (basis) where: ρkl (commodity) shall be equal to 1 where the two commodities of sensitivities k and l are identical, otherwise it shall be equal to the intra-bucket correlations in Table 10; ρkl (tenor) shall be equal to 1 where the two vertices of the sensitivities k and l are identical, otherwise it shall be equal to 99 %; and ρkl (basis) shall be equal to 1 where the two sensitivities are identical in the delivery location of a commodity, otherwise it shall be equal to 99,90 %. 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 % 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; 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. 20 % where the two buckets fall within bucket numbers 1 to 10; 0 % where either of the two buckets is bucket number 11. the risk weight referred to in paragraph 1, divided by 3; 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. | RWk = the risk weight for a given vega risk factor k; | RWσ shall be set at 55 %; and | LHrisk class is the regulatory liquidity horizon to be prescribed in the determination of each vega risk factor k. LHrisk class is determined in accordance with the following table: Table 11 Risk class LHrisk class GIRR 60 CSR non-securitisations 120 CSR securitisations (ACTP) 120 CSR securitisations (non-ACTP) 120 Equity (large cap) 20 Equity (small cap) 60 Commodity 120 Foreign exchange 40 | shall be equal to where α shall be set at 1 %, Tk and Tl shall be equal to the maturities of the options for which the vega sensitivities are derived, expressed as a number of years; and | is equal to , where α is set at 1 %, and shall be equal to the maturities of the underlyings of the options for which the vega sensitivities are derived, minus the maturities of the corresponding options, expressed in both cases as a number of years. | shall be equal to the delta intra-bucket correlation corresponding to the bucket to which vega risk factors k and l would be allocated; and | shall be set in accordance with paragraph 1. the trading desks were established in accordance with Article 104b; 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; the trading desks have met the back-testing requirements referred to in Article 325bf(3) for the preceding year; the institution has reported to its competent authorities the results of the profit and loss attribution (‘P&L attribution’) requirement for the trading desks set out in Article 325bg; 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; no securitisation or re-securitisation positions have been assigned to the trading desks. 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; the assessment methodology under which competent authorities verify an institution's compliance with the requirements set out in Articles 325bh, 325bi, 325bn, 325bo and 325bp. to continue using its alternative internal models for the purpose of calculating the own funds requirements for the market risk of a trading desk that no longer meets the conditions referred to in point (c) of paragraph 2 of this Article and in Article 325bg(1); to limit the add-on to the one resulting from overshootings under back-testing hypothetical changes. the sum of the following values: the institution's previous day's expected shortfall risk measure, calculated in accordance with Article 325bb (ESt-1), and the institution's previous day's stress scenario risk measure, calculated in accordance with Section 5 (SSt-1); or the sum of the following values: 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 (ESavg), multiplied by the multiplication factor (mc); and 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 (SSavg). the most recent own funds requirement for default risk, calculated in accordance with Section 3; the average of the amount referred to in point (a) over the preceding 12 weeks. ESt | = | the expected shortfall risk measure; i | = | the index that denotes the five broad categories of risk factors listed in the first column of Table 2 of Article 325bd; UESt | = | the unconstrained expected shortfall measure calculated as follows: | = | the unconstrained expected shortfall measure for broad risk factor category i and calculated as follows: ρ = the supervisory correlation factor across broad categories of risk; ρ = 50 %; = the partial expected shortfall measure that shall be calculated for all the positions in the portfolio in accordance with Article 325bc(2); = the partial expected shortfall measure that shall be calculated for all the positions in the portfolio in accordance with Article 325bc(3); = the partial expected shortfall measure that shall be calculated for all the positions in the portfolio in accordance with Article 325bc(4); | = | the partial expected shortfall measure for broad risk factor category i that shall be calculated for all the positions in the portfolio in accordance with Article 325bc(2); | = | the partial expected shortfall measure for broad risk factor category i that shall be calculated for all the positions in the portfolio in accordance with Article 325bc(3); and | = | the partial expected shortfall measure for broad risk factor category i that shall be calculated for all the positions in the portfolio in accordance with of Article 325bc(4). the institution is able to demonstrate to its competent authority that calculating the unconstrained expected shortfall measure does not underestimate the market risk of the relevant trading book positions; the institution is able to increase the frequency of calculation of , , and from weekly to daily where required by its competent authority. daily calculations of the partial expected shortfall measures; at 97,5th percentile, one tailed confidence interval; for a given portfolio of trading book positions, institution shall calculate the partial expected shortfall measure at time ‘t’ 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 in calculating , institutions shall only apply scenarios of future shocks to a subset of the modellable risk factors of the positions in the portfolio which has been chosen by the institution, to the satisfaction of the competent authorities, so that the following condition is met with the sum taken over from the preceding 60 business days: 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; in calculating , institutions shall only apply scenarios of future shocks to the subset of the modellable risk factors of the positions in the portfolio chosen by the institution for the purposes of point (a) of this paragraph and which have been mapped to the broad risk factor category ‘i’ in accordance with Article 325bd; 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 a continuous 12-month period of financial stress that shall be identified by the institution in order to maximise the value of ; for the purpose of identifying that stress period, institutions shall use an observation period starting at least from 1 January 2007, to the satisfaction of the competent authorities; and the data inputs of shall be calibrated to the 12-month stress period that has been identified by the institution for the purposes of point (c). in calculating , institutions shall only apply scenarios of future shocks to the subset of the modellable risk factors of the positions in the portfolio referred to in point (a) of paragraph 2; in calculating , institutions shall only apply scenarios of future shocks to the subset of the modellable risk factors of the positions in the portfolio referred to in point (b) of paragraph 2; 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. in calculating , institutions shall apply scenarios of future shocks to all the modellable risk factors of the positions in the portfolio; in calculating , institutions shall apply scenarios of future shocks to all the modellable risk factors of the positions in the portfolio which have been mapped to the broad risk factor category i in accordance with Article 325bd; 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. EffectiveLH = | | SubCatLH if Mat > LH5 min (SubCatLH, minj{LHj/LHj ≥ Mat}) if LH1 ≤ Mat ≤ LH5 LH1 if Mat < LH1 EffectiveLH | = | the effective liquidity horizon; Mat | = | the maturity of the trading book position; SubCatLH | = | the length of liquidity horizon of the modellable risk factor determined in accordance with paragraph 1; and minj {LHj/LHj ≥ Mat} | = | the length of one of the liquidity horizons listed in Table 1 of Article 325bc which is the nearest liquidity horizon above the maturity of the trading book position. 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; which currencies constitute the most liquid currencies sub-category of the broad category of interest rate risk factor of Table 2; which currency pairs constitute the most liquid currency pairs sub-category of the broad category of foreign exchange risk factor of Table 2; 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. 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 the calculation of the value at risk shall be subject to a one-day holding period; 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; 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); 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). 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; 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; 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; 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. 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; 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; 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. 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: a one-day holding period; a 99th percentile, one tailed confidence interval; 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; 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); 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); 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 the criteria necessary to ensure that the theoretical changes in the value of a trading desk's portfolio is sufficiently close to the hypothetical changes in the value of a trading desk's portfolio for the purposes of paragraph 2, taking into account international regulatory developments; the consequences for an institution where the theoretical changes in the value of a trading desk's portfolio are not sufficiently close to the hypothetical changes in the value of a trading desk's portfolio for the purposes of paragraph 2; the frequency at which the P&L attribution is to be performed by an institution; 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; the manner in which institutions that use the internal model are to aggregate the total own funds requirement for market risk for all their trading book positions and non-trading book positions that are subject to foreign exchange risk or commodity risk, taking into account the consequences referred to in point (b). 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; the internal risk-measurement model shall capture nonlinearities for options and other products as well as correlation risk and basis risk; 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; 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; foreign exchange positions of a CIU of which an institution is not aware of shall be carved out from the internal models approach and treated in accordance with Chapter 1a; 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; 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; 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); 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. 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; 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 be responsible for designing and implementing any internal risk-measurement model; that unit shall conduct the initial and on-going validation of any internal model used for the purposes of this Chapter and shall be responsible for the overall risk management system; that unit shall produce and analyse daily reports on the output of any internal model used to calculate capital requirements for market risk, as well as reports on the appropriateness of measures to be taken in terms of trading limits; 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; 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; 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; 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; 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; 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. the adequacy of the documentation of the risk management system and process and the organisation of the risk control unit; the integration of risk measures into daily risk management and the integrity of the management information system; the processes the institution employs for approving the risk-pricing models and valuation systems that are used by front and back-office personnel; 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; 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; 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; 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; where the review is performed by a third-party undertaking in accordance with point (h) of paragraph 1 of this Article, the verification that the internal validation process set out in Article 325bj fulfils its objectives. when any internal risk-measurement model is initially developed and when any significant changes are made to that model; on a periodic basis, and where there have been significant structural changes in the market or changes to the composition of the portfolio which might lead to the internal risk-measurement model no longer being adequate. tests to verify whether the assumptions made in the internal model are appropriate and do not underestimate or overestimate the risk; own internal model validation tests, including back-testing in addition to the regulatory back-testing programmes, in relation to the risks and structures of their portfolios; the use of hypothetical portfolios to ensure that the internal risk-measurement model is able to account for particular structural features that may arise, for example, material basis risks and concentration risk, or the risks associated with the use of proxies. how institutions are to develop extreme scenarios of future shock applicable to non-modellable risk factors and how they are to apply those extreme scenarios of future shock to those risk factors; a regulatory extreme scenario of future shock for each broad sub-category of risk factors listed in Table 2 of Article 325bd, which institutions may use when they are unable to develop an extreme scenario of future shock in accordance with point (a) of this subparagraph, or which competent authorities may require that institution apply if those authorities are not satisfied with the extreme scenario of future shock developed by the institution; the circumstances under which institutions may calculate a stress scenario risk measure for more than one non-modellable risk factor; how institutions are to aggregate the stress scenario risk measures of all non-modellable risk factors included in their trading book positions and non-trading book positions that are subject to foreign exchange risk or commodity risk. the own funds requirements shall be equal to a value-at-risk number measuring potential losses in the market value of the portfolio caused by the default of issuers related to those positions at the 99,9 % confidence interval over a one-year time horizon; the potential loss referred to in point (a) means a direct or indirect loss in the market value of a position which was caused by the default of the issuers and which is incremental to any losses already taken into account in the current valuation of the position; the default of the issuers of equity positions shall be represented by the value for the issuers' equity prices being set to zero; institutions shall determine default correlations between different issuers on the basis of a conceptually sound methodology, using objective historical data on market credit spreads or equity prices that cover at least a 10 year period that includes the stress period identified by the institution in accordance with Article 325bc(2); the calculation of default correlations between different issuers shall be calibrated to a one-year time horizon; the internal default risk model shall be based on a one-year constant position assumption. the default probabilities shall be floored at 0,03 %; the default probabilities shall be based on a one-year time horizon, unless stated otherwise in this Section; the default probabilities shall be measured using, solely or in combination with current market prices, data observed during a historical period of at least five years of actual past defaults and extreme declines in market prices equivalent to default events; default probabilities shall not be inferred solely from current market prices; an institution that has been granted permission to estimate default probabilities in accordance with Section 1 of Chapter 3 of Title II shall use the methodology set out therein to calculate default probabilities; an institution that has not been granted permission to estimate default probabilities in accordance with Section 1 of Chapter 3 of Title II shall develop an internal methodology or use external sources to estimate default probabilities; in both situations, the estimates of default probabilities shall be consistent with the requirements set out in this Article. the loss given default estimates are floored at 0 %; the loss given default estimates shall reflect the seniority of each position; an institution that has been granted permission to estimate loss given default in accordance with Section 1 of Chapter 3 of Title II shall use the methodology set out therein to calculate loss given default estimates; an institution that has not been granted permission to estimate loss given default in accordance with Section 1 of Chapter 3 of Title II shall develop an internal methodology or use external sources to estimate loss given default; in both situations, the estimates of loss given default shall be consistent with the requirements set out in this Article. verify that their approach for the modelling of correlations and price changes is appropriate for their portfolio, including the choice and weights of the systematic risk factors in the model; perform a variety of stress tests, including sensitivity analyses and scenario analyses, to assess the qualitative and quantitative reasonableness of the internal default risk model, in particular with regard to the treatment of concentrations; and apply appropriate quantitative validation including relevant internal modelling benchmarks.

← (c) · All articles · (a) →

Source: EUR-Lex (Cellar) · retrieved 2026-10-12 · Text as adopted (Official Journal); later amendments are not incorporated in this text.