Market Risk: Internal Model Approach (CRR)

A1.

An institution which applies for an IMA permission in respect of a trading desk must provide, as part of its application, documentation which explains, to the satisfaction of the PRA, how the institution meets the IMA standards.

1.

An institution must:

1. (a) calculate its own funds requirements for the portfolio of all positions assigned to a trading desk by using its internal models in accordance with Article 325ba, except as provided otherwise in this Part; and
2. (b) ensure at all times that:
   1. (i) the trading desk (other than a notional trading desk) at all times meets the requirements of paragraph 2 of Trading Book (CRR) Part Article 104b;
   2. (ii) its rationale for the inclusion of the trading desk in the scope of the internal model approach continues to apply; and
   3. (iii) any ineligible positions assigned to the trading desk are treated separately for the purposes of calculating own funds requirements for market risk in respect of those ineligible positions as if they were assigned to a trading desk for which the institution has not been granted an IMA permission.

2.

An institution shall immediately notify the PRA when a trading desk that is subject to the permission no longer meets at least one of the requirements set out in paragraph 1. From the date of that notification, the institution:

1. (a) shall not use internal models in accordance with this Part in relation to any of the positions assigned to that trading desk; and
2. (b) shall apply the Market Risk: Advanced Standardised Approach (CRR) Part to calculate the own funds requirements for market risk for all the positions assigned to that trading desk from the next earliest reporting date.

The institution may resume the use of internal models in accordance with this Part to calculate own funds requirements for market risk for the positions of that trading desk if it provides to the PRA a reasoned confirmation that the trading desk is compliant with the requirements in paragraph 1.

3.

By way of derogation from paragraph 2, in exceptional circumstances, an institution may be granted permission by the PRA to continue using its internal models for the purpose of calculating the own funds requirements for the market risk of a trading desk that has ceased to meet either:

1. (a) the requirements set out in Article 325bf(3) for the preceding 12 months; or
2. (b) the requirements set out in in Article 325bg(1).

[Note: This is a permission under section 144G and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

4.

An institution shall identify and measure deficiencies in risk capture in its internal models used in accordance with Article 325ba. An institution that identifies material deficiencies in risk capture shall calculate and fulfil an additional own funds requirement within its internal model approach which is adequate to mitigate such material risk deficiencies in addition to the own funds requirements calculated under Article 325ba.

5.

An institution which is required to use the Market Risk: Advanced Standardised Approach (CRR) Part in the calculation of own funds requirements for market risk for all positions assigned to a trading desk in accordance with paragraph 2 shall also to continue to fulfil the additional own funds requirement calculated for those positions in accordance with paragraph 4.

6.

For positions assigned to a trading desk for which an institution has not been granted an IMA permission, the institution shall calculate the own funds requirements for market risk in accordance with the Market Risk: Advanced Standardised Approach (CRR) Part.

7.

Where ineligible positions are assigned to a trading desk for which an institution has been granted an IMA permission, the institution shall calculate the own funds requirements for market risk for those ineligible positions in accordance with the Market Risk: Advanced Standardised Approach (CRR) Part.

8.

For the purposes of the calculations in paragraphs 6 and 7 the institution shall include all those positions in the calculation of CU as defined in Article 325ba(3).

9.

For the purposes of this Part, an institution shall treat a position in a CIU which is a closed-ended investment fund as an equity position in accordance with this Part. For the purposes of this paragraph, the term ‘closed-ended investment fund’ shall have the meaning given to the term in the FCA Handbook.

[Note: Paragraphs 1, 2, 3 and 6 of this rule correspond to Article 325az (2), (4), (5) and (6) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution which has an IMA permission to use internal models may with the permission of the PRA make:

1. (a) a material change to the use of those internal models;
2. (b) a material extension of the use of those internal models; and
3. (c) a material change to the institution's choice of the subset of the modellable risk factors referred to in Article 325bc(2).

From the date specified in such permission, the institution shall calculate the own funds requirements using its internal models in accordance with and incorporating the permitted change or extension.

For the purpose of this paragraph, a change or extension to the use of internal models shall be considered material, if it fulfils any of the conditions set out in Part A of Annex 2.

When making an application for the permission referred to in this paragraph, an institution shall provide the PRA with the documentation specified in paragraph 1 of Part C of Annex 2.

[Note: This is a permission under section 144G and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

2.

Where an institution has been granted permission by the PRA for a change or extension:

1. (a) in the case of delay of the implementation of that permitted change or extension, the institution shall promptly notify the PRA and present to the PRA a plan for a timely implementation of the permitted change or extension; or
2. (b) an institution which fails to implement that permitted change or extension on the date specified in that permission, and which has not notified the PRA in accordance with point (a) of this paragraph must not implement the change or extension and may do so only with the further permission of the PRA, as referred to in paragraph 1.

3.

An institution must assign changes and extensions to the category of the highest potential materiality for the purpose of determining whether one or more of the materiality thresholds in Part A of Annex 2 is met. An institution must not split an extension or change into several changes or extensions of lower materiality.

4.

An institution shall notify the PRA of all changes and extensions to the use of the internal models other than those that are material for the purpose of paragraph 1:

1. (a) in the case of a change or extension set out in Part B of Annex 2, at least two weeks before implementation; and
2. (b) in all other cases, at least annually.

When making a notification in accordance with point (a) of this paragraph, an institution shall provide the PRA with the documentation specified in paragraph 2 of Part C of Annex 2. An institution shall notify the PRA promptly if, having notified the PRA of a change or extension in accordance with point (a) of this paragraph, it decides not to implement the extension or change.

[Note: Paragraph (1) of this rule corresponds to Article 325az(7) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution using an 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 an IMA permission as the higher of:

1. (a) the sum of the following values:
   1. (i) the institution's previous day's expected shortfall risk measure, calculated in accordance with Article 325bb (ES_t−1); and
   2. (ii) the institution's previous day's stress scenario risk measure, calculated in accordance with Article 325bk (SS_t−1); or
2. (b) the sum of the following values:
   1. (i) the average of the institution's daily expected shortfall risk measure, calculated in accordance with Article 325bb for each of the preceding 60 business days (ESavg), multiplied by the multiplication factor (m_c); and
   2. (ii) the average of the institution's daily stress scenario risk measure, calculated in accordance with Article 325bk for each of the preceding 60 business days (SSavg).

2.

An institution which holds 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:

1. (a) the most recent own funds requirement for default risk, calculated in accordance with Section 3 of this Part; or
2. (b) the average of the amount referred to in point (a) over the preceding 12 weeks.

3.

For the purpose of point (a) of paragraph 1, and in accordance with the back testing requirements and P&L attribution requirements, an institution shall calculate the total own funds requirements for all its trading book positions and all its non-trading book positions generating foreign exchange or commodity risks as the sum of the results of formulas (a) and (b) as follows:

1. (a) min (IMA_g&y+Capital surcharge + C_U;SA_{all desks})
2. (b) max (IMA_g&y − SA _g&y;0)

Where:

4.

An institution which calculates the own funds requirements in accordance with this Part for positions assigned to trading desks that have been classified as yellow zone desks in accordance with Article 325bg shall compute, in relation to those positions, a capital surcharge in accordance with the following formula:

\[Capital\ surcharge=k\times\max{(SA_{g \& y}-IMA_{g \& y};0)}\]

Where:

5.

For the purpose of paragraph 4, the coefficient k shall be calculated on the basis of the following formula:

\[k=0.5\times \frac{\sum _{i\epsilon y}SA_{i}}{\sum_{i\epsilon g \& y}SA_{i}}\]

6.

An institution shall deem a trading desk that has been classified as a red zone or orange zone desk in accordance with Article 325bg as a trading desk that is not meeting the P&L attribution requirements. The institution must notify the PRA promptly on making this determination. As from the day on which the institution determines such classification, the institution shall not use internal models in accordance with this Part in relation to any of the positions assigned to that trading desk; and shall apply the Market Risk: Advanced Standardised Approach (CRR) Part to calculate the own funds requirements for market risk for all the positions assigned to that trading desk. If the institution provides to the PRA a reasoned confirmation that the trading desk meets the conditions for classification as a green zone desk, the institution may resume the use of internal models in accordance with this Part to calculate own funds requirements for market risk for the positions of those trading desks.

[Note: Paragraphs 1 and 2 of this rule correspond to Article 325ba(1) and (2) of CRR as it applied immediately before revocation by the Treasury]

1.

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

\[{ES}_{t}=\rho.\left({UES}_t\right)+\left(1-\rho\right).\sum\nolimits_{i}UES_t^i\]

2.

An institution 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, an institution 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.

4.

By way of derogation from paragraph 1, if so specified in the IMA permission, an institution may reduce the frequency of the calculation of the ratio of undiversified unconstrained expected shortfall measures to diversified unconstrained expected shortfall measures:

\[\frac{\sum\nolimits_{i}UES_t^i}{UES_t}\]

from daily to weekly, provided that both of the following conditions are met:

1. (a) the institution is able to demonstrate that weekly calculation of the ratio of undiversified unconstrained expected shortfall measures to diversified unconstrained expected shortfall measures:

\[\frac{\sum\nolimits_{i}UES_t^i}{{UES}_t}\]

does not underestimate the market risk of the relevant trading book positions relative to a daily calculation; and

1. (b) the institution is able to increase the frequency of calculation of:

\[{UES}_t^{i}\]
\[{PES}_t^{RS,i}\]
\[{PES}_t^{RC,i}\]

and

\[{PES}_t^{FC,i}\]

from weekly to daily if required by the PRA.

[Note: This rule corresponds to Article 325bb of CRR as it applied immediately before revocation by the Treasury]

1.

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

1. (a) daily calculations of the partial expected shortfall measures;
2. (b) at 97.5th percentile, one tailed confidence interval; and
3. (c) for a given portfolio of trading book positions and non-trading book positions that are subject to foreign exchange or commodity risk, an institution shall calculate the partial expected shortfall measure at time ‘t’ in accordance with the following formula:

\[PES_t=\sqrt{\left(PES_t(T)\right)^2+\sum_{j\geq2}\left(PES_t(T,j)\cdot\sqrt{\frac{({LH}_j-{LH}_{j-1})\ }{10}}\right)^2}\]

where:

Table 1

2.

For the purpose of calculating the partial expected shortfall measures:

\[{PES}_t^{RS}\]

and

\[{PES}_t^{RS,i}\]

referred to in Article 325bb(1), in addition to the requirements set out in paragraph 1, an institution shall meet the following requirements:

1. (a) in calculating:

\[{PES}_t^{RS}\]

an institution shall only apply scenarios of future shocks to a subset of the modellable risk factors of the positions in the portfolio as specified in the institution’s IMA permission so that the following requirement is met with the sum taken over from the preceding 60 business days:

\[\frac{1}{60}\cdot\sum_{k-0}^{59}\frac{{PES}_{t-k}^{RC}}{{PES}_{t-k}^{FC}}\geq75%\]

Where an institution no longer meets the requirement referred to in the first sub-paragraph of point (a) of this paragraph 2 the institution shall immediately notify the PRA thereof and, in order to meet that requirement, shall update the subset of the modellable risk factors within one month. If, after one month, that institution continues to fail to meet that requirement, the institution:

1. (i) shall cease use of internal models in accordance with this Part in relation to the positions assigned to the number of trading desks which it is necessary to exclude from the calculation in paragraph 1 in order for the institution to meet the requirements; and
2. (ii) shall apply Market Risk: Advanced Standardised Approach (CRR) Part to calculate the own funds requirements for market risk for all the positions assigned to those trading desks.

If the institution provides to the PRA a reasoned confirmation that the institution is compliant with the requirements referred to in the first sub-paragraph of point (a) of this paragraph 2, it may resume the use of internal models in accordance with this Part to calculate own funds requirements for market risk for the positions assigned to those trading desks;

1. (b) in calculating:

\[{PES}_t^{RS,i}\]

an institution 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;

1. (c) the data inputs used to determine the scenarios of future shocks applied to the modellable risk factors referred to in points (a) and (b) shall be calibrated to historical data from a continuous 12-month period of financial stress that shall be identified by the institution in order to maximise the value of:

\[{PES}_t^{RS}\]

and for the purpose of identifying that stress period, an institution shall use an appropriate observation period starting at least from 1 January 2007. The institution shall assess the appropriateness of the stress period at each quarterly reporting reference date and shall adjust the stress period as necessary; and

1. (d) the data inputs of:

\[{PES}_t^{RS,i}\]

shall be calibrated to the 12-month stress period that has been identified by the institution for the purposes of point (c).

3.

For the purpose of calculating the partial expected shortfall measures:

\[{PES}_t^{RC}\]

and

\[{PES}_t^{RC,i}\]

referred to in Article 325bb(1), an institution shall, in addition to the requirements set out in paragraph 1, meet the following requirements:

1. (a) in calculating:

\[{PES}_t^{RC}\]

an institution 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;

1. (b) in calculating:

\[{PES}_t^{RC,i}\]

an institution 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;

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

4.

For the purpose of calculating the partial expected shortfall measures:

\[{PES}_t^{FC}\]

and

\[{PES}_t^{FC,i}\]

referred to in Article 325bb(1), an institution shall, in addition to the requirements set out in paragraph 1, meet the following requirements:

1. (a) in calculating:

\[{PES}_t^{FC}\]

an institution shall apply scenarios of future shocks to all the modellable risk factors of the positions in the portfolio;

1. (b) in calculating:

\[{PES}_t^{FC,i}\]

an institution 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; and

1. (c) the data inputs used to determine the scenarios of future shocks applied to the modellable risk factors referred to in points (a) and (b) shall be calibrated to historical data from the preceding 12-month period; provided that 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, the institution must use historical data for a period shorter than the preceding 12 months, but of at least the preceding six months.

5.

In calculating a given partial expected shortfall measure as referred to in Article 325bb(1), an institution 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.

[Note: This rule corresponds to Article 325bc of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall, in accordance with the methodologies set out in this Article and in Article 325bdx, map each risk factor of positions assigned to the trading desks for which it has been granted an IMA 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.

For the purposes of paragraph 1, the liquidity horizon of a risk factor 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, 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 PRA of the trading desks and the broad sub-categories of risk factors to which it decides to apply the treatment referred to in this paragraph.

4.

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

5.

[Note: Provision left blank]

6.

An institution shall verify the appropriateness of the mapping referred to in paragraph 1 on at least a quarterly basis.

7.

An institution shall map risk factors of positions referred to in paragraph 1 to the broad risk factor categories and broad risk factor subcategories of Table 2 in accordance with Article 325bdx.

Table 2

8.

For the purpose of this Article:

1. (a) the currencies that constitute the most liquid currencies for the purposes of the relevant subcategory in the interest rate broad risk factor sub-category of Table 2 shall be, in addition to the domestic currency mentioned in that Table, the following currencies: Australian dollar (AUD); Canadian dollar (CAD); Euro (EUR); Pound sterling (GBP); Japanese yen (JPY); Swedish kroner (SEK); United States dollar (USD); and
2. (b) the currency pairs that constitute the most liquid currency pairs subcategory in the foreign exchange broad risk factor category of Table 2 shall be any currency pairs formed from any two of the following currencies: Australian dollar (AUD); Brazilian lire (BRL); Canadian dollar (CAD); Swiss franc (CHF); Chinese yuan (CNY); Euro (EUR); Pound sterling (GBP); Hong Kong Dollar (HKD); Indian rupee (INR); Japanese Yen (JPY); South Korean won (KRW); Mexican peso (MXN); Norwegian kroner (NOK); New Zealand dollar (NZD); Russian rouble (RUB); Swiss kroner (SEK); Singapore dollar (SGD); Turkish lira (TRY); United States dollar (USD); and South African rand (ZAR).

9.

For the purpose of this Article, an equity shall be considered as an equity with large capitalisation where its market capitalisation is greater than GBP 1.60 billion. All other equities shall be considered as equities with small capitalisation.

[Note: Paragraphs 1 to 6 of this rule correspond to Article 325bd(1) to (6) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall map risk factors of positions referred to in paragraph 1 of Article 325bd to the broad risk factor categories and broad risk factor subcategories of Table 2 of Article 325bd in accordance with the following:

1. (a) it shall map the risk factor to the most appropriate broad risk factor category, having regard to the nature of the risk captured by the risk factor and the data used as inputs for the risk factor in the risk measurement model;
2. (b) it shall map the risk factor to the most appropriate broad risk factor subcategory under the broad risk factor category identified in accordance with point (a), having regard to the nature of the risk captured by the risk factor and the data used as inputs for the risk factor in the risk measurement model.

2.

Where the nature of the risk factor does not correspond to any broad risk factor category, the institution shall map that risk factor to the broad risk factor category ‘commodity’ and to the broad risk factor subcategory ‘other types’ under the ‘commodity’ broad risk factor category.

3.

Where the nature of the risk captured by the risk factor and the data used as inputs for that risk factor correspond to risk factors that could fall under more than one broad risk factor category or broad risk factor subcategory, the institution shall apply the following steps in sequence:

1. (a) it shall first identify the broad risk factor categories and the corresponding broad risk factor subcategories that could be identified for that risk factor on the basis of its nature and the data used as inputs;
2. (b) among the broad risk factor categories and the corresponding broad risk factor subcategories identified in accordance with point (a), it shall map the risk factor to the broad risk factor category and the corresponding broad risk factor subcategory that results in the longest liquidity horizon; and
3. (c) where, based on the process referred to in point (b), more than one broad risk factor category and corresponding broad risk factor subcategory would result in the longest liquidity horizon, it may map the risk factor to any of those broad risk factor categories and their corresponding broad risk factor subcategories.

4.

By way of derogation from paragraph 1, where a single risk factor is used to model a homogeneous index instrument, an institution may apply instead the following steps in sequence:

1. (a) it shall map the risk factor to the broad risk factor category corresponding to the risk embedded in the homogenous index. Where the risk factor is the price of a homogenous index made of bonds and indices composed by bonds only, it shall map that risk factor to the credit spread broad risk factor category;
2. (b) it shall apply paragraph 1 to 3 to each of the constituents of the index to obtain the liquidity horizons of each constituent;
3. (c) it shall compute the weighted average of the liquidity horizons obtained pursuant to point (b) and rounded to the nearest integer, by first multiplying the liquidity horizon of each individual constituent of the index by its weight in the index and then by summing the weighted liquidity horizons for all constituents of the index; and
4. (d) it shall map the risk factor to that subcategory of Table 2 of Article 325bd, among those belonging to the broad risk factor category identified in accordance with point (a), that has the shortest liquidity horizon which is greater or equal to the liquidity horizon identified in accordance with point (c).

For the purposes of this paragraph, ‘homogeneous index’ shall refer to an index that has one of the following compositions:

1. (i) equities and indices composed by equities only;
2. (ii) bonds and indices composed by bonds only;
3. (iii) credit default swaps and indices composed of credit default swaps only; or
4. (iv) commodities and indices composed of commodities only.

5.

An institution shall map the following risk factors as follows:

1. (a) inflation risk factors for a given currency shall be mapped to the interest rate broad risk category and to the broad risk factor subcategory of that currency;
2. (b) mono-currency basis risk and cross-currency basis risk factors shall be mapped to the interest rate broad risk factor category and to the broad factor subcategory of the currency denominating the basis;
3. (c) equity repo rates and dividend risk factors shall be mapped to the equity broad risk factor category; and
4. (d) for the purpose of determining the broad risk factor subcategory, equity repo rates and dividend risk factors for a given equity shall be treated as risk factors corresponding to the volatility of that equity.

1.

An institution shall assess the modellability of all the risk factors of the positions assigned to the trading desks for which it has been granted an IMA permission.

2.

As part of the assessment referred to in paragraph 1, an institution shall calculate the own funds requirements for market risk in accordance with Article 325bk for those risk factors that are not modellable.

3.

With the exception of the cases referred to paragraphs 8 to 10, an institution shall consider a risk factor subject to the assessment referred to in paragraph 1 to be modellable where, over an observation period of 12 months ending at the preceding quarterly reporting reference date an institution has identified for that risk factor either of the following:

1. (a) a minimum of 24 prices which are verifiable in accordance with paragraphs 5 and 6 with distinct observation dates, which are representative of the risk factor in accordance with paragraph 7 and for which there are no 90-day periods with less than four of those verifiable prices; and
2. (b) a minimum of 100 prices which are verifiable in accordance with paragraphs 5 and 6, with distinct observation dates and which are representative of the risk factor in accordance with paragraph 7.

4.

An institution may replace the 12-month period referred to in paragraph 3 by a 12-month period that is ending no earlier than one month before the preceding quarterly reporting reference date where all of the following conditions are met:

1. (a) the institution applies the shifted 12-month period consistently across all risk factors of the same type as that risk factor;
2. (b) the institution applies the shifted 12-month period consistently across time; and
3. (c) the institution documents the use of a 12-month period in accordance with this paragraph.

5.

For the purposes of this Article:

1. (a) an institution shall consider a price to be verifiable where any of the following conditions and the requirements of paragraph 6 are met:
   1. (i) the price is obtained from an actual transaction to which the institution was one of the parties and which was entered into at arm’s length;
   2. (ii) the price is obtained from an actual transaction which was entered into by third parties at arm’s length; or
   3. (iii) the institution has identified, on a given observation date, an actual bona fide competitive bid and offer quotations provided at arm’s length by the institution itself or by third parties, at which, conforming to trade custom, the institution or the third parties have committed to execute a transaction.
2. (b) an institution shall not consider a price to be verifiable where any of the following conditions are met:
   1. (i) the price is obtained from a transaction or quotation between two entities of the same group;
   2. (ii) the price is obtained from a transaction or quotation of a negligible volume as compared to usual volume of transactions or quotes, reflective of current market conditions; or
   3. (iii) the price is obtained from a quotation that is substantially further off mid-market than the institution identified on a given observation date actual bona fide competitive bid and offer quotations, with a bid–offer spread deviating substantially from bid–offer spreads reflective of current market conditions;
3. (c) transactions shall not be conducted and quotations shall not be committed with the sole purpose of identifying a sufficient number of verifiable prices to meet the criteria specified in points (a) and (b) of paragraph 3; or
4. (d) the observation date of a verifiable price shall correspond to the day of execution for transactions and to the day on which the quotation was committed for quotations. The observation date of verifiable prices shall be recorded based on a consistent single time zone across all data sources.

6.

An institution shall use a transaction or a quotation for the purpose of points (a)(ii) and (a)(iii) of paragraph 5 only if all the following conditions are met:

1. (a) the transaction or quotation has been processed through, or collected by, a third-party vendor;
2. (b) the third-party vendor or the institution has agreed to provide evidence of the transaction or quotation and evidence of the verifiability of its price to the PRA upon request;
3. (c) the third-party vendor has provided to the institution the observation date and a minimum set of information about the transaction or quotation on the basis of which the institution is able to map the verifiable price to its risk factors for which it is representative in accordance with paragraph 7;
4. (d) the institution has verified that the third-party vendor is subject, at least annually, to an independent audit by a third-party undertaking, within the meaning of Article 325bi(1)(i), regarding the validity of its price information, governance and processes, and has access to audit results and reports, in case these are requested by the PRA.
   1. For the purpose of point (d), the independent audit by a third-party undertaking shall include, at a minimum, all of the following elements:
   2. (i) that the third-party vendor possesses the information necessary to verify that a price is verifiable in accordance with paragraph 5, as well as the information necessary to map the verifiable prices to the risk factors for which they are representative in accordance with paragraph 7;
   3. (ii) that the third-party vendor is able to demonstrate the integrity of the information referred to in point (a);
   4. (iii) that the third-party vendor has in place internal processes and a sufficient number of staff with a level of skills appropriate for the management of the information referred to in point (a); and
   5. (iv) that, where a third-party vendor does not provide the institution with the information to verify that a price is verifiable in accordance with paragraph 5, the third-party vendor is contractually obliged to verify itself that the price is verifiable in accordance with this Article; and
5. (e) where a third-party vendor does not provide the institution with the information to verify that a price is verifiable in accordance with paragraph 5, the institution must ensure that the third-party vendor is contractually obliged to verify itself that a price is verifiable in accordance with paragraph 5.

7.

In relation to the representativeness of risk factors, an institution:

1. (a) shall consider a verifiable price to be representative of a risk factor at its observation date only where both the following conditions are met:
   1. (i) there is a close relationship between the risk factor and the verifiable price; and
   2. (ii) the institution has a specific conceptually sound methodology to extract the value of the risk factor from the verifiable price. Any input data or risk factor used in that methodology other than that verifiable price shall be based on objective data;
2. (b) may count a verifiable price for the purpose of this Article for more than one risk factor for which it is representative in accordance with paragraph 1. An institution shall document and validate all instances where a verifiable price is counted for more than one risk factor, and shall notify the PRA of the justification for this; and
3. (c) where it uses a systematic credit or equity risk factor to capture market-wide movements for given attributes of a pool of issuers, such as the country, region or sector of those issuers, verifiable prices of market indices or instruments of individual issuers shall be considered representative for that systematic risk factor only where they share the same attributes as that systematic risk factor.

8.

In relation to the modellability of risk factors belonging to curves, surfaces and cubes, an institution shall comply with the following:

1. (a) where an institution defines one or more points of a curve, a surface or a cube as the risk factors in its risk measurement model, the institution shall assess the modellability of those risk factors by applying the following steps in sequence:
   1. (i) for each curve, surface or cube, it shall determine relevant buckets of risk factors in accordance with paragraph 9;
   2. (ii) it shall determine the modellability of the buckets determined pursuant to point (i) in accordance with point (b) of paragraph 8; and
   3. (iii) it shall consider as modellable risk factor any risk factor that belongs to a bucket that has been considered modellable pursuant to point (a)(ii) of paragraph 8;
2. (b) an institution shall consider a bucket modellable where, over an observation period of 12 months ending at the preceding quarterly reporting reference date, the institution has identified, for that bucket, either of the following:
   1. (i) a minimum of 24 prices which are verifiable in accordance with paragraphs 5 and 6, with distinct observation dates, which are allocated to that bucket and for which there shall be no 90-day period with less than four of those verifiable prices; or
   2. (ii) a minimum of 100 prices which are verifiable in accordance with paragraphs 5 and 6, with distinct observation dates and which are allocated to that bucket.
3. (c) an institution may replace the 12-month period referred to in this paragraph by a 12-month period that is ending no earlier than one month before the preceding quarterly reporting reference date where all of the following conditions are met:
   1. (i) the institution applies the shifted 12-month period consistently across all the buckets of a curve, a surface or a cube;
   2. (ii) the institution applies the shifted 12-month period consistently across time; and
   3. (iii) the institution documents the use of a 12-month period in accordance with this paragraph.

An institution shall allocate a verifiable price to a bucket where it is representative in accordance with paragraph 7 for a risk factor that belongs to that bucket. For this purpose, the institution may consider as a risk factor any point of the curve, surface or cube belonging to the bucket, regardless of whether such point is a risk factor included in the risk measurement model.

9.

In relation to each given curve, surface or cube to which a risk factor belongs:

1. (a) an institution shall determine the buckets of that curve, surface or cube using the standard pre-defined buckets in point (b), unless it meets the requirements for the derogation in point (c), in which case it may either define those buckets itself or define them using a combination of its own definitions and the standard pre-defined buckets in point (b), provided that only one method may be used within each dimension;
2. (b) The standard, pre-defined buckets are:
   1. (i) the nine buckets defined in row i. of Table 1 of this paragraph for risk factors with one maturity dimension t, expressed in years, which have been assigned to the following broad risk factor categories:
      1. (1) Interest rate, except those risk factors assigned to the broad risk factor subcategory Volatility;
      2. (2) Foreign Exchange, except those risk factors assigned to the broad risk factor subcategory Volatility; or
      3. (3) Commodity, except those risk factors assigned to the broad risk factor subcategories Energy volatility and carbon emissions volatility, Precious metal volatility and nonferrous metal volatility and Other commodity volatilities;
   2. (ii) the six buckets defined in row ii. of Table 1 for each maturity dimension ‘t’ of risk factors with more than one maturity dimension, expressed in years, which have been assigned to the following broad risk factor categories:
      1. (1) Interest rate, except those risk factors assigned to the broad risk factor subcategory Volatility;
      2. (2) Foreign Exchange, except those risk factors assigned to the broad risk factor subcategory Volatility; or
      3. (3) Commodity, except those risk factors assigned to the broad risk factor subcategories Energy volatility and carbon emissions volatility, Precious metal volatility and nonferrous metal volatility and Other commodity volatilities;
   3. (iii) the five buckets defined in row iii. of Table 1 for each maturity dimension ‘t’ for risk factors with one or several maturity dimensions, expressed in years, which have been assigned to the following broad risk factor categories:
      1. (1) Credit spread, except those risk factors assigned to the broad risk factor subcategory Volatility; or
      2. (2) Equity, except those risk factors assigned to the broad risk factor subcategories Volatility (Large capitalisation) and Volatility (Small capitalisation);
   4. (iv) the five buckets defined in row iv. of Table 1 for any risk factors with one or several moneyness dimensions, as expressed using the delta ('𝛿') convention. For option markets where alternative definitions of moneyness are standard, an institution shall convert the buckets defined in row iv. of Table 1 to the market-standard convention using formulae which are consistent with their own documented and independently reviewed pricing models;
   5. (v) the five buckets defined in row iii. and the five buckets defined in row iv. of Table 1 for risk factors assigned to the following broad risk factor categories:
      1. (1) Foreign Exchange, exclusively those risk factors assigned to the broad risk factor subcategory Volatility;
      2. (2) Credit spread, exclusively those risk factors assigned to the broad risk factor subcategory Volatility;
      3. (3) Equity, exclusively those risk factors assigned to the broad risk factor subcategories Volatility (Large capitalisation) and Volatility (Small capitalisation); or
      4. (4) Commodity, exclusively those risk factors assigned to the broad risk factor subcategories Energy volatility and carbon emissions volatility, Precious metal volatility and non-ferrous metal volatility and Other commodity volatilities;
   6. (vi) the six buckets defined in row ii., the five buckets defined in row iii. and the five buckets defined in row iv. of Table 1 for risk factors assigned to the broad risk factor category Interest rate and to the broad risk factor subcategory Volatility with a maturity, expiry and moneyness dimension;

Table 1

A given standard bucket may be subdivided in smaller buckets.

1. (c) By way of derogation from point (a) only where all the following conditions are met, an institution may either define the buckets of a curve, surface or cube themselves or define them using a combination of their own definitions and the standard pre-defined buckets in point (b), provided that only one method may be used within each dimension:
   1. (i) the buckets cover the whole curve, surface or cube;
   2. (ii) the buckets are non-overlapping; and
   3. (iii) each bucket includes exactly one risk factor that is part of the calculation of the theoretical changes in the trading desk portfolios’ values of the institution for the purposes of assessing the compliance with the profit and loss attribution requirements in accordance with Article 325bg;
2. (d) For the assessment of the modellability of risk factors of the broad risk factor category Credit spread belonging to a certain maturity bucket, an institution may reallocate the verifiable prices of a bucket to the adjacent bucket related to shorter maturities only where all the following conditions are met:
   1. (i) the institution does not have exposure to any risk factor belonging to the bucket corresponding to the longer maturities and hence does not use any of these risk factors within its risk measurement model;
   2. (ii) any verifiable price is only counted in a single maturity bucket; and
   3. (iii) any verifiable price is only reallocated once.

10.

In relation to the modellability of risk factors belonging to parametric curves, surfaces and cubes:

1. (a) where an institution uses one or more parametric functions to represent a curve, a surface or a cube and defines the function parameters as the risk factors in its risk measurement model, the institution shall assess the modellability of those function parameters used as risk factors by applying for each parametric function the following steps in sequence:
   1. (i) it shall identify the set of points of the curve, surface or cube that were used to calibrate the parametric function;
   2. (ii) it shall apply the bucketing approach set out in paragraph 9 as if the risk factors in the risk measurement model were the points identified pursuant to point (i);
   3. (iii) it shall assess, in accordance with paragraph 8, the modellability of the buckets resulting from the application of the bucketing approach referred to in paragraph 9, as if the risk factors in the risk measurement model were the points identified in point (i);
2. (b) for the purpose of assessing the modellability of a parameter of the parametric function, the institution shall apply the following steps in sequence:
   1. (i) it shall identify the set of points of the curve, surface or cube that were used to calibrate that function parameter;
   2. (ii) it shall assess that function parameter as modellable, where the points identified pursuant to point (i) belong only to buckets assessed as modellable pursuant to point (a)(iii); and
3. (c) it shall assess that function parameter as non-modellable, where a point identified pursuant to point (i) belongs to a bucket assessed as non-modellable pursuant to point (a)(iii).

11.

An institution shall clearly document in its internal policies:

1. (a) the set and definitions of risk factors in its risk measurement model subject to the modellability assessment;
2. (b) the sources of verifiable price information used to assess the modellability of risk factors;
3. (c) the criteria for a price to be considered verifiable in accordance with paragraphs 5 and 6, including an outline of how the institution assesses whether the volume of a transaction or committed quote is non-negligible in accordance with point (b)(ii) of paragraph 5 and whether the bid–offer spread of a quote is reasonable in accordance with point (b)(iii) of paragraph 5 and paragraph 6;
4. (d) the mapping process and the criteria used to determine the representativeness of verifiable prices to risk factors in accordance with paragraph 7, including an outline of the methodology specified for the extraction of the value of the risk factor and any additional input the methodology potentially requires;
5. (e) the modellability assessment for parametric curves, surfaces or cubes in accordance with paragraph 10;
6. (f) the use of the bucketing approaches in accordance with paragraph 9, also specifying whether and how the institution reallocates the verifiable prices of a bucket to the adjacent bucket related to shorter maturities; and
7. (g) the use of the 12-month period in accordance with paragraphs 3 and 8.

12.

For each risk factor, an institution shall keep a record of at least one year of the results of their modellability assessment, including the documentation referred to in points (a) to (g) of paragraph 11. For risk factors for which one year of results is not yet available, an institution shall keep the maximum available track record of results.

[Note: Paragraphs 1 and 2 of this rule correspond to Article 325be(1) and (2) of CRR as it applied immediately before revocation by the Treasury]

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 internal model in accordance with the following requirements:

1. (a) the calculation of the value at risk shall be subject to a one-day holding period;
2. (b) scenarios of future shocks shall apply to the risk factors of the trading desk's positions referred to in Article 325bg(3), including risk factors that are considered non-modellable in accordance with Article 325be;
3. (c) data inputs used to determine the scenarios of future shocks applied to the risk factors shall be calibrated to historical data referred to in point (c) of Article 325bc(4); and
4. (d) 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).

2.

An institution 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:

1. (a) 12 overshootings for the value-at-risk number, calculated at a 99th percentile one tailed-confidence interval on the basis of back-testing of the hypothetical changes in the value of the portfolio;
2. (b) 12 overshootings for the value-at-risk number, calculated at a 99th percentile one tailed-confidence interval on the basis of back-testing of the actual changes in the value of the portfolio;
3. (c) 30 overshootings for the value-at-risk number, calculated at a 97.5th percentile one tailed-confidence interval on the basis of back-testing of the hypothetical changes in the value of the portfolio; or
4. (d) 30 overshootings for the value-at-risk number, calculated at a 97.5th percentile one tailed-confidence interval on the basis of back-testing of the actual changes in the value of the portfolio.

4.

An institution shall count daily overshootings in accordance with the following:

1. (a) it shall base the back-testing of hypothetical changes in the value of the portfolio 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;
2. (b) it shall base the back-testing of actual changes in the value of the portfolio 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; and
3. (c) it shall count an overshooting 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.

5.

An institution shall calculate, in accordance with paragraphs 6 and 7, the multiplication factor (m_c) referred to in Article 325ba for the portfolio of all the positions assigned to the trading desks for which it has been granted an IMA permission.

6.

An institution shall calculate the multiplication factor (m_c) as 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, the institution shall calculate that add-on 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 paragraph. The institution’s calculation of the add-on shall be subject to the following requirements:

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

Table 3

7.

An institution shall promptly notify the PRA of overshootings that result from their back-testing programme and provide an explanation for those overshootings, and in any case shall notify the PRA thereof no later than within five business days after the occurrence of an overshooting.

8.

By way of derogation from paragraph 6, an institution may, with the permission of the PRA, exclude an overshooting from a count if, on applying for such permission, it can demonstrate to the satisfaction of the PRA that:

1. (a) the overshooting is not attributable to a deficiency in the internal risk model; and
2. (b) it meets either of the following requirements:
1. (i) if the overshooting is attributable to a non-modellable risk factor, the one-day change in the portfolio’s value does not exceed the related value-at-risk number referred to in point (a) of paragraph 6 but calculated by applying the scenarios of future shocks to all risk factors of the trading desk's positions referred to in Article 325bg(3), including non-modellable risk factors; or
2. (ii) if the overshooting is attributable to deficiencies in risk capture and where the institution fulfils an additional own funds requirement in accordance with Article 325az(4), the additional own funds requirement calculated in accordance with Article 325az(4) is higher than the positive difference between the change in the value of the institution's portfolio and the related value-at-risk number.

[Note: This is a permission created under sections 144G(2) and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

9.

For the purpose of the trading desk back-testing referred to in paragraph 3, an institution shall:

1. (a) compute actual changes in the trading desk portfolio’s value using the same pricing methods, model parametrisations, market data and any other technique as those used in the end-of-day valuation process, taking into account the independent price verification process in accordance with paragraph 8 of Trading Book (CRR) Part Article 105;
2. (b) reflect the passage of time in the actual changes in the trading desk portfolio’s value;
3. (c) compute the value of an adjustment on the basis of only the positions assigned to that trading desk and shall reflect changes in its value only on the reference date for the calculation of the adjustment;
4. (d) include in the actual changes in the trading desk portfolio’s value only the adjustments that have been considered in the end-of-day valuation process referred to in point (a) that are market risk related, with the exception of all of the following:
   1. (i) credit valuation adjustments reflecting the current market value of the credit risk of counterparties to the institution;
   2. (ii) adjustments attributed to the institution’s own credit risk that have been excluded from own funds in accordance with point (b) or (c) of paragraph 1 of Own Funds (CRR) Part Article 33;
   3. (iii) additional value adjustments deducted from Common Equity Tier 1 capital in accordance with Own Funds (CRR) Part Article 34;

provided that, an institution may also exclude from the calculation of the actual changes an adjustment that is computed, in the end-of-day valuation process, across sets of positions assigned to more than one trading desk on a net basis, where all of the following conditions are met:

1. (1) that adjustment is computed across sets of positions assigned to more than one trading desk on a net basis due to its nature;
2. (2) the internal risk management of that adjustment is consistent with the level at which it is calculated;
3. (3) the institution documents all of the following:
   1. (a) the sets of positions on which the adjustment is computed;
   2. (b) the reasoning underpinning the computation of the adjustment on the sets of positions referred to in point (1); and
   3. (c) the justification for not computing the adjustment on the basis of positions assigned to that trading desk only.

10.

For the purpose of the back-testing referred to in paragraph 6, an institution shall:

1. (a) compute actual changes in the portfolio’s value using the same pricing methods, model parametrisations, market data and any other technique as those used in the end-of-day valuation process, taking into account the independent price verification process in accordance with paragraph 8 of Trading Book (CRR) Part Article 105;
2. (b) reflect the passage of time in the actual changes in the portfolio’s value;
3. (c) include in the actual changes in the portfolio’s value the adjustments that have been considered in the end-of-day valuation process referred to in point (a) that are market risk related, with the exception of all of the following:
   1. (i) credit valuation adjustments reflecting the current market value of the credit risk of counterparties to the institution;
   2. (ii) adjustments attributed to the institution’s own credit risk that have been excluded from own funds in accordance with point (b) or (c) of paragraph 1 of Own Funds (CRR) Part of Article 33; and
   3. (iii) additional value adjustments deducted from Common Equity Tier 1 capital in accordance with Own Funds (CRR) Part Article 34;
4. (d) compute the value of an adjustment in either of the following ways:
   1. (i) on the basis of only those positions that are assigned to trading desks for which an institution calculate the own funds requirements for market risk in accordance with this Part; or
   2. (ii) on the basis of all positions subject to own funds requirements for market risk; and
5. (e) reflect changes in the value of that adjustment only on the reference date for the calculation of the adjustment.

11.

For the purpose of the trading desk back-testing referred to in paragraph 3, an institution shall:

1. (a) compute hypothetical changes in the trading desk portfolio’s value using the same pricing methods, model parametrisations, market data and any other technique as those used in the end-of-day valuation process, without considering any fees and commissions;
2. (b) reflect the passage of time effect in the hypothetical changes in the trading desk portfolio’s value consistently with the treatment they apply in relation to such effect in the calculation of the expected shortfall risk measure referred to in Article 325bb and in the calculation of the stress scenario risk measure referred to in Article 325bk; and
3. (c) include in the hypothetical changes in the trading desk portfolio’s value only adjustments that have been considered in the end-of-day valuation process referred to in point (a) that are market risk related and are calculated on a daily basis, with the exception of all of the following:
1. (i) credit valuation adjustments reflecting the current market value of the credit risk of counterparties to the institution;
2. (ii) adjustments attributed to the institution’s own credit risk that have been excluded from own funds in accordance with point (b) or (c) of paragraph 1 of Own Funds (CRR) Part of Article 33;
3. (iii) additional value adjustments deducted from Common Equity Tier 1 capital pursuant to Own Funds (CRR) Part Article 34; and
4. (iv) any other adjustment specified for the purposes of this paragraph in the institution’s IMA permission.

12.

By way of derogation from point (a) of paragraph 11, an institution may also exclude from the calculation of the hypothetical changes an adjustment that is computed, in the end-of-day valuation process, across sets of positions assigned to more than one trading desk on a net basis, where all of the following conditions are met:

1. (a) that adjustment is computed across sets of positions assigned to more than one trading desk on a net basis due to its nature;
2. (b) the internal risk management of that adjustment is consistent with the level at which it is calculated;
3. (c) the institution documents all of the following:
1. (i) the sets of positions on which the adjustment is computed;
2. (ii) the reasoning underpinning the computation of the adjustment on the sets of positions referred to in point (i); and
3. (iii) the justification for not computing the adjustment on the basis of positions assigned to that trading desk only.

13.

An institution shall compute the value of an adjustment on the basis of the positions assigned to that trading desk only and shall reflect changes based on a comparison between the end-of-day value of that adjustment and, assuming unchanged positions in the trading desk’s portfolio, the value of that adjustment at the end of the subsequent day.

14.

For the purpose of the back-testing referred to in paragraph 6, an institution shall:

1. (a) compute hypothetical changes in the portfolio’s value using the same pricing methods, model parametrisations, market data and any other technique as those used in the end-of-day valuation process, without considering any fees and commissions;
2. (b) reflect the passage of time effect in the hypothetical changes in the portfolio’s value consistently with the treatment the institution applies for such effect in the calculation of the expected shortfall risk measure as referred to in Article 325bb and in the calculation of the stress scenario risk measure referred to in Article 325bk;
3. (c) include in the hypothetical changes in the portfolio’s value only the adjustments that have been considered in the end-of-day valuation process referred to in point (a) that are market risk related, are calculated on a daily basis, with the exception of all of the following:
   1. (i) credit valuation adjustments reflecting the current market value of the credit risk of counterparties to the institution;
   2. (ii) adjustments attributed to the institution’s own credit risk that have been excluded from own funds in accordance with point (b) or (c) of paragraph 1 of Own Funds (CRR) Part of Article 33 of ;
   3. (iii) additional valuation adjustments deducted from Common Equity Tier 1 capital as per Own Funds (CRR) Part Article 34; and
   4. (iv) other adjustments which are specified for the purposes of this paragraph in the institution’s IMA permission;
4. (d) compute the value of an adjustment in either of the following ways:
   1. (i) on the basis of only those positions that are assigned to trading desks for which an institution calculates the own funds requirements for market risk using internal models in accordance with this Part; or
   2. (ii) on the basis of all positions subject to own funds requirements for market risk; in this case, an institution shall include the changes in the value of that adjustment in the calculation of the actual changes in the portfolio’s value.

15.

An institution shall have policies and procedures in place defining how they calculate the actual and hypothetical changes in accordance with paragraphs 9 to 12, which shall include at least the following elements:

1. (a) a description of how the actual changes in the relevant portfolio’s value are calculated, an outline of the differences between the changes in the end-of-day portfolio values produced by the end-of-day valuation process and the actual changes in the relevant portfolio’s value;
2. (b) the definitions of fees and commissions and the methods used to apply the exclusion referred to in point (b) of paragraph 4;
3. (c) a list of all adjustments specifying for each adjustment all of the following:
1. (i) definitions;
2. (ii) calculation methodology and process;
3. (iii) frequency of calculation and reasoning in case of a less than daily calculation frequency;
4. (iv) whether the adjustment is sensitive to market risk;
5. (v) the sets of positions on which the adjustment is calculated and the reasoning for performing the computation on such sets;
6. (vi) whether and how the risk stemming from changes in the adjustment is actively hedged and which trading desk or desks are responsible for this;
7. (vii) whether and how each adjustment is taken into account in the actual changes in the relevant portfolio value for the purpose of the back-testing referred to in paragraph 6 and the back-testing referred to in paragraph 3; and
8. (viii) whether and how each adjustment is taken into account in the hypothetical changes in the relevant portfolio value for the purpose of this Article 325bf and Article 325bg, also outlining how the change in the adjustment is calculated if one assumes unchanged positions in the portfolio.

[Note: Paragraphs 1 to 8 of this rule correspond to Article 325bf(1) to (8) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution must ensure that a trading desk meets the P&L attribution requirements in compliance with the requirements set out in this Article.

2.

An institution shall in compliance with the P&L attribution requirements 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 requirements 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 requirements set out in Article 325bf.

4.

With regard to ensuring that the theoretical changes in a trading desk portfolio’s value are sufficiently close to the hypothetical changes in the trading desk portfolio’s value for the purposes of paragraph 2, an institution shall calculate the Spearman correlation coefficient as laid down in paragraph 5, and the Kolmogorov-Smirnov test metric as laid down in paragraph 6.

For the purposes of this Article, an institution may align the snapshot time for which it calculates the theoretical changes in the trading desk portfolio’s value with the snapshot time for which it calculates the hypothetical changes in the trading desk portfolio’s value.

5.

In order to calculate the Spearman correlation coefficient for a trading desk referred to in paragraph 4, an institution shall perform the following steps in sequence:

1. (a) determine the time series of observations of the hypothetical and theoretical changes in the trading desk portfolio’s value for the most recent 250 business days;
2. (b) from the time series of the hypothetical and theoretical changes referred to in point (a), produce the corresponding time series of ranks in the manner set out below, treating the time series of the hypothetical and theoretical changes as the originating time series;
3. (c) compute the Spearman correlation coefficient in accordance with the following formula:

\[r_s=\frac{cov(R_{HPL},R_{RTPL})}{\sigma_{R_{HPL}}\times\sigma_{R_{RTPL}}}\]

1. (d) An institution shall produce the time series of ranks referred to in point (b) from an originating time series by performing the following steps in sequence:
   1. (i) for each observation within the originating time series, count the number of observations with a lower value than that observation within that time series;
   2. (ii) label each observation with the number resulting from the application of point (i) increased by one;
   3. (iii) where, as a result of the application of point (ii), two or more observations are labelled with the same number, an institution shall in addition increase the numbers of those labels with the decimal fraction of one divided by the quantity of the labels with the same number;
   4. (iv) consider as time series of ranks the time series of the labels obtained in accordance with points (ii) and (iii).
2. (e) An institution shall calculate the standard deviation of the time series of ranks R_HPL in accordance with the formula in point (i), the standard deviation of the time series of ranks R_RTPL in accordance with the formula in point (ii) and the covariance between them in accordance with the formula in point (iii) as follows:
   
   1. (i)

\[\sigma_{R_{HPL}}=\sqrt{\frac{\sum_{i=1}^{250}\left(R_{HPL_i}-\mu_{R_{HPL}}\right)^2}{249}}\]

(ii)

\[\sigma_{R_{RTPL}}=\sqrt{\frac{\sum_{i=1}^{250}\left(R_{RTPL_i}-\mu_{R_{RTPL}}\right)^2}{249}}\]

(iii)

\[cov\left(R_{HPL},R_{RTPL}\right)=\ \frac{\sum_{i=1}^{250}{(R_{HPL_i}-\mu_{R_{HPL}})\times(R_{RTPL_i}-\mu_{R_{RTPL}})}}{249}\]

6.

In order to calculate the Kolmogorov-Smirnov test metric for a trading desk referred to in paragraph 4, an institution shall perform the following steps in sequence:

1. (a) determine the time series of the most recent 250 business days of observations of the hypothetical and theoretical changes in the trading desk portfolio’s value;
2. (b) compute the empirical cumulative distribution function of the hypothetical changes in the trading desk portfolio’s value from the time series of the hypothetical changes referred to in point (a);
3. (c) compute the empirical cumulative distribution function of the theoretical changes in the trading desk portfolio’s value from the time series of theoretical changes referred to in point (a); and
4. (d) obtain the Kolmogorov-Smirnov test metric by calculating the maximum difference observed between the two empirical cumulative distributions calculated in accordance with points (b) and (c) at any possible value of profit and loss.

For the purpose of this paragraph, the empirical distribution function obtained from a time series shall be understood as the function that, given any number as input, results in the ratio of the number of observations within the time series with lower or equal value than the input number, to the number of observations within the full time series.

7.

For the purpose of determining the consequences for trading desks for which theoretical changes in their portfolio’s value are not sufficiently close to the hypothetical changes in the trading desk portfolio’s value, an institution shall classify each of the trading desks as green zone, orange zone, yellow zone or red zone trading desk as set out in paragraphs 2 to 5. An institution shall classify trading desks as follows:

1. (a) A trading desk shall be classified as a ‘green zone desk’ where both of the following conditions are met:
   1. (i) the Spearman correlation coefficient for the trading desk, is greater than 0.8; and
   2. (ii) the Kolmogorov-Smirnov test metric for the trading desk, is lower than 0.09;
2. (b) A trading desk shall be classified as a ‘red zone desk’ where either of the following conditions is met:
   1. (i) the Spearman correlation coefficient for the trading desk is lower than 0.7; or
   2. (ii) the Kolmogorov-Smirnov test metric for the trading desk, is greater than 0.12;
3. (c) a trading desk which is not classified as either a green zone or a red zone desk, and where the own funds requirements for the positions assigned to the trading desk was computed in the previous quarter in accordance with the Market Risk: Advanced Standardised Approach (CRR) Part, shall be classified as an orange zone desk; and
4. (d) a trading desk which is not a green zone, orange zone or red zone desk shall be classified as a yellow zone desk.

8.

An institution shall perform the tests relating to the P&L attribution requirement on a quarterly basis for all trading desks for which the institution has an IMA permission to calculate the own funds requirements using internal models.

9.

An institution shall:

1. (a) calculate the theoretical changes in a trading desk’s portfolio value based on a comparison between the portfolio’s end-of-day value and, assuming unchanged positions, the value of that portfolio at the end of the subsequent day;
2. (b) base theoretical changes in a trading desk’s portfolio on the pricing methods, model parametrisations, market data and any other technique used in the risk measurement model; and
3. (c) only include in the theoretical changes in a trading desk’s portfolio value the changes in the value of all risk factors included in the risk measurement model to which an institution applies the scenarios of future shocks for the purpose of calculating the expected shortfall risk measure referred to in Article 325bb or the stress scenario risk measure referred to in Article 325bk.

10.

An institution shall compute hypothetical changes in a trading desk portfolio’s value as set out in paragraph 11 of Article 325bf.

11.

An institution may replace the input data of a risk factor used for calculation of theoretical changes with data for hypothetical changes in accordance with the following:

1. (a) it may replace such input data only in the following situations:
   1. (i) to use the same provider of input data for theoretical changes as is used for hypothetical changes;
   2. (ii) to align the time of day of input data for theoretical changes with the time of day of input data for hypothetical changes;
2. (b) for the purpose of this replacement, an institution shall either:
   1. (i) directly replace the input data for theoretical changes with the input data used for hypothetical changes; or
   2. (ii) use the input data used for hypothetical changes as the basis for calculating data to replace the input data for theoretical changes, provided that for the approach in this point (ii), an institution shall document, validate and justify all instances where data calculated from the input data for hypothetical changes is calculated using techniques or transformation methods other than those in the institution’s risk measurement model;
3. (c) for the purpose of this replacement, an institution shall not apply further adjustments to theoretical or hypothetical changes to address residual operational noise that may remain after the replacement; and
4. (d) an institution shall document its reasons for all instances where the replacement referred to in this paragraph is applied.

12.

An institution shall have policies and procedures in place defining how they calculate the theoretical changes in accordance with paragraphs 9 and 11 in accordance with the following:

1. (a) the policies and procedures shall include at least an explanation of how the theoretical changes in the trading desk portfolio’s value are calculated for modellable and non-modellable risk factors;
2. (b) where designing the procedures for aligning the data in accordance with paragraph 11, an institution shall:
   1. (i) compare the theoretical changes in the trading desk portfolio’s value without the alignments referred to in paragraph 11, and the theoretical changes in the trading desk portfolio’s value with the alignments referred to in paragraph 11 and they shall document that comparison; and
   2. (ii) assess the effect of the alignments on the metrics of the test relating to the P&L attribution requirements referred to in paragraphs 5 and 6 and document that assessment; and
3. (c) An institution shall document any adjustments to input data for the risk factors within the calculation of the theoretical changes in the trading desk portfolios performed in accordance with paragraph 11, as well as the rationale for such adjustments.

[Note: Paragraphs 1 to 3 of this rule correspond to Article 325bg(1) to (3) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution using a 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:

1. (a) the risk measurement model shall capture a sufficient number of risk factors, which shall include at least the risk factors referred to in Market Risk: Advanced Standardised Approach (CRR) Part Articles 325l to 325q unless the institution is able:
   1. (i) to demonstrate that the omission of one or more of those risk factors does not have a material impact on the results of the P&L attribution requirement; and
   2. (ii) to justify why it has incorporated a risk factor in its pricing model but not in its risk measurement model;
   3. and the omission of the risk factor is specified in the institution’s IMA permission.
2. (b) the risk measurement model shall capture nonlinearities for options and other products as well as correlation risk and basis risk;
3. (c) the 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;
4. (d) the yield curves shall meet the following requirements:
   1. (i) the institution shall model the yield curves using one of the generally accepted approaches;
   2. (ii) the yield curve shall be divided into various maturity segments to capture the variations of volatility of rates along the yield curve;
   3. (iii) 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;
   4. (iv) 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; and
   5. (v) 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;
5. (e) the risk measurement model shall incorporate risk factors corresponding to gold and to the individual foreign currencies in which the institution's positions are denominated;
6. (f) the actual foreign exchange positions of a CIU shall be taken into account, provided that:
   1. (i) for this purpose, an institution may rely on third-party reporting of the foreign exchange position of the CIU, provided that the correctness of that report is adequately ensured; and
   2. (ii) the institution shall carve out from the internal models those foreign exchange positions of a CIU of which it is not aware, and shall treat them in accordance with the Market Risk: Advanced Standardised Approach (CRR) Part;
7. (g) the sophistication of the modelling technique shall be proportionate to the materiality of the institution’s activities in the equity markets. The 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;
8. (h) the 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;
9. (i) 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);
10. (j) for material exposures to volatility risks in instruments with optionality, the risk measurement model shall capture the dependency of implied volatilities across strike prices and options' maturities; and
11. (k) an institution shall periodically and at least annually demonstrate that the modelling of positions in CIUs in their risk measurement model leads to own funds requirements that are at least as conservative as if a look-through approach was applied to those positions.

2.

An institution may use empirical correlations within broad categories of risk factors and, for the purpose of calculating the unconstrained expected shortfall measure UES_t 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.

An institution shall ensure that:

1. (a) for the purpose of calculating the partial expected shortfall calculations referred to in Article 325bc, the data inputs used in their risk measurement model meet the requirements in paragraphs 4 to 10;
2. (b) where the data inputs used for a risk factor in the risk measurement model do not meet the requirements in paragraphs 4 to 10, institution deems the risk factor shall be deemed as non-modellable and shall calculate the own funds requirements for market risk in accordance with Article 325bk for that risk factor; and
3. (c) it considers the coefficients of a multifactor model as non-modellable risk factors in accordance with Article 325be unless the coefficients of that multifactor model are determined empirically based on historical data.

4.

An institution shall ensure that:

1. (a) it derives data input used in an institution’s risk measurement model from only modellable risk factors. An institution may use interpolation from a combination of modellable risk factors to determine a data input; provided that if so specified in the IMA permission, an institution may use extrapolation to determine a data input if the extrapolation is only a reasonable distance from the closest modellable risk factor;
2. (b) where an institution uses interpolation or extrapolation to generate a data input for the institution’s risk measurement model, it must determine the theoretical changes in portfolio value for the P&L attribution requirements in accordance with Article 325bg using that same interpolation or extrapolation; and
3. (c) by way of derogation, where an institution additionally calculates a stress scenario risk measure referred to in Article 325bk for one or more non-modellable risk factors that relate to that data input, the institution may also include the changes in those non-modellable risk factors for the purposes of determining the theoretical changes in portfolio value for the P&L attribution requirements in accordance with Article 325bg.

5.

An institution shall ensure the data inputs used for their risk measurement model are appropriate for adequately capturing both systematic and idiosyncratic market risk.

Where the data inputs in paragraph 11 do not allow for adequate capture of systematic or idiosyncratic market risks, the institution shall ensure that the systematic or idiosyncratic market risk is capitalised separately through non-modellable risk factors in accordance with the methodology set out in Article 325bk.

6.

An institution shall ensure that:

1. (a) the data inputs used in their risk measurement model accurately reflect the volatilities of and correlations between risk factors that are included in the risk measurement model; and
2. (b) any transformations applied to data inputs shall not have the effect of reducing the accuracy of the volatility of and correlations between risk factors that are included in the risk measurement model.

7.

An institution shall perform at least quarterly analysis to compare prices series in point (a) with the alternative price series in points (b), (c) and (d) as follows:

1. (a) the price series used in the risk measurement model;
2. (b) price data used to generate the actual changes in the value of the portfolio and the hypothetical changes in the value of the portfolio;
3. (c) verifiable prices in accordance with Article 325be; and
4. (d) price data used in the independent price verification process in accordance with paragraph 8 of Trading Book (CRR) Article 105 including daily and intra-month data where this is collected.

8.

For the purpose of performing the analysis in paragraph 7, the institution:

1. (a) shall compare the levels, volatilities and correlations of price series from these four alternative price series for the purpose of highlighting differences between the sources that are material in terms of their impact on the measurement of the expected shortfall;
2. (b) shall, where the four alternative price series are derived from overlapping underlying data, explicitly reflect this in the analysis. The institution shall give due considerations to price uncertainty; and
3. (c) shall combine all available information, including information about intra-day movements, to derive a statistical test or tests that monitor price series referred to this paragraph to assess whether the price data used in the risk measurement model results in an understatement of the measurement of the expected shortfall,

provided that, for the purposes of any analysis involving the price series in point (c) of paragraph 7, the institution may perform the assessment on a best efforts basis.

9.

An institution shall appropriately review and escalate the methodologies and results of the analysis in this Article. Where a potential understatement of ES is detected, an institution shall consider at least one of the following actions:

1. (a) make appropriate adjustments to the inputs or output of the risk measurement;
2. (b) consider those risk factors to be non-modellable in accordance with Article 325be.

10.

An institution shall ensure that:

1. (a) the data inputs used for their risk measurement model are updated at least weekly; provided that by way of derogation from this requirement, an institution may update certain data inputs for their risk measurement model less frequently than weekly but not less frequently than monthly, where the institution is able to demonstrate that less frequent updates are appropriate or necessary;
2. (b) where it uses regressions to estimate model parameters for their risk measurement model, it re-estimates such parameters with sufficient frequency and at least fortnightly. By way of derogation from this requirement an institution may re-estimate certain model parameters for their risk measurement model less frequently than fortnightly if the institution is able to demonstrate that less frequent re-estimation is appropriate or necessary and this is specified in the institution’s IMA permission;
3. (c) its risk measurement models are calibrated to current market prices which are of the same observation period as the calibration of front office pricing models;
4. (d) it has a workflow process for updating the sources of data that allows it to obtain alternative data sources in a timely manner where the data sources presently used cease to be available; and
5. (e) it has clear policies for backfilling and gap-filling missing data in a timely manner where appropriate.

11.

An institution shall ensure that the data inputs used for their risk measurement model for the purpose of calculating the partial expected shortfall calculations referred to in Article 325bc(2) are determined directly from market prices in the period of significant financial stress identified in accordance with point (c) of article Article 325bc(2); provided that, by way of derogation from this requirement, where the fundamental characteristics of a certain risk factor now differ from the characteristics of that risk factor in the identified period of significant financial stress and the institution is able to empirically justify each instance where the derogation is applied, an institution may determine stressed data inputs from market prices other than those in the identified period of significant financial stress.

12.

Where a risk factor did not exist in the identified period of significant financial stress, an institution may determine data inputs from market prices other than those relating to that risk factor in the identified period of significant financial stress, subject to the following requirements:

1. (a) it shall be able to empirically justify that the data inputs used are consistent with the level of changes observed in similar risk factors in the identified historical period; and
2. (b) it shall not include the idiosyncratic component of name-specific risk factors in the subset of modellable risk factors chosen in point (a) of Article 325bc(2), unless specified otherwise in its IMA permission;

provided that, where an institution is unable to empirically justify that the data inputs used are consistent with the level of changes observed in similar risk factors in the identified historical period, the risk factor shall not be included in the subset of modellable risk factors chosen in point (a) Article 325bc(2) and specified in the institution’s IMA permission.

13.

Where an institution uses as proxy for a risk factor one or more other risk factors, an institution shall ensure that:

1. (a) the methodologies for generating the proxy are conceptually and empirically sound; and
2. (b) the proxy appropriately represents the characteristics of the risk factor being proxied.

14.

Where an institution uses a proxy to represent a risk factor in the risk measurement model, it must use the value of the proxy rather than the risk factor itself for calculating the theoretical changes in portfolio value for the P&L attribution requirements in accordance with Article 325bg. By way of derogation from this requirement, an institution may use the value of the actual risk factor for calculating the theoretical changes in portfolio value for the P&L attribution requirements in accordance with Article 325bg, subject to meeting the following conditions:

1. (a) the institution is able to identify the basis between the proxy and the actual risk factor; and
2. (b) the institution adequately capitalises the basis identified between the proxy and the actual risk factor either through the methodology set out in Article 325bb or through Article 325bk if the risk factor is non-modellable in accordance with Article 325be.

[Note: Paragraphs 1 and 2 of this rule correspond to Article 325bh(1) and (2) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall ensure that any risk measurement model used for the purposes of this Part shall be conceptually sound and be calculated and implemented with integrity, and ensure that it meets the following qualitative requirements:

1. (a) any 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;
2. (b) an institution shall have a risk control unit that:
   1. (i) is independent from business trading units and that reports directly to senior management;
   2. (ii) is responsible for designing and implementing any risk measurement model;
   3. (iii) conducts the initial and on-going validation of any internal model used for the purposes of this Part;
   4. (iv) is responsible for the overall risk management system; and
   5. (v) produces and analyses 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;
3. (c) the management body and senior management shall be actively involved in the risk-control process;
4. (d) 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;
5. (e) the institution shall have a sufficient number of staff with a level of skills that is appropriate to the sophistication of the risk measurement model, and a sufficient number of staff with skills in the trading, risk control, audit and back-office area;
6. (f) 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 risk measurement models;
7. (g) each of its risk measurement models, 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;
8. (h) the institution shall frequently conduct rigorous programmes of stress testing, including reverse stress tests that meet the following requirements:
   1. (i) the tests shall encompass each risk measurement model;
   2. (ii) the results of those stress tests shall be reviewed by senior management at least on a monthly basis;
   3. (iii) the stress tests shall comply with the policies and limits approved by the management body; and
   4. (iv) 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; and
9. (i) the institution shall conduct an independent review of its risk measurement models, either as part of its regular internal auditing process, or by mandating a third-party undertaking to conduct that review. Such independent review shall include both the activities of the business trading units and the independent risk control unit.

For the purposes of point (i), 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 institution shall conduct a review of its overall risk management process at least once a year which shall assess the following:

1. (a) the adequacy of the documentation of the risk management system and process and the organisation of the risk control unit;
2. (b) the integration of risk measures into daily risk management and the integrity of the management information system;
3. (c) the processes the institution employs for approving the risk-pricing models and valuation systems that are used by front and back-office personnel;
4. (d) the scope of risks captured by the model, the accuracy and appropriateness of the risk-measurement system, and the validation of any significant changes to the risk measurement model;
5. (e) the accuracy and completeness of position data, the accuracy and appropriateness of volatility and correlation assumptions, the accuracy of valuation and risk sensitivity calculations, and the accuracy and appropriateness for generating data proxies where the available data are insufficient to meet the requirement set out in this Part;
6. (f) the verification process that the institution employs to evaluate the consistency, timeliness and reliability of the data sources used to run any of its risk measurement models, including the independence of those data sources;
7. (g) the verification process that the institution employs to evaluate back-testing requirements and P&L attribution requirements that are conducted in order to assess the accuracy of its risk measurement models; and
8. (h) where the review is performed by a third-party undertaking in accordance with point (i) of paragraph 1, the verification that the internal validation process set out in Article 325bj fulfils its objectives.

3.

An institution shall update the techniques and practices it uses for any of the risk measurement models used for the purposes of this Part to take into account the evolution of new techniques and best practices that develop in respect of those risk measurement models.

[Note: This rule corresponds to Article 325bi of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall have processes in place to ensure that any risk measurement models used for the purposes of this Part 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.

An institution shall conduct the validation referred to in paragraph 1 in the following circumstances:

1. (a) when any risk measurement model is initially developed and when any significant changes are made to that model; and
2. (b) 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 risk measurement model no longer being adequate.

3.

An institution shall not limit the validation of the risk measurement models of an institution to back-testing requirements and P&L attribution requirements, but shall, at a minimum, include the following:

1. (a) tests to verify whether the assumptions made in the internal model are appropriate and do not underestimate or overestimate the risk;
2. (b) 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; and
3. (c) the use of hypothetical portfolios to ensure that the 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.

[Note: This rule corresponds to Article 325bj of CRR as it applied immediately before revocation by the Treasury]

1.

For the purposes of this Article, 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.

An institution shall develop appropriate extreme scenarios of future shock for all non-modellable risk factors.

3.

An institution shall develop the extreme scenarios of future shock for a single non-modellable risk factor for the purposes of paragraph 2 such that the resulting stress scenario risk measure is at least as conservative as:

1. (a) an expected shortfall measure calculated for that non-modellable risk factor alone;
2. (b) for the stress period in accordance with paragraph 10;
3. (c) at 97.5^th percentile, one tailed confidence interval;
4. (d) calculated with base time horizon of 10 days; and
5. (e) scaled to a time horizon that is the greater of 20 days and the liquidity horizon of that non-modellable risk factor in accordance with the following formula:

\[SS_j=SS_j(T)\sqrt{\frac{max{(20,LH_j})}{10}}\]

4.

An institution may use a variety of methodologies for developing the extreme scenarios of future shock for different non-modellable risk factors and shall:

1. (a) apply those methodologies in a consistent manner across similar non-modellable risk factors;
2. (b) document a clear rationale for the methodology used for each non-modellable risk factor; and
3. (c) validate that the methodologies meet the conditions in paragraph 3.

5.

In developing the extreme scenarios of future shocks in accordance with paragraph 3 an institution shall ensure that the extreme scenarios of future shock adequately consider any limitations to the methodologies used, including but not limited to:

1. (a) any skewness or kurtosis in the distribution of returns on the non-modellable risk factor; and
2. (b) any material non-linearity in the institution’s portfolio with respect to that non-modellable risk factor.

Conceptually, an institution shall estimate the confidence interval around the extreme scenarios of future shocks produced by their methodologies due to the methodological limitations, and ensure that the extreme scenarios of future shocks used are at the conservative end of that confidence interval.

6.

Where an institution determines the extreme scenarios of future shock based on a proxy risk factor, the institution shall demonstrate that that proxy results in a stress scenario risk measure that meets the conditions in paragraph 3 with a high degree of confidence. Where an institution determines the extreme scenarios of future shock indirectly by scaling to the stress period a risk measure calibrated to another period of time, the institution shall demonstrate that the scalar is generally appropriate for the non-modellable risk factors to which it is applied and results in stress scenario risk measures that meet the conditions in paragraph 3 with a high degree of confidence.

7.

By way of derogation from paragraph 3, where an institution has simultaneously assessed the modellability of more than one non-modellable risk factor by assessing the modellability of a single standardised bucket in accordance with Article 325be, the institution may instead develop joint extreme scenarios of future shock for all risk factors in that single standardised bucket for the purposes of paragraph 2 such that the resulting stress scenario risk measure is at least as conservative as:

1. (a) an expected shortfall measure calculated for non-modellable risk factors included in that standardised bucket only;
2. (b) for the stress period in accordance with paragraph 10;
3. (c) at 97.5^th percentile, one tailed confidence interval;
4. (d) calculated with base time horizon of 10 days; and
5. (e) scaled to a time horizon that is the greater of 20 days and the liquidity horizon of that non-modellable risk factor in accordance with the following formula:

\[SS_j=SS_j(T)\sqrt{\frac{max{(20,LH_j)}}{10}}\]

For the extreme scenarios of future shock, an institution shall comply with the requirements in paragraph 3.

8.

Where an institution elects to determine the extreme scenarios of future shock based on a time series of returns on the non-modellable risk factor or returns on other risk factors, the institution shall use a time series of 10 business days returns that are determined as follows:

1. (a) they shall determine the time series of observations for the non-modellable risk factor for the relevant period;
2. (b) by way of derogation from the first paragraph, they may extend the time series referred to in point (a) by including the observations available within the period of 20 business days following the stress period; where the reference date for the calculation of the stress scenario risk measure is less than 20 business days after the end of the stress period, an institution may include those observations that are available from the end of the stress period to the reference date;
3. (c) in relation to each date D_t, for which there is an observation in the time series resulting from point (a) excluding the last observation, an institution shall determine the date D_t′  following D_t , that minimises the following value:

\[v=\left|\frac{10\ business\ days}{D_{t^{ \ \prime}}-D_t}-1\right|\]

Where there is more than one date minimising that value, the date \[\rm D_{t^{ \ \prime}}\] shall be the date among those minimising that value that occurred later in time;

\[\sqrt\frac{10\ business\ days}{D_{t^{\ \prime}}-D_t}\]

9.

Where an institution does not have a complete time series of returns as determined in accordance with paragraph 8 to develop their extreme scenarios of future shock for a non-modellable risk factor, the institution shall demonstrate that the methodologies they use to determine the extreme scenarios of future shock are accurate and result in stress scenario risk measures that meet the conditions in paragraph 3 with a high degree of confidence.

10.

An institution shall determine the stress period for the non-modellable risk factors in each broad risk factor category referred to in Article 325bd by identifying the 12-months observation period maximising the following value:

\[\sum_{j\in i}{SS_j}\]

By way of derogation from the first paragraph, an institution may determine the stress period for the non-modellable risk factors in each broad risk factor category by identifying the 12-months observation period maximising the partial expected shortfall measure PES^RS,i referred to in paragraph 1 of Article 325bb. Where the institution applies this derogation, it shall provide evidence that the stress period identified represents a period of financial stress for its non-modellable risk factors; when doing so, it shall take into account how its portfolio is exposed to the non-modellable risk factors in the broad risk factor category.

For the purposes of identifying the stress period, an institution shall use historical data starting at least from 1 January 2007. An institution shall review the stress period identified at least with a quarterly frequency.

11.

Where an institution is unable to develop an extreme scenario of future shock in accordance with paragraphs 3 to 7, the institution must use a regulatory extreme scenario of future shock, being a shock that leads to the stress scenario risk measure being the maximum loss that may occur due to a change in the non-modellable risk factor where such maximum loss is finite.

12.

Where the maximum loss referred to in paragraph 11 is not finite, an institution shall apply the following steps in sequence for determining the regulatory extreme scenario of future shock:

1. (a) it shall use an expert-based approach using qualitative and quantitative information available to identify a loss due to a change in the value taken by the non-modellable risk factor that will not be exceeded with a level of certainty equal to 99.95% on a 10 business day horizon in a future period of financial stress equivalent to the stress period identified for the non-modellable risk factor; when doing so, an institution shall take into account the skewness and the excess kurtosis that may characterise the returns of the non-modellable risk factor in a period of financial stress and shall justify any distributional or statistical assumptions taken for identifying that loss;
2. (b) it shall determine the maximum loss as follows:

\[loss_{max}=\ max{({loss}_x\ \ ,}\ loss_{Hist^+}\ \ ,loss_{Hist^-})\]

1. (c) it shall multiply the maximum loss obtained in accordance with point b by

\[\sqrt{\frac{\max\:(20,LH)}{10}};\]

1. (d) it shall identify the regulatory extreme scenario of future shock as the shock leading to the stress scenario risk measure being the scaled maximum loss identified in point (c).

An institution shall not use the regulatory extreme scenario of future shock to calculate a single stress scenario risk measure for more than one non-modellable risk factor in a standardised bucket.

13.

An institution shall calculate the aggregate stress scenario risk measure for the purposes of Article 325ba by applying the following formula:

14.

An institution shall ensure that non-modellable risk factors that the institution classifies as reflecting only idiosyncratic credit spread risk meet all the following conditions:

1. (a) the nature of the risk factor is such that it shall reflect idiosyncratic credit spread risk only;
2. (b) the value taken by the risk factor shall not be driven by systematic risk components;
3. (c) the correlation among risk factors is negligible;
4. (d) there are no material subsets within that set of idiosyncratic risk factors that have non-negligible correlation;
5. (e) there are no important systematic risk factors that are not considered and that could explain some of the movements in those non-modellable risk factors; and
6. (f) the institution performs and documents the statistical tests used to verify the conditions in points (c), (d) and (e) of this paragraph.

15.

The institution shall ensure that non-modellable risk factors that the institution classifies as reflecting only idiosyncratic equity risk meet all the following conditions:

1. (a) the nature of the risk factor is such that it shall reflect idiosyncratic equity risk only;
2. (b) the value taken by the risk factor shall not be driven by systematic risk components;
3. (c) the correlation among risk factors is negligible;
4. (d) there are no material subsets within that set of idiosyncratic risk factors that have non-negligible correlation;
5. (e) there are no important systematic risk factors that are not considered and that could explain some of the movements in those non-modellable risk factors; and
6. (f) the institution performs and documents the statistical tests used to verify the conditions in points (c), (d) and (e) of this paragraph.

[Note: Paragraphs 1 and 2 of this rule correspond to Article 325bk(1) and (2) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall hold an own funds requirement for default risk in respect of all the positions of the institution that have been assigned to the trading desks for which the institution has been granted an IMA permission 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).

2.

The institution shall calculate the own funds requirement for default risk, which is incremental to the risks captured by the own funds requirements referred to in Article 325ba (1), using the institution's internal default risk model.

3.

An institution shall ensure that the internal default risk model complies with the requirements laid down in Articles 325bl to 325bp.

4.

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.

[Note: This rule corresponds to Article 325bl of CRR as it applied immediately before revocation by the Treasury]

1.

Subject to paragraph 3, an institution which has been granted an IMA permission by the PRA must 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, the institution must calculate the own funds requirements for market risk of all positions in that trading desk in accordance with the approach set out in the Market Risk: Advanced Standardised Approach (CRR) Part. The institution may resume the use of internal models in accordance with this Part to calculate own funds requirements for market risk for the positions of those trading desks if the institution provides to the PRA a reasoned confirmation that the trading desk again fulfils all the requirements set out in paragraph 1.

3.

An institution must calculate the own funds requirements referred to in Article 325ba(2) for any trading book positions to which paragraph 2(a) and paragraph 3 of Credit Risk: Internal Ratings Based Approach (CRR) Part Article 147 applies (or would apply if the institution had permission from the PRA to use the IRB Approach) using the approach set out in Section 5 of Market Risk: Advanced Standardised Approach (CRR) Part. An institution may not use an internal default risk model for this purpose.

[Note: this rule corresponds to Article 325bm of CRR as it applied immediately before revocation by the Treasury]

1.

An institution 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:

1. (a) 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;
2. (b) 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; and the default of the issuers of equity positions shall be represented by the value for the issuers' equity prices being set to zero;
3. (c) an institution 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; and
4. (d) it shall base the internal default risk model on a one-year constant position assumption.

2.

An institution 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 60 days for the purpose of calculating the default risk of some or all of the equity positions, where appropriate. In such case, the institution shall ensure that the calculation of default correlations between equity prices and PDs shall be consistent with a time horizon of 60 days and the calculation of default correlations between equity prices and bond prices shall be consistent with a one-year time horizon.

[Note: This rule corresponds to Article 325bn of CRR as it applied immediately before revocation by the Treasury]

1.

An institution may incorporate hedges in its internal default risk model and may net positions where the long positions and short positions relate to the same financial instrument.

2.

In its internal default risk model, an institution 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 its internal default risk model, an institution shall:

1. (a) 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; and
2. (b) recognise a hedging instrument only to the extent that it can be maintained even as the obligor approaches a credit event or other event.

[Note: This rule corresponds to Article 325bo of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall ensure that its internal default risk model 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, an institution shall model the default of each individual issuer using two types of systematic risk factors.

2.

An institution shall ensure that its internal default risk model reflects the economic cycle, including the dependency between recovery rates and the systematic risk factors referred to in paragraph 1.

3.

An institution shall ensure that its internal default risk model reflects the nonlinear impact of options and other positions with material nonlinear behaviour with respect to price changes. An institution shall also have due regard to the amount of model risk inherent in the valuation and estimation of price risks associated with those products. An institution may use approximations when modelling default of individual issuers as well as the simultaneous default of multiple issuers for equity derivatives with multiple underlyings if so specified in its IMA permission.

4.

An institution shall ensure that its internal default risk model is 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 shall ensure that its estimates of PDs meet the following requirements:

1. (a) PDs shall be floored at 0.03%;
2. (b) PDs shall be based on a one-year time horizon, unless stated otherwise in this Section;
3. (c) PDs 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; PDs shall not be inferred solely from current market prices; and
4. (d) if the institution has been granted permission to estimate PDs in accordance with the Credit Risk: Internal Ratings Based Approach (CRR) Part, it shall use the methodology set out therein to calculate PDs; or
5. (e) if the institution has not been granted permission to estimate PDs in accordance with the Credit Risk: Internal Ratings Based Approach (CRR) Part, it shall develop an internal methodology or use external sources to estimate PDs; in both situations, the estimates of PDs shall be consistent with the requirements set out in this Article.

6.

To simulate the default of issuers in the internal default risk model, the institution shall ensure that its estimates of loss given default shall meet the following requirements:

1. (a) the loss given default estimates are floored at 0%;
2. (b) the loss given default estimates shall reflect the seniority of each position;
3. (c) if the institution has been granted permission to estimate loss given default in accordance with the Credit Risk: Internal Ratings Based Approach (CRR) Part, it shall use the methodology set out therein to calculate loss given default estimates; and
4. (d) if the institution has not been granted permission to estimate loss given default in accordance with the Credit Risk: Internal Ratings Based Approach (CRR) Part, it 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.

7.

As part of the independent review and validation of the internal models that it uses for the purposes of this Part, including for the risk-measurement system, an institution shall:

1. (a) 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;
2. (b) 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
3. (c) apply appropriate quantitative validation including relevant internal modelling benchmarks.

The tests referred to in point (b) shall not be limited to the range of past events experienced.

8.

An institution shall ensure that its internal default risk model appropriately reflects issuer concentrations and concentrations that can arise within and across product classes under stressed conditions.

9.

An institution shall ensure that its internal default risk model is consistent with the institution's internal risk management methodologies for identifying, measuring, and managing trading risks.

10.

An institution shall have clearly defined policies and procedures for determining:

1. (a) the default assumptions for correlations between different issuers in accordance with point (c) of Article 325bn(1);
2. (b) the preferred choice of method for estimating PDs in point (e) of paragraph 5; and
3. (c) the loss given default in point (d) of paragraph 6.

11.

An institution shall document its internal models so that its correlation assumptions and other modelling assumptions are transparent.

12.

[Note: Provision left blank]

[Note: Paragraphs 1 to 11 of this rule correspond to Article 325bp(1) to (11) of CRR as it applied immediately before revocation by the Treasury]

Position risk on a traded debt instrument or equity instrument or derivative thereof may be divided into two components for purposes of this Chapter. The first shall be its specific risk component and shall encompass the risk of a price change in the instrument concerned due to factors related to its issuer or, in the case of a derivative, the issuer of the underlying instrument. The general risk component shall encompass the risk of a price change in the instrument due in the case of a traded debt instrument or debt derivative to a change in the level of interest rates or in the case of an equity or equity derivative to a broad equity-market movement unrelated to any specific attributes of individual securities.

[Note: This rule corresponds to Article 362 of CRR as it applied immediately before revocation by the Treasury]

1.

1.  
2. (a) An institution may, with the prior permission of the PRA, calculate its own funds requirements for one or more of the following risk categories by using its internal models instead of or in combination with the methods in the Market Risk: Advanced Standardised Approach (CRR) Part, to the extent and subject to any modifications in the permission:
   1. (i) general risk of equity instruments;
   2. (ii) specific risk of equity instruments;
   3. (iii) general risk of debt instruments;
   4. (iv) specific risk of debt instruments;
   5. (v) foreign-exchange risk;
   6. (vi) commodities risk.
3. (b) An institution applying for a permission under this paragraph must be able to demonstrate to the satisfaction of the PRA that it complies with the requirements of Sections 2, 3 and 4 as relevant.

[Note: This is a permission created under sections 144G and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

2.

For risk categories for which the institution has not been granted the permission referred to in paragraph 1 to use its internal models, that institution shall calculate own funds requirements in accordance with the Market Risk: Advanced Standardised Approach (CRR) Part. Permission by the PRA for the use of internal models shall be required for each risk category. An institution applying for the permission in paragraph 1 must be able to demonstrate to the satisfaction of the PRA that the internal model covers a significant share of the positions of a certain risk category.

2A.

An institution with an IMA transitional permission shall not use its internal models to calculate own funds requirements for positions assigned to the non-trading book in accordance with the Trading Book (CRR) Part, other than for the purposes of point (c) paragraph 3 of Article 92 of the Required Level of Own Funds (CRR) Part.

3.

Material changes to the use of internal models that the institution has received permission to use, the extension of the use of internal models that the institution has received permission to use, in particular to additional risk categories, and the initial calculation of stressed value-at-risk in accordance with Article 365(2) require a separate permission by the PRA.

Institutions shall notify the PRA of all other extensions and changes to the use of those internal models that the institution has received permission to use.

[Note: This is a permission created under sections 144G and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

4.

[Note: Provision left blank]

[Note: This rule corresponds to Article 363 of CRR as it applied immediately before revocation by the Treasury]

1.

Each institution using an internal model shall fulfil, in addition to own funds requirements calculated in accordance with the Market Risk: Advanced Standardised Approach (CRR) Part for those risk categories for which permission to use an internal model has not been granted, an own funds requirement expressed as the sum of points (a) and (b):

1. (a) the higher of the following values:
   1. (i) its previous day’s value-at-risk number calculated in accordance with Article 365(1) (VaR_t-1);
   2. (ii) an average of the daily value-at-risk numbers calculated in accordance with Article 365(1) on each of the preceding sixty business days (VaR_avg), multiplied by the multiplication factor (m_c) in accordance with Article 366;
2. (b) the higher of the following values:
   1. (i) its latest available stressed-value-at-risk number calculated in accordance with Article 365(2) (sVaR_t-1); and
   2. (ii) an average of the stressed value-at-risk numbers calculated in the manner and frequency specified in Article 365(2) during the preceding sixty business days (sVaR_avg), multiplied by the multiplication factor (m_s) in accordance with Article 366;

2.

Institutions that use an internal model to calculate their own funds requirement for specific risk of debt instruments shall fulfil an additional own funds requirement expressed as the sum of the following points (a) and (b):

1. (a) the own funds requirement calculated in accordance with Article 337 and 338 of the CRR, as it applied immediately before revocation by the Treasury, for the specific risk of securitisation positions and n^th to default credit derivatives in the trading book with the exception of those incorporated in an own funds requirement for the specific risk of the correlation trading portfolio in accordance with Article 377 and, where applicable, the own funds requirement for specific risk in accordance with Chapter 2, Section 6 of the CRR, as it applied immediately before revocation by the Treasury, for those positions in CIUs for which neither the conditions in Article 350(1) nor Article 350(2) of the CRR, as it applied immediately before revocation by the Treasury, are fulfilled;
2. (b) the higher of:
   1. (i) the most recent risk number for the incremental default and migration risk calculated in accordance with Section 3;
   2. (ii) the average of this number over the preceding 12 weeks.

3.

Institutions that have a correlation trading portfolio, which meets the requirements in Article 338(1) to (3) of the CRR, as it applied immediately before revocation by the Treasury, may fulfil an own funds requirement on the basis of Article 377 instead of the own funds requirement calculated in accordance with the Market Risk: Advanced Standardised Approach (CRR) Part, calculated as the higher of the following:

1. (a) the most recent risk number for the correlation trading portfolio calculated in accordance with Article 377;
2. (b) the average of this number over the preceding 12 weeks;
3. (c) 8% of the own funds requirement that would, at the time of calculation of the most recent risk number referred to in point (a), be calculated in accordance with Article 338(4) of the CRR, as it applied immediately before revocation by the Treasury, for all those positions incorporated into the internal model for the correlation trading portfolio.

[Note: This rule corresponds to Article 364 of CRR as it applied immediately before revocation by the Treasury]

1.

The calculation of the value-at-risk number referred to in Article 364 shall be subject to the following requirements:

1. (a) daily calculation of the value-at-risk number;
2. (b) a 99^th percentile, one-tailed confidence interval;
3. (c) a 10-day holding period;
4. (d) an effective historical observation period of at least one year except where a shorter observation period is justified by a significant upsurge in price volatility;
5. (e) at least monthly data set updates.

The institution may use value-at-risk numbers calculated according to shorter holding periods than 10 days scaled up to 10 days by an appropriate methodology that is reviewed periodically.

2.

In addition, the institution shall at least weekly calculate a ‘stressed value-at-risk’ of the current portfolio, in accordance with the requirements set out in the first paragraph, with value-at-risk model inputs calibrated to historical data from a continuous 12-month period of significant financial stress relevant to the institution’s portfolio. The choice of such historical data shall be subject to at least annual review by the institution, which shall notify the outcome to the PRA.

1.

The results of the calculations referred to in Article 365 shall be scaled up by the multiplication factors (m_c) and (m_s).

2.

Each of the multiplication factors (m_c) and (m_s) shall be the sum of at least 3 and an addend between 0 and 1 in accordance with Table 1. That addend shall depend on the number of overshootings for the most recent 250 business days as evidenced by the institution’s back-testing of the value-at-risk number as set out in Article 365(1).

Table 1

3.

The institutions shall count daily overshootings on the basis of back-testing on hypothetical and actual changes in the portfolio’s value. An overshooting is a one-day change in the portfolio’s value that exceeds the related one-day value-at-risk number generated by the institution’s model. For the purpose of determining the addend the number of overshootings shall be assessed at least quarterly and shall be equal to the higher of the number of overshootings under hypothetical and actual changes in the value of the portfolio.

Back-testing on hypothetical changes in the portfolio’s value shall be based on a comparison between the portfolio’s end-of-day value and, assuming unchanged positions, its value at the end of the subsequent day.

Back-testing on actual changes in the portfolio’s value shall be based on a comparison between the portfolio’s end-of-day value and its actual value at the end of the subsequent day excluding fees, commissions, and net interest income.

4.

An institution may, with the prior permission of the PRA, limit the addend to that resulting from overshootings under hypothetical changes, where the number of overshootings under actual changes does not result from deficiencies in the internal model, to the extent and subject to any modifications set out in the permission.

[Note: This is a permission created under sections 144G and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

5.

In order to allow the PRA to monitor the appropriateness of the multiplication factors on an ongoing basis, institutions shall notify promptly, and in any case no later than within five business days, the PRA of overshootings that result from their back-testing programme.

[Note: This rule corresponds to Article 366 of CRR as it applied immediately before revocation by the Treasury]

1.

Any internal model used to calculate capital requirements for position risk, foreign exchange risk, commodities risk and any internal model for correlation trading shall meet all of the following requirements:

1. (a) the model shall capture accurately all material price risks;
2. (b) the model shall capture a sufficient number of risk factors, depending on the level of activity of the institution in the respective markets. Where a risk factor is incorporated into the institution’s pricing model but not into the risk-measurement model, the institution shall be able to justify such an omission to the satisfaction of the PRA. The risk-measurement model shall capture nonlinearities for options and other products as well as correlation risk and basis risk. Where proxies for risk factors are used they shall show a good track record for the actual position held.

2.

Any internal model used to calculate capital requirements for position risk, foreign exchange risk or commodities risk shall meet all of the following requirements:

1. (a) the model shall incorporate a set of risk factors corresponding to the interest rates in each currency in which the institution has interest rate sensitive on-balance sheet or off-balance sheet positions. The institution shall model the yield curves using one of the generally accepted approaches. For material exposures to interest-rate risk in the major currencies and markets, the yield curve shall be divided into a minimum of six maturity segments, to capture the variations of volatility of rates along the yield curve. The model shall also capture the risk of less than perfectly correlated movements between different yield curves;
2. (b) the 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, where the correctness of that report is adequately ensured. If an institution is not aware of the foreign exchange positions of a CIU, this position shall be carved out and treated in accordance with Article 353(3) of the CRR, as it applied immediately before revocation by the Treasury;
3. (c) the model shall use a separate risk factor at least for each of the equity markets in which the institution holds significant positions;
4. (d) the model shall use a separate risk factor at least for each commodity in which the institution holds significant positions. The model shall also capture the risk of less than perfectly correlated movements between similar, but not identical, commodities and the exposure to changes in forward prices arising from maturity mismatches. It shall also take account of market characteristics, notably delivery dates and the scope provided to traders to close out positions;
5. (e) the institution’s internal model shall conservatively assess the risk arising from less liquid positions and positions with limited price transparency under realistic market scenarios. In addition, the internal model shall meet minimum data standards. Proxies shall be appropriately conservative and shall be used only where available data is insufficient or is not reflective of the true volatility of a position or portfolio.

3.

Institutions may, in any internal model used for purposes of this Chapter, use empirical correlations within risk categories and across risk categories only if the institution’s approach for measuring correlations is sound and implemented with integrity.

[Note: This rule corresponds to Article 367 of CRR as it applied immediately before revocation by the Treasury]

1.

Any internal model used for purposes of this Chapter shall be conceptually sound and implemented with integrity and, in particular, all of the following qualitative requirements shall be met:

1. (a) any internal model used to calculate capital requirements for position risk, foreign exchange risk or commodities risk shall be closely integrated into the daily risk-management process of the institution and serve as the basis for reporting risk exposures to senior management;
2. (b) the institution shall have a risk control unit that is independent from business trading units and reports directly to senior management. The unit shall be responsible for designing and implementing any internal model used for purposes of this Chapter. The unit shall conduct the initial and on-going validation of any internal model used for purposes of this Chapter, being responsible for the overall risk management system. The unit shall produce and analyse daily reports on the output of any internal model used for calculating capital requirements for position risk, foreign exchange risk and commodities risk, and on the appropriate measures to be taken in terms of trading limits;
3. (c) the institution’s management body and senior management shall be actively involved in the risk-control process and the daily reports produced by the risk-control unit are reviewed by a level of management with sufficient authority to enforce both reductions of positions taken by individual traders as well as in the institution’s overall risk exposure;
4. (d) the institution shall have sufficient numbers of staff skilled in the use of sophisticated internal models, and including those used for purposes of this Chapter, in the trading, risk-control, audit and back-office areas;
5. (e) the institution shall have established procedures for monitoring and ensuring compliance with a documented set of internal policies and controls concerning the overall operation of its internal models, and including those used for purposes of this Chapter;
6. (f) any internal model used for purposes of this Chapter shall have a proven track record of reasonable accuracy in measuring risks;
7. (g) the institution shall frequently conduct a rigorous programme of stress testing, including reverse stress tests, which encompasses any internal model used for purposes of this Chapter and the results of these stress tests shall be reviewed by senior management and reflected in the policies and limits it sets. This process shall particularly address illiquidity of markets in stressed market conditions, concentration risk, one-way markets, event and jump-to-default risks, non-linearity of products, deep out-of-the-money positions, positions subject to the gapping of prices and other risks that may not be captured appropriately in the internal models. The shocks applied shall reflect the nature of the portfolios and the time it could take to hedge out or manage risks under severe market conditions;
8. (h) the institution shall conduct, as part of its regular internal auditing process, an independent review of its internal models, and including those used for purposes of this Chapter.

2.

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

1. (a) the adequacy of the documentation of the risk-management system and process and the organisation of the risk-control unit;
2. (b) the integration of risk measures into daily risk management and the integrity of the management information system;
3. (c) the process the institution employs for approving risk-pricing models and valuation systems that are used by front and back-office personnel;
4. (d) the scope of risks captured by the risk-measurement model and the validation of any significant changes in the risk-measurement process;
5. (e) the accuracy and completeness of position data, the accuracy and appropriateness of volatility and correlation assumptions, and the accuracy of valuation and risk sensitivity calculations;
6. (f) the verification process the institution employs to evaluate the consistency, timeliness and reliability of data sources used to run internal models, including the independence of such data sources;
7. (g) the verification process the institution uses to evaluate back-testing that is conducted to assess the model’s accuracy.

3.

As techniques and best practices evolve, institutions shall apply those new techniques and practices in any internal model used for purposes of this Chapter.

[Note: This rule corresponds to Article 368 of CRR as it applied immediately before revocation by the Treasury]

1.

Institutions shall have processes in place to ensure that all their internal models used for the purposes of this Chapter have been adequately validated by suitably qualified parties independent of the development process to ensure that they are conceptually sound and adequately capture all material risks. The validation shall be conducted when the internal model is initially developed and when any significant changes are made to the internal model. The validation shall also be conducted on a periodic basis but especially where there have been any significant structural changes in the market or changes to the composition of the portfolio which might lead to the internal model no longer being adequate. As techniques and best practices for internal validation evolve, institutions shall apply these advances. Internal model validation shall not be limited to back-testing, but shall, at a minimum, also include the following:

1. (a) tests to demonstrate that any assumptions made within the internal model are appropriate and do not underestimate or overestimate the risk;
2. (b) in addition to the regulatory back-testing programmes, institutions shall carry out their own internal model validation tests, including back-testing, in relation to the risks and structures of their portfolios;
3. (c) the use of hypothetical portfolios to ensure that the internal model is able to account for particular structural features that may arise, for example material basis risks and concentration risk.

2.

The institution shall perform back-testing on both actual and hypothetical changes in the portfolio’s value.

[Note: This rule corresponds to Article 369 of CRR as it applied immediately before revocation by the Treasury]

An internal model used for calculating own funds requirements for specific risk and an internal model for correlation trading shall meet the following additional requirements:

1. (a) it explains the historical price variation in the portfolio;
2. (b) it captures concentration in terms of magnitude and changes of composition of the portfolio;
3. (c) it is robust to an adverse environment;
4. (d) it is validated through back-testing aimed at assessing whether specific risk is being accurately captured. If the institution performs such back-testing on the basis of relevant sub-portfolios, these shall be chosen in a consistent manner;
5. (e) it captures name-related basis risk and shall in particular be sensitive to material idiosyncratic differences between similar but not identical positions;
6. (f) it captures event risk.

[Note: This rule corresponds to Article 370 of CRR as it applied immediately before revocation by the Treasury]

1.

An institution may choose to exclude from the calculation of its specific risk own funds requirement using an internal model those positions for which it fulfils an own funds requirement for specific risk in accordance with Article 332(1)(e) or Article 337 of the CRR, as it applied immediately before revocation by the Treasury, with exception of those positions that are subject to the approach set out in Article 377.

2.

An institution may choose not to capture default and migration risks for traded debt instruments in its internal model where it is capturing those risks through the requirements set out in Section 4.

[Note: This rule corresponds to Article 371 of CRR as it applied immediately before revocation by the Treasury]

An institution that uses an internal model for calculating own funds requirements for specific risk of traded debt instruments shall also have an internal incremental default and migration risk (‘IRC’) model in place to capture the default and migration risks of its trading book positions that are incremental to the risks captured by the value-at-risk measure as specified in Article 365(1). The institution shall be able to demonstrate to the PRA that its internal model meets the following standards under the assumption of a constant level of risk, and adjusted where appropriate to reflect the impact of liquidity, concentrations, hedging and optionality:

1. (a) the internal model provides a meaningful differentiation of risk and accurate and consistent estimates of incremental default and migration risk;
2. (b) the internal model’s estimates for potential losses play an essential role in the risk management of the institution;
3. (c) the market and position data used for the internal model are up-to-date and subject to an appropriate quality assessment;
4. (d) the requirements in Article 367(3), Article 368, Article 369(1) and points (b), (c), (e) and (f) of Article 370 are met.

[Note: This rule corresponds to Article 372 of CRR as it applied immediately before revocation by the Treasury]

The internal IRC model shall cover all positions subject to an own funds requirement for specific interest rate risk, including those subject to a 0% specific risk capital charge under Article 336 of the CRR, as it applied immediately before revocation by the Treasury, but shall not cover securitisation positions and n-th-to-default credit derivatives.

The institution may, with the prior permission of the PRA, choose to consistently include all listed equity positions and derivatives positions based on listed equities where such inclusion is consistent with how the institution internally measures and manages risk, and to the extent and subject to any modifications set out in the permission.

[Note: This is a permission created under sections 144G and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

[Note: This rule corresponds to Article 373 of CRR as it applied immediately before revocation by the Treasury]

1.

Institutions shall use the internal model to calculate a number which measures losses due to default and internal or external ratings migration at the 99.9% confidence interval over a time horizon of one year. Institutions shall calculate this number at least weekly.

2.

Correlation assumptions shall be supported by analysis of objective data in a conceptually sound framework. The internal model shall appropriately reflect issuer concentrations. Concentrations that can arise within and across product classes under stressed conditions shall also be reflected.

3.

The internal IRC model shall reflect the impact of correlations between default and migration events. The impact of diversification between, on the one hand, default and migration events and, on the other hand, other risk factors shall not be reflected.

4.

The internal model shall be based on the assumption of a constant level of risk over the one-year time horizon, implying that given individual trading book positions or sets of positions that have experienced default or migration over their liquidity horizon are re-balanced at the end of their liquidity horizon to attain the initial level of risk. Alternatively, an institution may choose to consistently use a one-year constant position assumption.

5.

The liquidity horizons shall be set according to the time required to sell the position or to hedge all material relevant price risks in a stressed market, having particular regard to the size of the position. Liquidity horizons shall reflect actual practice and experience during periods of both systematic and idiosyncratic stresses. The liquidity horizon shall be measured under conservative assumptions and shall be sufficiently long that the act of selling or hedging, in itself, would not materially affect the price at which the selling or hedging would be executed.

6.

The determination of the appropriate liquidity horizon for a position or set of positions is subject to a floor of three months.

7.

The determination of the appropriate liquidity horizon for a position or set of positions shall take into account an institution’s internal policies relating to valuation adjustments and the management of stale positions. When an institution determines liquidity horizons for sets of positions rather than for individual positions, the criteria for defining sets of positions shall be defined in a way that meaningfully reflects differences in liquidity. The liquidity horizons shall be greater for positions that are concentrated, reflecting the longer period needed to liquidate such positions. The liquidity horizon for a securitisation warehouse shall reflect the time to build, sell and securitise the assets, or to hedge the material risk factors, under stressed market conditions.

[Note: This rule corresponds to Article 374 of CRR as it applied immediately before revocation by the Treasury]

1.

Hedges may be incorporated into an institution’s internal model to capture the incremental default and migration risks. Positions may be netted when long and short positions refer to the same financial instrument. 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, may only be recognised by explicitly modelling gross long and short positions in the different instruments. Institutions shall reflect the impact of material risks that could occur during the interval between the hedge’s maturity and the liquidity horizon as well as the potential for significant basis risks in hedging strategies by product, seniority in the capital structure, internal or external rating, maturity, vintage and other differences in the instruments. An institution shall reflect a hedge only to the extent that it can be maintained even as the obligor approaches a credit or other event.

2.

For positions that are hedged via dynamic hedging strategies, a rebalancing of the hedge within the liquidity horizon of the hedged position may be recognised provided that the institution:

1. (a) chooses to model rebalancing of the hedge consistently over the relevant set of trading book positions;
2. (b) is able to demonstrate to the PRA that the inclusion of rebalancing results in a better risk measurement;
3. (c) is able to demonstrate to the PRA that the markets for the instruments serving as hedges are liquid enough to allow for such rebalancing even during periods of stress. Any residual risks resulting from dynamic hedging strategies shall be reflected in the own funds requirement.

[Note: This rule corresponds to Article 375 of CRR as it applied immediately before revocation by the Treasury]

1.

The internal model to capture the incremental default and migration risks shall reflect the nonlinear impact of options, structured credit derivatives and other positions with material nonlinear behaviour with respect to price changes. The institution shall also have due regard to the amount of model risk inherent in the valuation and estimation of price risks associated with such products.

2.

The internal model shall be based on data that are objective and up-to-date.

3.

As part of the independent review and validation of their internal models used for purposes of this Chapter, inclusively for purposes of the risk measurement system, an institution shall in particular do all of the following:

1. (a) validate that its modelling approach for correlations and price changes is appropriate for its portfolio, including the choice and weights of its systematic risk factors;
2. (b) perform a variety of stress tests, including sensitivity analysis and scenario analysis, to assess the qualitative and quantitative reasonableness of the internal model, particularly with regard to the treatment of concentrations. Such tests shall not be limited to the range of events experienced historically;
3. (c) apply appropriate quantitative validation including relevant internal modelling benchmarks.

4.

The internal model shall be consistent with the institution’s internal risk management methodologies for identifying, measuring, and managing trading risks.

5.

Institutions shall document their internal models so that its correlation and other modelling assumptions are transparent to the PRA.

6.

The internal model shall conservatively assess the risk arising from less liquid positions and positions with limited price transparency under realistic market scenarios. In addition, the internal model shall meet minimum data standards. Proxies shall be appropriately conservative and may be used only where available data is insufficient or is not reflective of the true volatility of a position or portfolio.

[Note: This rule corresponds to Article 376 of CRR as it applied immediately before revocation by the Treasury]

1.

An institution that is allowed to use an internal model for specific risk of debt instruments and that meets the requirements in paragraphs 2 to 6 of this Article and in Article 367(1) and (3), Article 368, Article 369(1) and points (a), (b), (c), (e) and (f) of Article 370 may, with the prior permission of the PRA, use an internal model for the own funds requirement for the correlation trading portfolio instead of the own funds requirement in accordance with the advanced standardised approach for ACTP CSR positions set out in the Market Risk: Advanced Standardised Approach (CRR) Part, to the extent and subject to any modifications set out in the permission.

[Note: This is a permission created under sections 144G and 192XC of FSMA to which Part 8 of the Capital Requirements Regulations applies]

2.

Institutions shall use this internal model to calculate a number which adequately measures all price risks at the 99.9% confidence interval over a time horizon of one year under the assumption of a constant level of risk, and adjusted where appropriate to reflect the impact of liquidity, concentrations, hedging and optionality. Institutions shall calculate this number at least weekly.

3.

The following risks shall be adequately captured by the model referred to in paragraph 1:

1. (a) the cumulative risk arising from multiple defaults, including different ordering of defaults, in tranched products;
2. (b) CSR, including the gamma and cross-gamma effects;
3. (c) volatility of implied correlations, including the cross effect between spreads and correlations
4. (d) basis risk, including both of the following:
   1. (i) the basis between the spread of an index and those of its constituent single names;
   2. (ii) the basis between the implied correlation of an index and that of bespoke portfolios;
5. (e) recovery rate volatility, as it relates to the propensity for recovery rates to affect tranche prices;
6. (f) to the extent the comprehensive risk measure incorporates benefits from dynamic hedging, the risk of hedge slippage and the potential costs of rebalancing such hedges;
7. (g) any other material price risks of positions in the correlation trading portfolio.

4.

An institution shall use sufficient market data within the model referred to in paragraph 1 in order to ensure that it fully captures the salient risks of those exposures in its internal approach in accordance with the requirements set out in this Article. It shall be able to demonstrate to the PRA through back testing or other appropriate means that its model can appropriately explain the historical price variation of those products.

The institution shall have appropriate policies and procedures in place in order to separate the positions for which it holds permission to incorporate them in the own funds requirement in accordance with this Article from other positions for which it does not hold such permission.

5.

With regard to the portfolio of all the positions incorporated in the model referred to in paragraph 1, the institution shall regularly apply a set of specific, predetermined stress scenarios. Such stress scenarios shall examine the effects of stress to default rates, recovery rates, credit spreads, basis risk, correlations and other relevant risk factors on the correlation trading portfolio. The institution shall apply stress scenarios at least weekly and report at least quarterly to the PRA the results, including comparisons with the institution’s own funds requirement in accordance with this Article. Any instances where the stress test results materially exceed the own funds requirement for the correlation trading portfolio shall be reported to the PRA in a timely manner.

6.

The internal model shall conservatively assess the risk arising from less liquid positions and positions with limited price transparency under realistic market scenarios. In addition, the internal model shall meet minimum data standards. Proxies shall be appropriately conservative and may be used only where available data is insufficient or is not reflective of the true volatility of a position or portfolio.

[Note: This rule corresponds to Article 377 of CRR as it applied immediately before revocation by the Treasury]

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1.

The materiality of the extensions and changes for the internal model approach (‘extensions and changes in the IMA’) shall be classified into one of the following categories:

1. (a) material extensions and changes, which, according to Article 363(3) of Part A of this Annex, require permission from the PRA;
2. (b) other extensions and changes, which require notification to the PRA.

2.

The extensions and changes referred to in point (b) of paragraph 1 shall further be classified into:

1. (a) extensions and changes that require notification before their implementation;
2. (b) extensions and changes that require notification after their implementation.

[Note: This rule corresponds to Article 2 of Commission Delegated Regulation (EU) No 529/2014 as it applied immediately before revocation by the Treasury]

1.

The classification of extensions and changes in the IMA shall be carried out in accordance with this Article and Articles 7a and 7b.

2.

Where institutions are required to calculate the quantitative impact of any extension or change on own funds requirements or, where applicable, on risk-weighted exposure amounts, they shall apply the following methodology:

1. (a) for the purpose of the assessment of the quantitative impact institutions shall use the most recent data available;
2. (b) where a precise assessment of the quantitative impact is not feasible, institutions shall instead perform an assessment of the impact based on a representative sample or other reliable inference methodologies;
3. (c) for changes having no direct quantitative impact, no quantitative impact as laid down in Article 7a(1)(c) for the internal model approach needs to be calculated.

3.

One material extension or change shall not be split into several changes or extensions of lower materiality.

4.

In case of doubt, institutions shall assign extensions and changes to the category of the highest potential materiality.

5.

Where the PRA has provided its permission in relation to a material extension or change, institutions shall calculate the own funds requirements based on the approved extension or change from the date specified in the new permission which shall replace the prior one. The non-implementation on the date specified in the new permission of an extension or change for which permission from the PRA has been given, shall require a new permission from the PRA which shall be applied for without undue delay.

6.

In case of delay of the implementation of an extension or change for which permission from the PRA has been granted, the institution shall notify the PRA and present to the PRA a plan for a timely implementation of the approved extension or change, which it shall realise within a reasonable period.

7.

Where an extension or change is classified as one requiring prior notification to the PRA, and where, subsequently to the notification, institutions decide not to implement the extension or change, institutions shall notify without undue delay the PRA of this decision.

[Note: This rule corresponds to Article 3 of Commission Delegated Regulation (EU) No 529/2014 as it applied immediately before revocation by the Treasury]

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1.

Extensions and changes to the IMA shall be considered material, if they fulfil any of the following conditions:

1. (a) they fall under any of the extensions described in Annex III, Part I, Section 1;
2. (b) they fall under any changes described in Annex III, Part II, Section 1;
3. (c) they result in a change in absolute value of 1% or more, computed for the first business day of the testing of the impact of the extension or change, of one of the relevant risk numbers referred to in Article 364(1)(a)(i), or Article 364(1)(b)(i), or Article 364(2)(b)(i) or Article 364(3)(a) of Part A of this Annex, and associated with the scope of application of the relevant internal model to which the risk number refers, and result in either of the following:
   1. (i) in a change of 5% or more of the sum of the risk numbers referred to in Article 364(1)(a)(i), Article 364(1)(b)(i), scaled up by the multiplication factors (m_c) and (m_s) respectively according to Article 366 of Part A of this Annex, Article 364(2)(b)(i) and Article 364(3)(a) of Part A of this Annex, and the own funds requirements according to the Market Risk: Advanced Standardised Approach (CRR) Part computed at the level of the UK parent institution or, in the case of an institution which is neither a parent institution nor a subsidiary, at the level of that institution;
   2. (ii) in a change of 10% or more of one or more of the relevant risk numbers referred to in Article 364(1)(a)(i), or Article 364(1)(b)(i), or Article 364(2)(b)(i) or Article 364(3)(a) of Part A of this Annex, and associated with the scope of application of the relevant internal model to which the risk number refers.

2.

For the purposes of paragraph (1)(c)(i), and in accordance with Article 3(2), the impact of any extension or change shall be assessed as the highest absolute value over the period referred to in paragraph 4 of this Article of a ratio calculated as follows:

1. (a) in numerator, the difference between the sum referred to in paragraph (1)(c)(i) with and without the extension or change;
2. (b) in the denominator, the sum referred to in paragraph (1)(c)(i) without the extension or change.

3.

For the purposes of paragraph (1)(c)(ii), and in accordance with Article 3(2), the impact of any extension or change shall be assessed as the highest absolute value over the period referred to in paragraph 4 of this Article of a ratio calculated as follows:

1. (a) in the numerator, the difference between the risk number referred to in Article 364(1)(a)(i), Article 364(1)(b)(i), Article 364(2)(b)(i) or Article 364(3)(a) of Part A of this Annex with and without the extension or change;
2. (b) in the denominator, the risk number referred to, respectively, in Article 364(1)(a)(i), Article 364(1)(b)(i), Article 364(2)(b)(i) or Article 364(3)(a) of Part A of this Annex without the extension or change.

4.

For the purposes of paragraph (1)(c)(i) and (1)(c)(ii) the ratios referred to in paragraphs 2 and 3 shall be calculated for a period the duration of which is the shortest between the following points (a) and (b):

1. (a) 15 consecutive business days starting from the first business day of the testing of the impact of the extension or change;
2. (b) until such day where a daily calculation of either one of the ratios referred to in paragraphs 2 and 3 results in an impact equal or greater than the percentages referred to in either paragraph (1)(c)(i) or paragraph (1)(c)(ii), respectively.

[Note: This rule corresponds to Article 7a of Commission Delegated Regulation (EU) No 529/2014 as it applied immediately before revocation by the Treasury]

Extensions and changes to the IMA, which are not material but are to be notified to the PRA according to the second subparagraph of Article 363(3) of Part A of this Annex, shall be notified in the following manner:

1. (a) extensions and changes falling under Annex III, Part I, Section 2, and Part II, Section 2, shall be notified to the PRA two weeks before their planned implementation;
2. (b) all other extensions and changes shall be notified to the PRA after implementation at least on an annual basis.

[Note: This rule corresponds to Article 7b of Commission Delegated Regulation (EU) No 529/2014 as it applied immediately before revocation by the Treasury]

1.

For extensions and changes to the IMA classified as requiring the PRA’s approval, institutions shall submit, together with the application, the following documentation:

1. (a) description of the extension or change, its rationale and objective;
2. (b) implementation date;
3. (c) scope of application affected by the model extension or change, with volume characteristics;
4. (d) technical and process document(s);
5. (e) reports of the institutions’ independent review or validation;
6. (f) confirmation that the extension or change has been approved through the institution’s approval processes by the competent bodies and date of approval;
7. (g) where applicable, the quantitative impact of the change or extension on the risk weighted exposure amounts, or on the own funds requirements, or on the relevant risk numbers or sum of relevant own funds requirements and risk numbers;
8. (h) records of the institution’s current and previous version number of internal models which are subject to approval.

2.

For extensions and changes classified as requiring notification either before or after implementation, institutions shall submit, together with the notification, the documentation referred to in points (a), (b), (c), (f) and (g) of paragraph 1.

[Note: This rule corresponds to Article 8 of Commission Delegated Regulation (EU) No 529/2014 as it applied immediately before revocation by the Treasury]

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1.

Extension of the market risk model to an additional location in another jurisdiction, including extending the market risk model to the positions of a desk located in a different time zone, or for which different front office or IT systems are used.

2.

Integration in the scope of an internal model of product classes, for which the VaR number, computed according to Article 364(1)(a)(i) of Part A of this Annex, exceeds 5% of the VaR number, computed according to Article 364(1)(a)(i) of Part A of this Annex, of the total portfolio forming the scope of that model before the integration.

3.

Any reverse extensions such as cases where the institutions aim at applying the standardized method to risk categories for which they are granted permission to use an internal market risk model.

The inclusion in the scope of an internal model of product classes requiring other risk modelling techniques than those forming part of the permission to use that model, such as path-dependent products, or multi-underlying positions, according to Article 367 of Part A of this Annex.

1.

Changes between historical simulation, parametric or Monte Carlo VaR.

2.

Changes in the aggregation scheme such as where a simple summation of risk numbers is replaced by integrated modelling.