Market Risk: Advanced Standardised Approach (CRR)

1.

[Note: Provision left blank]

2.

An institution shall calculate the own funds requirements for market risk in accordance with the advanced standardised approach for a portfolio of:

1. (a) trading book positions; or
2. (b) non-trading book positions that are subject to foreign exchange or commodity risk,

as the sum of the following three components:

1. (i) the own funds requirement under the sensitivities-based method set out in Section 2;
2. (ii) the own funds requirement for residual risks set out in Section 4 which is only applicable to the trading book positions referred to in that Section; and
3. (iii) the own funds requirement for the default risk set out in Section 5 which is only applicable to the trading book positions referred to in that Section.

[Note: Paragraph 2 of this rule corresponds to paragraph 2 of Article 325c of CRR as it applied immediately before revocation by the Treasury]

1.

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

1. (a) ‘bucket’ means a sub-category of positions within one risk class with a similar risk profile to which a risk factor as defined in Sub-section 1 of Section 3 is assigned.
2. (b) ‘risk class’ means one of the following seven categories:
   1. (i) GIRR;
   2. (ii) CSR for non-securitisation;
   3. (iii) non-ACTP CSR;
   4. (iv) ACTP CSR;
   5. (v) equity risk;
   6. (vi) commodity risk; or
   7. (vii) foreign exchange risk.
3. (c) ‘sensitivity’ means the relative change in the value of a position, as a result of a change in the value of one of the relevant risk factors of the position, calculated using the institution's pricing model in accordance with Sub-section 2 of Section 3.

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

1.

An institution shall calculate the own funds requirement for market risk under the sensitivities-based method by aggregating the following three own funds requirements in accordance with Article 325h:

1. (a) own funds requirements for delta risk which capture the risk of changes in the value of an instrument due to movements in its non-volatility related risk factors;
2. (b) own funds requirements for vega risk which capture the risk of changes in the value of an instrument due to movements in its volatility-related risk factors; and
3. (c) own funds requirements for curvature risk which capture the risk of changes in the value of an instrument due to movements in the main non-volatility related risk factors not captured by the own funds requirements for delta risk.

2.

For the purpose of the calculation referred to in paragraph 1:

1. (a) all the positions of instruments with optionality shall be subject to the own funds requirements referred to in points (a), (b) and (c) of paragraph 1 for the risks other than exotic underlyings of the instruments as referred to in point (a) of Article 325u(2); and
2. (b) all the positions of instruments without optionality shall only be subject to the own funds requirements referred to in point (a) of paragraph 1 for the risks other than exotic underlyings of the instruments as referred to in point (a) of Article 325u(2).

For the purposes of this Part, instruments with optionality include, among others: calls, puts, caps, floors, swap options, barrier options, embedded options (such as prepayment or behavioural options) and exotic options.

For the purposes of this Part, instruments whose cash-flows can be written as a linear function of the underlying's notional amount shall be considered to be instruments without optionality.

3.

By way of derogation from point (b) of paragraph 2, an institution may with the prior permission of the PRA to the extent and subject to any modifications set out in the permission, subject all the positions of instruments without optionality to the own funds requirements referred to in point (c) of paragraph 1, in addition to the requirements referred to in point (a) of paragraph 1.

If an institution is granted permission by the PRA to apply the approach in the first sub-paragraph, it may only cease applying such approach with the permission of the PRA.

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

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

1.

An institution shall apply the delta and vega risk factors described in Sub-section 1 of Section 3 to calculate the own funds requirements for delta and vega risks.

2.

An institution shall apply the process set out in paragraphs 3 to 8 to calculate own funds requirements for delta and vega risks.

3.

For each risk class, the sensitivity of all instruments in scope of the own funds requirements for delta or vega risks to each of the applicable delta or vega risk factors included in that risk class shall be calculated by using the corresponding formulas in Sub-section 2 of Section 3. If the value of an instrument depends on several risk factors, the sensitivity shall be determined separately for each risk factor.

4.

Sensitivities shall be assigned to one of the buckets ‘b’ within each risk class.

5.

Within each bucket ‘b’, the positive and negative sensitivities to the same risk factor shall be netted, giving rise to net sensitivities (s_k) to each risk factor ‘k’ within a bucket.

6.

The net sensitivities to each risk factor within each bucket shall be multiplied by the corresponding risk weights set out in Section 6, giving rise to weighted sensitivities to each risk factor within that bucket in accordance with the following formula:

WS_k = RW_k · s_k

where:

WS_k = the weighted sensitivities;

RW_k = the risk weights;

s_k = the net sensitivities to each risk factor k.

7.

The weighted sensitivities to the different risk factors within each bucket shall be aggregated in accordance with the formula below, where the quantity within the square root function is floored at zero, giving rise to the bucket-specific sensitivity. The corresponding correlations for weighted sensitivities within the same bucket (ρ_kl), set out in Section 6, shall be used.

\[K_b=\sqrt{\sum_{k}{WS_k^2}+\sum_{k}\sum_{l\neq k}{\rho_{kl}WS_kWS_l}}\]

where:

K_b = the bucket-specific sensitivity;

WS = the weighted sensitivities.

8.

The bucket-specific sensitivity shall be calculated for each bucket within a risk class in accordance with paragraphs 5, 6 and 7. Once the bucket-specific sensitivity has been calculated for all buckets, weighted sensitivities to all risk factors across buckets shall be aggregated in accordance with the formula below, using the corresponding correlations \[\gamma _{bc}\] for weighted sensitivities in different buckets set out in Section 6, giving rise to the risk class-specific own funds requirement for delta or vega risk:

Risk class-specific own fund requirement for delta or vega risk \[=\sqrt{\sum\nolimits_{b} K_{b}^2 + \sum\nolimits_{b} \sum\nolimits_{c\neq b} \gamma _{bc} S_{b} S_{c}}\]

where:

\[S_b=\sum\nolimits_{k} WS_{k}\] for all risk factors in bucket b and \[S_c=\sum\nolimits_{k} WS_{k}\] in bucket c; where those values for S_b and S_c produce a negative number for the overall sum of \[\sum\nolimits_{b} K_{b}^2 + \sum\nolimits_{b}\sum\nolimits_{c\neq b}\gamma _{bc} S_{b} S_{c}\] the institution shall calculate the risk class-specific own funds requirements for delta or vega risk using an alternative specification whereby:

\[S_{b} = max[min(\sum_{k} WS_{k}, K_{b}),-K_{b}]\]

\[S_{c} = max[min(\sum_{k} WS_{k}, K_{c}),-K_{c}]\]

The risk class-specific own funds requirements for delta or vega risk shall be calculated for each risk class in accordance with paragraphs 1 to 8.

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

1.

An institution shall perform the calculations laid down in paragraph 2 for each risk factor of the instruments subject to the own funds requirement for curvature risk, except for the risk factors referred to in paragraph 3.

For a given risk factor, an institution shall perform those calculations on a net basis across all the positions of the instruments subject to the own funds requirement for curvature risk that contain that risk factor.

2.

For a given risk factor k included in one or more instruments referred to in paragraph 1, an institution shall calculate the upward net curvature risk position of that risk factor \[(CVR_k^+)\] and the downward net curvature risk position of that risk factor \[(CVR_k^-)\] as follows:

\[CVR_k^+=-\sum_{i}{CVR_{ik}^+}\]

\[CVR_k^-=-\sum_{i}{CVR_{ik}^-}\]

\[CVR_{ik}^+=V_i\left(x_k^{RW\left(Curvature\right)^+}\right)-V_i\left(x_k\right)-RW_k^{Curvature}\times s_{ik}\]

\[CVR_{ik}^-=V_i\left(x_k^{RW\left(Curvature\right)^-}\right)-V_i\left(x_k\right)+RW_k^{Curvature}\times s_{ik}\]

where:

\[i=\] the index that denotes all the positions of instruments referred to in paragraph 1 and including risk factor k;

\[x_{k}=\] the current value of risk factor k;

\[V_{i}\ (x_{k})=\] the value of instrument i as estimated by the pricing model of the institution based on the current value of risk factor k;

\[V_{i}\ (x_{k}^{RW(Curvature)^{+}})=\] the value of instrument i as estimated by the pricing model of the institution based on an upward shift of the value of risk factor k;

\[V_{i}\ (x_{k}^{RW(Curvature)^{-}})=\] the value of instrument i as estimated by the pricing model of the institution based on a downward shift of the value of risk factor k;

\[RW_{k}^{Curvature}=\] the risk weight applicable to risk factor k determined in accordance with Section 6;

\[S_{ik}=\] the delta sensitivity of instrument i with respect to risk factor k, calculated in accordance with Article 325r.

3.

By way of derogation from paragraph 2, for curves of risk factors that belong to the GIRR, CSR and commodity risk classes, an institution shall perform the calculations laid down in paragraph 6 at the level of the entire curve instead of at the level of each risk factor that belongs to the curve.

For the purposes of the calculation referred to in paragraph 2, where x_k is a curve of risk factors allocated to the GIRR, CSR and commodity risk classes, s_ik shall be the sum of the delta sensitivities to the risk factor of the curve across all tenors of the curve.

4.

In order to determine a bucket-level own funds requirement for curvature risk, an institution shall aggregate, in accordance with the following formula the upward and downward net curvature risk positions, calculated in accordance with paragraph 2, of all the risk factors assigned to that bucket in accordance with Sub-section 1 of Section 3:

\[K_{b} = \left\{\begin{matrix}\textrm{max}\left ( K_{b}^{+},K_{b}^{-} \right ); \mathrm{where} \ K_{b}^{+} \neq K_{b}^{-} \\K_{b}^{+};\textrm{where} \ K_{b}^{+} = K_{b}^{-} \textrm{and}\sum\nolimits_{k}CVR_{k}^{+} > \sum\nolimits_{k}CVR_{k}^{-} \\K_{b}^{-}; \textrm{otherwise} \end{matrix}\right.\]

where:

b = the index that denotes a bucket of a given risk class;

K_b= the own funds requirement for curvature risk for bucket 𝑏;

\[K_b^+=\sqrt{\max{\left(0,\sum\nolimits_{k}{{\max{\left(CVR_k^+,0\right)}}^2+\sum\nolimits_{l\neq k}\sum\nolimits_{k}{\rho_{kl}CVR_k^+CVR_l^+\psi\left(CVR_k^+,CVR_l^+\right)}}\right)}};\]

\[K_b^-=\sqrt{\max{\left(0,\sum\nolimits_{k}{{\max{\left(CVR_k^-,0\right)}}^2+\sum\nolimits_{l\neq k}\sum\nolimits_{k}{\rho_{kl}CVR_k^-CVR_l^-\psi\left(CVR_k^-,CVR_l^-\right)}}\right)}};\]

\[\psi \left ( x,y \right )= \left\{\begin{matrix}0;\ \textrm{where} \ x < 0\ \textrm{and} \ y < 0 \\1; \textrm{otherwise}\end{matrix}\right. ;\]

ρ_kl = the intra-bucket correlations between risk factors k and l as prescribed in Section 6;

k,l = the indices that denote all the risk factors k and l as included in one or more instruments referred to in paragraph 1;

\[CVR_k^+=\] the upward net curvature risk position;

\[CVR_k^-=\] the downward net curvature risk position.

5.

By way of derogation from paragraph 4, for the bucket-level own funds requirements for curvature risk of bucket 16 of Table 4 in Article 325ah, of bucket 16 of Table 6 in Article 325ak, of bucket 25 of Table 7 in Article 325am and of bucket 11 of Table 8 in Article 325ap, an institution shall use the following formula:

\[K_b = \textrm{max} \left ( \sum_{k}max(CVR_k^+,0), \sum_{k}max(CVR_k^-,0) \right )\]

6.

An institution shall calculate the risk class own funds requirements for curvature risk by aggregating all the bucket-level own funds requirements for curvature risk within a given risk class as follows:

\[RCCR=\sqrt{\max{\left(0,\sum_{b}{K_b^2+\sum_{c\neq b}\sum_{b}{\gamma_{bc}S_bS_c\psi\left(S_b,S_c\right)}}\right)}}\]

where:

b, c = the indices that denote all the buckets of a given risk class that corresponds to instruments referred to in paragraph 1;

\[K_b\] = own funds requirements for curvature risk for bucket b;

\[S_b =  \left\{\begin{matrix}\sum _k CVR_k^+;\textrm{where} \ K_b = K_b^+ \textrm{in accordance with paragraph 4}
 \\\sum_k CVR_k^-; \textrm{otherwise}
\end{matrix}\right.\]

\[\psi \left ( x,y \right )= \left\{\begin{matrix}0;\textrm{where} \ x < 0 \ \textrm{and} \ y< 0
 \\1; \textrm{otherwise}
\end{matrix}\right.\]

\[\gamma_{bc}=\] the inter-bucket correlations between buckets b and c as set out in Section 6.

7.

An institution must ensure the own funds requirement for curvature risk is the sum of the risk class own funds requirements for curvature risk calculated in accordance with paragraph 6 across all risk classes to which at least one risk factor of the instruments referred to in paragraph 1 belongs.

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

1.

An institution shall aggregate risk class-specific own funds requirements for delta, vega and curvature risks in accordance with the process set out in paragraphs 2, 3 and 4.

2.

The process to calculate the risk class-specific own funds requirements for delta, vega and curvature risks described in Articles 325f and 325g shall be performed three times per risk class, each time using a different set of correlation parameters \[\rho_{kl}\] (correlation between risk factors within a bucket) and \[\gamma_{bc}\] (correlation between buckets within a risk class). Each of those three sets shall correspond to a different scenario, as follows:

3.

An institution shall calculate the sum of the delta, vega and curvature risk class-specific own funds requirements for each scenario to determine three scenario-specific own funds requirements.

4.

The own funds requirement under the sensitivities-based method shall be the highest of the three scenario-specific own funds requirements referred to in paragraph 3.

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

1.

An institution shall use a look-through approach for index and other multi-underlying instruments in accordance with the following:

1. (a) for the purposes of calculating the own funds requirements for delta and curvature risk, an institution shall consider that they hold individual positions directly in the underlying constituents of the index or other multi-underlying instruments, except for a position in an index included in the ACTP for which they shall calculate a single sensitivity to the index;
2. (b) an institution may net the sensitivities to a risk factor of a given constituent of an index instrument or other multi-underlying instrument with the sensitivities to the same risk factor of the same constituent of single name instruments, except for positions included in the ACTP; and
3. (c) for the purposes of calculating the own funds requirements for vega risk, an institution may either consider that they directly hold individual positions in the underlying constituents of the index or other multi-underlying instrument, or calculate a single sensitivity to the underlying of that instrument. In the latter case, an institution shall assign the single sensitivity to the relevant bucket as set out in Sub-section 1 of Section 6 as follows:
1. (i) where, taking into account the weightings of that index, more than 75% of constituents in that index would be mapped to the same bucket, an institution shall assign the sensitivity to that bucket and treat it as a single-name sensitivity in that bucket;
2. (ii) in all other cases, an institution shall assign the sensitivity to the relevant index bucket.

2.

By way of derogation from point (a) of paragraph 1, an institution may calculate a single sensitivity to a position in a listed equity or credit index for the purposes of calculating the own funds requirements for delta and curvature risks provided the listed equity or credit index meets the conditions set out in paragraph 3. In that case, an institution shall assign the single sensitivity to the relevant bucket as set out in Sub-section 1 of Section 6 as follows:

1. (a) where, taking into account the weightings of that listed index, more than 75% of constituents in that listed index would be mapped to the same bucket, that sensitivity shall be assigned to that bucket and treated as a single-name sensitivity in that bucket;
2. (b) in all other cases, an institution shall assign the sensitivity to the relevant listed index bucket.

3.

An institution may use the approach set out in paragraph 2 for all instruments referencing a listed equity or credit index where all the following conditions are met:

1. (a) the constituents of the listed index and their respective weightings in that index are known;
2. (b) the listed index contains at least 20 constituents;
3. (c) no single constituent contained within the listed index represents more than 25% of the total index;
4. (d) no set comprising one tenth of the total number of constituents of the listed index, rounded up to the next integer, represents more than 60% of the total index; and
5. (e) the total market capitalisation of all the constituents of the listed index is no less than GBP 32 billion.

4.

An institution must exclusively use either:

1. (a) the approach set out in paragraph 1; or
2. (b) the approach set out in paragraph 2,

for all instruments that reference the same listed equity or credit index that meets the conditions set out in paragraph 3. An institution which has used the approach set out in paragraph 1 for a type of instrument referencing a particular index may only with the prior permission of the PRA change to the approach set out in paragraph 2 in respect of such instruments to the extent and subject to any modifications set out in the permission.

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

5.

An institution must ensure that for an index or other multi-underlying instrument, the sensitivity inputs for the calculation of delta and curvature risks is consistent, irrespective of the approaches used for that instrument.

6.

Index or multi-underlying instruments which bear other residual risks as referred to in paragraph 6 of Article 325u shall be subject to the residual risk add-on referred to in Section 4.

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

1.

Subject to paragraph 6, an institution shall calculate the own funds requirements for market risk of a position in a CIU using one of the following approaches:

1. (a) where an institution is able to obtain sufficient information about the individual underlying exposures of the CIU, which in aggregate amount to at least 50% of the value of the CIU, the institution shall calculate the own funds requirements for market risk of that CIU position by looking through to the underlying positions of the CIU as follows:
2. 1. (i) for the underlying exposures of the CIU to which the institution is able to look through that are eligible for the trading book in accordance with the Trading Book (CRR) Part, as if those underlying exposures were positions directly held by the institution; and
   2. (ii) for the underlying exposures of the CIU to which the institution is unable to look through or for underlying exposures to which the institution is able to look through that are not eligible for the trading book in accordance with the Trading Book (CRR) Part, in accordance with point (b)(i);
3. (b) where the institution is not able to obtain sufficient information about the individual underlying exposures of the CIU, but the institution has knowledge of the content of the mandate of the CIU and daily price quotes for the CIU can be obtained, the institution shall calculate the own funds requirements for market risk of that CIU position under the sensitivities-based method set out in Section 2 by using one of the following approaches:
   1. (i) the institution may consider the position in the CIU as a single equity position allocated to the bucket ‘other sector’, being item 11 in Table 8 of paragraph 1 of Article 325ap;
   2. (ii) with the prior permission of the PRA to the extent and subject to any modifications set out in the permission, an institution may calculate the own funds requirements for market risk of the CIU in accordance with the limits set in the CIU’s mandate and relevant law;
   3. (iii) in accordance with paragraph 4a, the institution may calculate the own funds requirements for market risk of the CIU on a stand-alone basis by treating the CIU as a single equity position and applying a risk weight calculated by a third party;
4. (c) where the institution does not meet the conditions in points (a) or (b), the institution shall allocate the CIU to the non-trading book.

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

Where the mandate of the CIU implies that some exposures in the CIU shall be subject to the own funds requirement for default risk, an institution that uses one of the approaches set out in point (b) shall apply the own funds requirement for default risk set out in Section 5 and the residual risk add-on set out in Section 4, provided that:

1. (1A) where an institution uses the approach set out in point (b)(i), that institution shall, for the purposes of determining any own funds requirement for default risk, consider the position in the CIU as a single unrated equity position allocated to the bucket ‘Unrated’ in Table 2 of paragraph 1 of Article 325y; and
2. (1B) where an institution uses the approach set out in point (b)(iii), that institution shall, for the purposes of determining the residual risk add-on and own funds requirement for default risk, apply separate risk weights calculated by a third party. An institution shall ensure the third party provides separate calculations for non-securitisations, securitisations that are not included in the ACTP and securitisations that are included in the ACTP.

An institution that uses the approach set out in point (b)(ii) may calculate the own funds requirements for counterparty credit risk and own funds requirements for CVA risk of derivative positions of the CIU, using the simplified approach set out in paragraph 3 of Credit Risk: Standardised Approach (CRR) Part Article 132A.

2.

By way of derogation from paragraph 1, where an institution has a position in a CIU that tracks an index benchmark so that the annualised return difference between the CIU and the tracked index benchmark over the last 12 months is below 1% in absolute terms, ignoring fees and commissions, the institution may treat that position as a position in the tracked index benchmark. An institution shall verify compliance with that condition when the institution enters into the position and, after that, at least annually.

For the purposes of the first sub-paragraph, where data over the last 12 months cannot as yet be obtained, an institution may use an annualised return difference for a period shorter than 12 months.

3.

An institution may use a combination of the approaches referred to in points (a), (b) and (c) of paragraph 1 for its positions in separate CIUs. However, an institution shall use only one of those approaches for all the positions in the same CIU.

4.

For the purposes of point (b)(ii) of paragraph 1 and where point (b)(ii) of paragraph 1 applies as the mandate of the CIU implies that some exposures in the CIU shall be subject to the own funds requirement for default risk in accordance with the second sub-paragraph of paragraph 1, an institution shall carry out the calculations under the following provisions:

1. (a) for the purposes of calculating the own funds requirement under the sensitivities-based method set out in Section 2, the CIU shall first take position to the maximum extent allowed under its mandate or relevant law in the exposures attracting the highest own funds requirements set out under that Section and shall then continue taking positions in descending order until the maximum total loss limit is reached;
2. (b) for the purposes of the own fund requirements for the default risk set out in Section 5, the CIU shall first take position to the maximum extent allowed under its mandate or relevant law in the exposures attracting the highest own funds requirements set out under that Section and shall then continue taking positions in descending order until the maximum total loss limit is reached; and
3. (c) the CIU shall apply leverage to the maximum extent allowed under its mandate or relevant law, where applicable.

The own funds requirements for all positions in the same CIU for which the calculations referred to in the first sub-paragraph are used shall be calculated on a stand-alone basis as a separate portfolio using the approach set out in this Part.

4A.

An institution may apply the treatment in point (b)(iii) of paragraph 1 where conditions (a), (b) and (c) are met and may apply the treatment in point (1B) of paragraph 1 where conditions (b) and (c) are met. The conditions are:

1. (a) the risk weight is determined as the own funds requirements of the CIU calculated on a stand-alone basis in accordance with point (a) of paragraph 1, divided by the delta sensitivity that would be determined if treating the position in the CIU as a single equity position in accordance with point (b)(i) of paragraph 1;
2. (b) an external auditor has confirmed the adequacy of the third party’s calculation of the risk weight, including that the third party has adequate information to perform the calculation in point (a) of this paragraph; and
3. (c) the institution verifies the appropriateness of the third party’s risk weight calculation.

5.

An institution may use the approaches referred to in point (a) or (b) of paragraph 1 only where the CIU meets all the conditions set out in paragraph 3 of Credit Risk: Standardised Approach (CRR) Part Article 132.

6.

An institution shall treat a position in a CIU which is also 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: This rule corresponds to Article 325j of CRR as it applied immediately before revocation by the Treasury]

[Note: Provision left blank]

1.

An institution shall ensure that for all GIRR factors, including inflation risk and cross-currency basis risk, there shall be one bucket per currency, each containing different types of risk factor.

An institution shall ensure that the delta GIRR factors applicable to interest rate-sensitive instruments shall be the relevant risk-free rates per currency and per each of the following maturities: 0.25 years, 0.5 years, one year, two years, three years, five years, 10 years, 15 years, 20 years, 30 years. An institution shall assign risk factors to the specified vertices by linear interpolation or by using a method that is most consistent with the pricing functions used by the independent risk control function of the institution to report market risk or profits and losses to senior management.

2.

An institution shall obtain the risk-free rates per currency from money-market instruments held in the trading book of the institution that have the lowest credit risk, such as overnight index swaps.

3.

Where an institution cannot apply the approach referred to in paragraph 2, the risk-free rates shall be based on one or more market-implied swap curves used by the institution to mark positions to market, such as the interbank offered rate swap curves.

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

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

For the purpose of constructing the risk-free rates per currency:

1. (a) an overnight index swap curve (such as Eonia or a new benchmark rate) and a bank offering rate swap curve (such as three-month Euribor or other benchmark rates) must be considered two different curves;
2. (b) two bank offering rate curves at different maturities (such as three-month Euribor and six-month Euribor) must be considered two different curves; and
3. (c) an onshore and an offshore currency curve (such as onshore Indian rupee and offshore Indian rupee) must be considered two different curves.

4.

An institution shall ensure that in the case of GIRR factors, each currency constitutes a separate bucket. An institution shall assign risk factors within the same bucket, but with different maturities a different risk weight in accordance with Section 6.

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

5.

An institution shall calculate the sensitivity of the instrument to the additional risk factor for inflation risk referred to in paragraph 4 as the change in the value of the instrument, according to its pricing model, as a result of a one basis point shift in each of the components of the vector. Each currency shall constitute a separate bucket. Within each bucket, an institution shall treat each inflation curve as a single risk factor, regardless of the number of components of each vector. An institution shall offset all sensitivities to a single inflation curve within a bucket, calculated as described in this paragraph, in order to give rise to a single net sensitivity per inflation curve.

6.

Debt instruments that involve payments in different currencies shall also be subject to cross-currency basis risk between those currencies. For the purposes of the sensitivities-based method, an institution shall apply risk factors which are the cross-currency basis risk of each currency over either US dollar or euro. An institution shall compute cross currency bases that do not relate to either basis over US dollar or basis over euro either on ‘basis over US dollar’ or ‘basis over euro’.

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

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

7.

The vega GIRR factors applicable to options with underlyings that are sensitive to general interest rate shall be the implied volatilities of the relevant risk-free rates as described in paragraphs 2 and 3, defined along two dimensions:

1. (a) the residual maturity of the option, mapped to one or several of the following tenors: 0.5 years, one year, three years, five years, 10 years; and
2. (b) the residual maturity of the underlying at the expiry date of the option, mapped to one or more of the following residual maturity tenors: 0.5 years, one year, three years, five years, 10 years.

Each vega GIRR factor shall be assigned to buckets depending on the currency, with one bucket per currency.

8.

An institution shall apply curvature GIRR factors which consist of one vector of risk-free rates, representing a specific risk-free yield curve, per currency. Each currency shall constitute a different bucket. For each instrument, the vector shall contain as many components as there are different maturities of risk-free rates used as variables by the institution's pricing model for that instrument.

9.

An institution shall calculate the sensitivity of the instrument to each risk factor used in the curvature risk formula in accordance with Article 325g. For the purposes of the curvature risk, an institution shall consider vectors corresponding to different yield curves and with a different number of components as the same risk factor, provided that those vectors correspond to the same currency. An institution shall offset sensitivities to the same risk factor. There shall be only one net sensitivity per bucket.

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

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

1.

An institution shall apply delta CSR factors to non-securitisation instruments that are sensitive to credit spread which are the issuer credit spread rates of those instruments, inferred from the relevant debt instruments and credit default swaps, and mapped to each of the following maturities: 0.5 years, one year, three years, five years, 10 years.

An institution shall identify two distinct risk factors per issuer and maturity: one risk factor for debt instruments and one risk factor for credit default swaps. The buckets shall be sector buckets, as referred to in Section 6, and each bucket shall include all the risk factors allocated to the relevant sector.

2.

An institution shall apply vega CSR factors to options with non-securitisation underlyings that are sensitive to credit spread which are the implied volatilities of the underlyings’ issuer credit spread rates inferred as laid down in paragraph 1, which shall be mapped to the following maturities in accordance with the maturity of the option subject to own funds requirements: 0.5 years, one year, three years, five years, 10 years. The same buckets shall be used as the buckets that were used for the delta CSR for non-securitisation.

3.

An institution shall apply curvature CSR factors to non-securitisation instruments which consist of one vector of credit spread rates, representing a credit spread curve specific to the issuer. For each instrument, the vector shall contain as many components as there are different maturities of credit spread rates used as variables in the institution's pricing model for that instrument. The same buckets shall be used as the buckets that were used for the delta CSR for non-securitisation.

4.

An institution shall calculate the sensitivity of the instrument to each risk factor used in the curvature risk formula in accordance with Article 325g. For the purposes of the curvature risk, an institution shall consider vectors inferred from either relevant debt instruments or credit default swaps and with a different number of components as the same risk factor, provided that those vectors correspond to the same issuer.

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

1.

An institution shall apply the CSR factors referred to in paragraph 3 to securitisation positions that are included in the ACTP, as referred to in paragraphs 6, 7 and 8 of Market Risk: General Provisions (CRR) Part Article 325.

An institution shall apply the CSR factors referred to in paragraph 5 to securitisation positions that are not included in the ACTP, as referred to in paragraphs 6, 7 and 8 of Market Risk: General Provisions (CRR) Part Article 325.

2.

The buckets applicable to the CSR for securitisations that are included in the ACTP shall be the same as the buckets applicable to the CSR for non-securitisations, as referred to in Section 6.

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

3.

An institution shall apply CSR factors to securitisation positions that are included in the ACTP as follows:

1. (a) the delta risk factors shall be all the relevant credit spread rates of the issuers of the underlying exposures of the securitisation position, inferred from the relevant debt instruments and credit default swaps, and for each of the following maturities: 0.5 years, one year, three years, five years, 10 years.
2. (b) the vega risk factors applicable to options with securitisation positions that are included in the ACTP as underlyings shall be the implied volatilities of the credit spreads of the issuers of the underlying exposures of the securitisation position, inferred as described in point (a) of this paragraph, which shall be mapped to the following maturities in accordance with the maturity of the corresponding option subject to own funds requirements: 0.5 years, one year, three years, five years, 10 years; and
3. (c) the curvature risk factors shall be the relevant credit spread yield curves of the issuers of the underlying exposures of the securitisation position expressed as a vector of credit spread rates for different maturities, inferred as indicated in point (a) of this paragraph; for each instrument, the vector shall contain as many components as there are different maturities of credit spread rates that are used as variables by the institution's pricing model for that instrument.

4.

An institution shall calculate the sensitivity of the securitisation position to each risk factor used in the curvature risk formula as specified in Article 325g. For the purposes of the curvature risk, an institution shall consider vectors inferred either from relevant debt instruments or credit default swaps and with a different number of components as the same risk factor, provided that those vectors correspond to the same issuer.

5.

An institution shall apply CSR factors to securitisation positions that are not included in the ACTP which refer to the spread of the tranche rather than the spread of the underlying instruments as follows:

1. (a) the delta risk factors shall be the relevant tranche credit spread rates, mapped to the following maturities, in accordance with the maturity of the tranche: 0.5 years, one year, three years, five years, 10 years;
2. (b) the vega risk factors applicable to options with securitisation positions that are not included in the ACTP as underlyings shall be the implied volatilities of the credit spreads of the tranches, each of them mapped to the following maturities in accordance with the maturity of the option subject to own funds requirements: 0.5 years, one year, three years, five years, 10 years; and
3. (c) the curvature risk factors shall be the same as those described in point (a) of this paragraph; to all those risk factors, a common risk weight shall be applied, as referred to in Section 6.

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

1.

The buckets for all equity risk factors shall be the sector buckets referred to in Section 6.

2.

An institution shall apply equity delta risk factors which shall be all the equity spot prices and all equity repo rates.

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

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

3.

An institution shall apply equity vega risk factors to options with underlyings that are sensitive to equity which shall be the implied volatilities of equity spot prices which shall be mapped to the following maturities in accordance with the maturities of the corresponding options subject to own funds requirements: 0.5 years, one year, three years, five years, 10 years. There shall be no own funds requirements for vega risk for equity repo rates.

4.

An institution shall apply equity curvature risk factors to options with underlyings that are sensitive to equity which shall be all the equity spot prices, regardless of the maturity of the corresponding options. There shall be no curvature risk own funds requirements for equity repo rates.

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

1.

The buckets for all commodity risk factors shall be the sector buckets referred to in Section 6.

2.

An institution shall apply commodity delta risk factors to commodity sensitive instruments which shall be all the commodity spot prices per commodity type and per each of the following maturities: 0 years, 0.25 years, 0.5 years, one year, two years, three years, five years, 10 years, 15 years, 20 years, 30 years. An institution shall only consider two commodity prices of the same type of commodity, and with the same maturity to constitute the same risk factor where the set of legal terms regarding the delivery location are identical.

3.

An institution shall apply commodity vega risk factors to options with underlyings that are sensitive to commodity which shall be the implied volatilities of commodity prices per commodity type, which shall be mapped to the following maturities in accordance with the maturities of the corresponding options subject to own funds requirements: 0.5 years, one year, three years, five years, 10 years. An institution shall consider sensitivities to the same commodity type and allocated to the same maturity to be a single risk factor which the institution shall then offset.

4.

An institution shall apply commodity curvature risk factors to options with underlyings that are sensitive to commodity which shall be one set of commodity prices with different maturities per commodity type, expressed as a vector. For each instrument, the vector shall contain as many components as there are prices of that commodity that are used as variables by the institution's pricing model for that instrument. An institution shall not differentiate between commodity prices by delivery location.

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

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

1.

An institution shall apply foreign exchange delta risk factors to foreign exchange sensitive instruments which shall be all the spot exchange rates between:

1. (a) the currencies either referenced by an instrument or in which an instrument is denominated; and
2. (b) the institution's reporting currency or the institution’s base currency, where the institution is using a base currency in accordance with paragraph 7.

There shall be one bucket per currency pair, containing a single risk factor and a single net sensitivity.

2.

An institution shall apply foreign exchange vega risk factors to options with underlyings that are sensitive to foreign exchange which shall be the implied volatilities of exchange rates between all applicable currency pairs. Those implied volatilities of exchange rates shall be mapped to the following maturities in accordance with the maturities of the corresponding options subject to own funds requirements: 0.5 years, one year, three years, five years, 10 years. There shall be one bucket per currency pair.

3.

An institution shall apply foreign exchange curvature risk factors to instruments with underlyings that are sensitive to foreign exchange which shall be the foreign exchange delta risk factors referred to in paragraph 1.

4.

An institution shall not be required to distinguish between onshore and offshore variants of a currency for all foreign exchange delta, vega and curvature risk factors.

5.

Where a foreign exchange rate that is the underlying of an instrument i that is subject to own funds requirements for curvature risks neither refers to the institution's reporting currency nor the institution’s base currency, if the institution has an approved base currency in accordance with paragraph 7, the institution may divide by 1.5 the corresponding components \[CVR_{ik}^{-}\] and \[CVR_{ik}^{+}\] set out in paragraph 2 of Article 325g for which \[x_{k}\] is the foreign exchange risk factor between one of the two currencies of the underlying and the institution's reporting currency or the institution’s base currency, as applicable.

6.

An institution may with the prior permission of the PRA divide by 1.5 the components \[CVR_{ik}^{-}\] and \[CVR_{ik}^{+}\] set out in paragraph 2 of Article 325g for all the foreign exchange risk factors of instruments concerning foreign exchange and subject to own funds requirement for curvature risk to the extent and subject to any modifications set out in the permission if, on applying for such permission, it is able to demonstrate to the satisfaction of the PRA that the institution calculates an additional set of curvature sensitivities for all foreign exchange risk factors under the assumption that the institution’s reporting currency or the institution’s base currency, if that institution has an approved base currency in accordance with paragraph 7, as applicable, simultaneously appreciates or depreciates against all other currencies. Those additional sensitivities shall be allocated to a single separate bucket.

An institution that has been granted the permission set out in the first sub-paragraph shall comply with the requirements set out in that first sub-paragraph.

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

7.

By way of derogation from paragraphs 1 and 3, an institution may with the prior permission of the PRA replace its reporting currency by another currency (‘the base currency’) in all the spot exchange rates to express the delta and curvature foreign exchange risk factors to the extent and subject to any modifications set out in the permission if, on applying for such permission, it is able to demonstrate to the satisfaction of the PRA that:

1. (a) it only uses one base currency;
2. (b) it applies the base currency consistently to all its trading book positions and non-trading book positions;
3. (c) its choice of base currency:
   1. (i) provides an appropriate risk representation for the institution’s positions subject to foreign exchange risks;
   2. (ii) is compatible with the manner in which the institution manages those foreign exchange risks internally; and
   3. (iii) is not driven primarily by the desire to reduce the institution’s own funds requirements; and
4. (d) it takes into account the translation risk between the reporting currency and the base currency.

An institution that has been permitted to use a base currency as set out in the first sub-paragraph shall:

1. (i) convert the resulting own funds requirements for foreign exchange risk into the reporting currency using the prevailing spot exchange rate between the base currency and the reporting currency; and
2. (ii) comply with the requirements set out in limbs (a) to (d).

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

[Note: Paragraphs 1 to 4 of this rule correspond to paragraphs 1 to 4 of Article 325q of CRR as applied immediately before revocation by the Treasury]

1.

An institution shall calculate delta GIRR sensitivities as follows:

1. (a) the sensitivities to risk factors consisting of risk-free rates shall be calculated as follows:

\[S_{rkt}=\frac{V_{i}(r_{kt}+0.0001,x,y \ ...)- V_{i}(r_{kt},x,y \ ...)}{0.0001}\]

where:

S_rkt = the sensitivities to risk factors consisting of risk-free rates;

r_kt = the rate of a risk-free curve k with maturity t;

V_i(. ) = the pricing function of instrument i;

x, y = risk factors other than r_kt in the pricing function V_i;

1. (b) the sensitivities to risk factors consisting of inflation risk and cross-currency basis shall be calculated as follows:

\[S_{xj}=\frac{V_{i}(X_{ji}+0.0001I_{m},y,z \ ...)- V_{i}(X_{ji},y,z \ ...)}{0.0001}\]

where:

S_xj = the sensitivities to risk factors consisting of inflation risk and cross-currency basis;

X_ji = a vector of m components representing the implied inflation curve or the cross-currency basis curve for a given currency j with m being equal to the number of inflation or cross-currency related variables used in the pricing model of instrument i;

l_m = the unity matrix of dimension (1 · m);

V_i(. ) = the pricing function of the instrument i;

y, z = other variables in the pricing model.

2.

An institution shall calculate the delta CSR sensitivities for all securitisation and non-securitisation positions as follows:

\[S_{CSkt}=\frac{V_{i}(CS_{kt}+0.0001,x,y \ ...)- V_{i}(CS_{kt},x,y \ ...)}{0.0001}\]

where:

S_CSkt = the delta CSR sensitivities for all securitisation and non-securitisation positions;

CS_kt = the value of the credit spread of an issuer k at maturity t;

V_i(. ) = the pricing function of instrument i;

x , y = risk factors other than CS_kt in the pricing function V_i.

3.

An institution shall calculate delta equity risk sensitivities as follows:

1. (a) the sensitivities to risk factors consisting of equity spot prices shall be calculated as follows:

\[S_{k}=\frac{V_{i}(1.01EQ_{k},x,y \ ...)- V_{i}(EQ_{k},x,y \ ...)}{0.01}\]

where:

S_k = the sensitivities to risk factors consisting of equity spot prices;

k = a specific equity security;

EQ_k = the value of the spot price of that equity security;

V_i(. ) = the pricing function of instrument i;

x , y = risk factors other than EQ_k in the pricing function V_i;

1. (b) the sensitivities to risk factors consisting of equity repo rates shall be calculated as follows:

\[S_{x_k}=\frac{V_{i}(X_{ki}+0.0001I_{m},y,z \ ...) - V_{i}(X_{ji},y,z \ ...)}{0.0001}\]

where:

S_xk = the sensitivities to risk factors consisting of equity repo rates;

k = the index that denotes the equity;

X_ki = a vector of m components representing the repo term structure for a specific equity k with m being equal to the number of repo rates corresponding to different maturities used in the pricing model of instrument i;

l_m = the unity matrix of dimension (1 · m);

V_i(. ) = the pricing function of the instrument i;

y, z = risk factors other than X_ki in the pricing function V_i.

4.

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

\[S_{k}=\frac{V_{i}(1.01CTY_{k},y,z \ ...)- V_{i}(CTY_{k},y,z \ ...)}{0.01}\]

where:

S_k = the delta commodity risk sensitivities;

k = a given commodity risk factor;

CTY_k = the value of risk factor k;

V_i(. ) = the pricing function of instrument i;

y, z = risk factors other than CTY_k in the pricing model of instrument i.

5.

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

\[S_{k}=\frac{V_{i}(1.01FX_{k},y,z \ ...)- V_{i}(FX_{k},y,z \ ...)}{0.01}\]

where:

S_k = the delta foreign exchange risk sensitivities;

k = a given foreign exchange risk factor;

FX_k = the value of the risk factor;

V_i(. ) = the pricing function of instrument i;

y, z = risk factors other than FX_k in the pricing model of instrument i.

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

1.

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

\[S_{k}=\frac{V_{i}(0.01+vol_{k},x,y)-V_{i}(vol_{k},x,y)}{0.01}\cdot vol_{k}\]

where:

S_k = the vega risk sensitivity of an option;

k = a specific vega risk factor, consisting of an implied volatility;

vol_k = the value of that risk factor, which should be expressed as a percentage;

x, y = risk factors other than vol_k in the pricing function V_i.

2.

In the case of risk classes where vega risk factors have a maturity dimension, but where the rules to map the risk factors are not applicable because the options do not have a maturity, an institution shall map those risk factors to the longest prescribed maturity. An institution shall subject those options to the residual risks add-on.

3.

In the case of options that do not have a strike or barrier and options that have multiple strikes or barriers, an institution shall apply the mapping to strikes and maturity used internally by the institution to price the option. An institution shall also subject those options to the residual risks add-on.

4.

An institution shall not calculate the vega risk for securitisation tranches included in the ACTP, as referred to in paragraphs 6, 7 and 8 of Market Risk: General Provisions (CRR) Part Article 325, that do not have an implied volatility. An institution shall compute own funds requirements for delta and curvature risk for those securitisation tranches.

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

1.

An institution shall derive sensitivities from the institution's pricing models that serve as a basis for reporting profit and loss to senior management, using the formulas set out in this Sub-section.

2.

When calculating delta risk sensitivities of instruments with optionality as referred to in point (a) of Article 325e(2), an institution may assume that the implied volatility risk factors remain constant.

3.

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

1. (a) for GIRR and CSR, an institution shall assume, for each currency, that the underlying of the volatility risk factors for which vega risk is calculated follows either a lognormal or normal distribution in the pricing models used for those instruments;
2. (b) for equity risk, commodity risk and foreign exchange risk, an institution shall assume that the underlying of the volatility risk factors for which vega risk is calculated follows a lognormal distribution in the pricing models used for those instruments.

4.

An institution shall calculate all sensitivities except for the sensitivities to CVAs.

5.

By way of derogation from paragraph 1, an institution may with the prior permission of the PRA use alternative definitions of delta risk sensitivities in the calculation of the own funds requirements of a trading book position under this Part to the extent and subject to any modifications set out in the permission if, on applying for such permission, it is able to demonstrate to the satisfaction of the PRA that:

1. (a) those alternative definitions are used for internal risk management purposes and for the reporting of profits and losses to senior management by an independent risk control unit within the institution; and
2. (b) those alternative definitions are more appropriate for capturing the sensitivities for the position than are the formulas set out in this Sub-section, and that the resulting sensitivities do not materially differ from those formulas.

An institution that has been granted the permission set out in the first sub-paragraph shall comply with the requirements set out in that first sub-paragraph.

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

6.

By way of derogation from paragraph 1, an institution may with the prior permission of the PRA calculate vega sensitivities on the basis of a linear transformation of alternative definitions of sensitivities in the calculation of the own funds requirements of a trading book position under this Part to the extent and subject to any modifications set out in the permission if, on applying for such permission, it is able to demonstrate to the satisfaction of the PRA that:

1. (a) those alternative definitions are used for internal risk management purposes and for the reporting of profits and losses to senior management by an independent risk control unit within the institution; and
2. (b) those alternative definitions are more appropriate for capturing the sensitivities for the position than are the formulas set out in this Sub-section, and that the linear transformation referred to in the first sub-paragraph reflects a vega risk sensitivity.

An institution that has been granted the permission set out in the first sub-paragraph shall comply with the requirements set out in that first sub-paragraph.

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

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

1.

In addition to the own funds requirements for market risk set out in Section 2, an institution shall apply additional own funds requirements to instruments exposed to residual risks in accordance with this Article.

2.

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

1. (a) the instrument is an instrument bearing residual risks where the instrument references an exotic underlying, which, for the purposes of this Part, means a trading book instrument referencing an underlying exposure that is not in the scope of the delta, vega or curvature risk treatments under the sensitivities-based method laid down in Section 2 or the own funds requirements for the default risk set out in Section 5;
2. (b) the instrument is an instrument bearing other residual risks, which, for the purposes of this Part, means any of the following instruments:
1. (i) instruments that are subject to the own funds requirements for vega and curvature risk under the sensitivities-based method set out in Section 2 and that generate pay-offs that cannot be replicated as a finite linear combination of plain-vanilla options with a single underlying equity price, commodity price, exchange rate, bond price, credit default swap price or interest rate swap;
2. (ii) instruments that are positions that are included in the ACTP referred to in paragraph 6 of Market Risk: General Provisions (CRR) Part Article 325; but
3. (iii) excluding hedges that are included in that ACTP, as referred to in paragraph 8 of Market Risk: General Provisions (CRR) Part Article 325.

3.

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

1. (a) 1% in the case of instruments referred to in point (a) of paragraph 2; and
2. (b) 0.1% in the case of instruments referred to in point (b) of paragraph 2.

3A.

By way of derogation from paragraph 3, an institution may, with the prior permission of the PRA, calculate the additional own funds requirement referred to in paragraph 1 for an instrument exposed to residual risks using the approaches specified in the permission, and to the extent and subject to any modifications set out in the permission, if, on applying for such permission, it is able to demonstrate to the satisfaction of the PRA that for the specified instrument:

1. (a) using the approach in paragraph 3 is inappropriate and the resulting own funds requirement disproportionate for the instrument; and
2. (b) the approach specified in the permission is appropriate and captures the residual risks of the instrument.

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

4.

By way of derogation from paragraph 1, an institution shall not apply the own funds requirement for other residual risks, as determined in accordance with point (b) of paragraph 2, to an instrument that meets any of the following conditions:

1. (a) the instrument is listed on a recognised exchange; or
2. (b) the instrument is eligible for central clearing in accordance with Regulation (EU) No 648/2012.

4a.

By way of derogation from paragraph 1, an institution shall not apply the own funds requirement for residual risks, as determined in accordance with points (a) and (b) of paragraph 2, to a position in an instrument where the instrument perfectly offsets the market risk of another matching position in the trading book, provided that such position is with a third party. Where the position in an instrument matches a position in that instrument with a third party in all respects other than the notional amount of the positions, the institution shall apply own funds requirements for residual risks for that instrument to any remaining net notional position in the instrument after offset of those positions.

5.

For the purposes of point (a) in paragraph 2, an exotic underlying shall include, without limitation, the following underlyings:

1. (a) longevity;
2. (b) weather;
3. (c) natural disasters; and
4. (d) future realised volatility.

6.

For the purposes of point (b) of paragraph 2, instruments bearing other residual risks shall include, without limitation, the following instruments:

1. (a) path-dependent options, which for the purpose of point (b) of paragraph 2 shall include, without limitation:
   1. (i) barrier options;
   2. (ii) Asian options; and
   3. (iii) digital options.
2. (b) instruments whose value depends on the correlation between multiple underlyings, which for the purpose of paragraph 2 shall include, without limitation:
   1. (i) basket options, excluding options specified in point (c) of paragraph 7;
   2. (ii) best-of-options;
   3. (iii) spread options;
   4. (iv) basis options;
   5. (v) Bermudan options; and
   6. (vi) Quanto options;
3. (c) instruments with behavioural risk where a retail client may prepay or exercise an option in a manner that does not maximise the value of the instrument for the client.

7.

Where an instrument includes one or more of the following risks, this, in itself, shall not cause the instrument to be exposed to residual risks in accordance with paragraph 2:

1. (a) risk arising from a ‘cheapest-to-deliver’ option;
2. (b) risk of a change in an implied volatility parameter necessary for determining the value of an instrument with optionality relative to the implied volatility of other instruments optionality with the same underlying and maturity, but different moneyness;
3. (c) correlation risk arising from instruments referencing an index; and/or
4. (d) dividend risk arising from instruments where the underlying is not solely dividend payments.

[Note: Paragraphs 1 to 4 of this rule correspond to paragraphs 1 to 4 of Article 325u of CRR as it applied immediately before revocation by the Treasury]

1.

For the purposes of this Section 5, the following definitions apply:

1. (a) ‘covered bonds’ means CRR covered bonds which meet the requirements set out in Credit Risk: Standardised Approach (CRR) Part Article 129;
2. (b) ‘short exposure’ means that the default of an issuer or group of issuers leads to a gain for the institution, regardless of the type of instrument or transaction creating the exposure;
3. (c) ‘long exposure’ means that the default of an issuer or group of issuers leads to a loss for the institution, regardless of the type of instrument or transaction creating the exposure;
4. (d) ‘gross jump-to-default (JTD) amount’ means the estimated size of the loss or gain that the default of the obligor would produce for a specific exposure;
5. (e) ‘net jump-to-default (JTD) amount’ means the estimated size of the loss or gain that an institution would incur due to the default of an obligor, after offsetting between gross JTD amounts has taken place;
6. (f) ‘loss given default or LGD’ means the loss given default of the obligor on an instrument issued by that obligor expressed as a share of the notional amount of the instrument;
7. (g) ‘default risk weight’ means the percentage representing the estimated probability of the default of each obligor, according to the creditworthiness of that obligor; and
8. (h) ‘Simple, transparent and standardised (STS) securitisation’ means securitisations which meet the requirements for simple, transparent and standardised securitisations pursuant to regulation 9 of the Securitisation Regulations 2024 (SI 2024/102).

2.

Own funds requirements for the default risk shall apply to debt and equity instruments, to derivative instruments having those instruments as underlyings and to derivatives, the pay-offs or fair values of which are affected by the default of an obligor other than the counterparty to the derivative instrument itself. An institution shall calculate default risk requirements separately for each of the following types of instruments: non-securitisations, securitisations that are not included in the ACTP and securitisations that are included in the ACTP. An institution shall apply final own funds requirements for the default risk which shall be the sum of those three components.

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

1.

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

JTD_long = max {V_A – V_D; 0}

where:

JTD_long = the gross JTD amount for the long exposure;

V_A = the market value of the instrument from which the exposures arises for the institution at the time of the calculation;

V_D = the market value of the instrument from which the exposures arises for the institution, calculated under the assumption that, at the time of the calculation, the debt instrument defaulted and experienced a recovery rate, calculated with respect to the face value of the debt instrument, equal to (1-LGD) where LGD is LGD as assigned to the debt instruments in accordance with paragraph 3.

2.

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

JTD_short = min {V_A − V_D; 0}

where:

JTD_short = the gross JTD amount for the short exposure;

V_A = the market value of the instrument from which the exposures arises for the institution at the time of the calculation;

V_D = the market value of the instrument from which the exposures arises for the institution, calculated under the assumption that, at the time of the calculation, the debt instrument defaulted and experienced a recovery rate, calculated with respect to the face value of the debt instrument, equal to (1-LGD) where LGD is LGD as assigned to the debt instruments in accordance with paragraph 3.

3.

For the purpose of determining the recovery rate for the calculation set out in paragraphs 1 and 2, an institution shall apply an LGD for debt instruments as follows:

1. (a) exposures to non-senior debt instruments shall be assigned an LGD of 100%;
2. (b) exposures to senior debt instruments shall be assigned an LGD of 75%; and
3. (c) exposures to covered bonds shall be assigned an LGD of 25%.

4.

For exposures to equity instruments, an institution shall calculate the gross JTD amounts as follows, instead of using the formulas referred to in paragraphs 1 and 2:

JTD_long = max {V_A − V_D; 0}

JTD_short = min {V_A − V_D; 0}

where:

JTD_long = the gross JTD amount for the long exposure;

JTD_short = the gross JTD amount for the short exposure;

V_A = the market value of the instrument from which the exposures arises for the institution at the time of the calculation;

V_D = the market value of the instrument from which the exposures arises for the institution, calculated under the assumption that, at the time of the calculation, the equity instrument defaulted and experienced a full loss in value.

5.

In the case of exposures to default risk arising from derivative instruments whose pay-offs in the event of the default of the obligor are not related to the notional amount of a specific instrument issued by that obligor or to the LGD of the obligor or an instrument issued by that obligor, an institution shall calculate the gross JTD amount as the difference between the market value of the instrument from which the exposure arises for the institution at the time of the calculation and the market value of the instrument from which the exposure arises calculated under the assumption that the obligor defaulted at that time.

6.

By way of derogation from paragraph 5, if the obligor was already defaulted at the time of the calculation, and the market value of the instrument from which the exposure arises for the institution at the time already reflects the gain or loss resulting from the default of the obligor, an institution shall regard the gross JTD amount of the exposure to be zero.

7.

By way of derogation from paragraphs 1, 2 and 4, if the contractual or legal terms of an instrument allow for the unwinding of that instrument with no exposure to default risk, then the gross JTD amount for such instrument shall be equal to zero.

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

1.

An institution shall calculate net JTD amounts by offsetting the gross JTD amounts of short exposures and long exposures in accordance with this Article. Offsetting shall only be possible between exposures to the same obligor where the short exposures have the same seniority as, or lower seniority than, the long exposures.

2.

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

1. (a) offsetting shall be full where all offsetting exposures have maturities of one year or more; and
2. (b) offsetting shall be partial where at least one of the offsetting exposures has a maturity of less than one year, in which case the size of the JTD amount of each exposure with a maturity of less than one year shall be multiplied by the ratio of the exposure's maturity relative to one year, with a floor of three months.

3.

Where no offsetting is possible gross JTD amounts shall equal net JTD amounts in the case of exposures with maturities of one year or more. Gross JTD amounts with maturities of less than one year shall be multiplied by the ratio of the exposure's maturity relative to one year, with a floor of three months, to calculate net JTD amounts.

4.

For the purposes of paragraphs 2 and 3, the maturities of the derivative contracts shall be considered, rather than those of their underlyings. An institution shall assign a maturity of either one year or three months to cash equity exposures and may assign a maturity of three months to equity derivative exposures, in each case at the institution's discretion.

5.

For the purposes of paragraph 1, an institution shall treat a guaranteed bond as an exposure to the underlying obligor, or where the conditions set out in paragraphs 1 and 3 of Credit Risk Mitigation (CRR) Part Article 213 and paragraph 1 of Credit Risk Mitigation (CRR) Part Article 215 are met, to the guarantor.

[Note: Paragraphs 1 to 4 of this rule correspond to paragraphs 1 to 4 of Article 325x of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall multiply net JTD amounts, irrespective of the type of counterparty, by the default risk weights that correspond to their credit quality, as specified in Table 2:

Table 2

[Note: Table 1 was previously included in Article 325k, which has now been deleted]

2.

Exposures which would receive a 0% risk-weight under the Standardised Approach shall receive a 0% default risk weight for the own funds requirements for default risk.

3.

The weighted net JTD amount shall be allocated to the following buckets: corporates, sovereigns, and local governments/municipalities.

4.

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

\[DRC_{b}=max\left\{ \left ( \sum\nolimits _{i\in long} RW_{i} \cdot net\ JTD_{i}\right) - WtS \times \left ( \sum\nolimits _{i\in short} RW_{i} \cdot | net\ JTD_{i} | \right ); 0 \right\}\]

where:

DRC_b = the own funds requirement for the default risk for bucket b;

i = the index that denotes an instrument belonging to bucket b;

RW_i = the risk weight;

WtS = a ratio recognising a benefit for hedging relationships within a bucket, which shall be calculated as follows:

\[WtS=\frac{ \sum{netJTD}_{long}}{\sum{{netJTD}_{long}+\sum\left|{netJTD}_{short}\right|}}\]

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

5.

The final own funds requirement for the default risk for non-securitisations shall be calculated as the simple sum of the bucket-level own funds requirements.

6.

The determination of rating for a net JTD amount shall be on the basis of an external credit assessment by a nominated ECAI of the corresponding issuer. For an individual issuer for which a credit assessment by a nominated ECAI is not available, an institution shall map the internal rating of the issuer to one of the external credit assessments using the approach referred to in the Credit Risk: Internal Ratings Based Approach (CRR) Part.

[Note: Paragraphs 1 to 5 of this rule correspond to paragraphs 1 to 5 of Article 325y of CRR as it applied immediately before revocation by the Treasury]

1.

Gross jump-to-default amounts for securitisation exposures shall be their market value or, if their market value is not available, their fair value determined in accordance with the applicable accounting framework.

2.

An institution shall determine net jump-to-default amounts by offsetting long gross jump-to-default amounts and short gross jump-to-default amounts. Offsetting shall only be possible between securitisation exposures with the same underlying asset pool and belonging to the same tranche. No offsetting shall be permitted between securitisation exposures with different underlying asset pools, even where the attachment and detachment points are the same.

3.

Where, by decomposing or combining existing securitisation exposures, other existing securitisation exposures can be perfectly replicated, except for the maturity dimension, the exposures resulting from that decomposition or combination may be used instead of the existing securitisation exposures for the purposes of offsetting.

4.

Where, by decomposing or combining existing exposures in underlying names, the entire tranche structure of an existing securitisation exposure can be perfectly replicated, the exposures resulting from that decomposition or combination may be used instead of the existing securitisation exposures for the purposes of offsetting. Where underlying names are used in that manner, they shall be removed from the non-securitisation default risk treatment.

5.

Article 325x shall apply to both existing securitisation exposures and to securitisation exposures used in accordance with paragraph 3 or 4 of this Article. The relevant maturities shall be those of the securitisation tranches.

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

1.

An institution shall multiply net JTD amounts of securitisation exposures by 8% of the risk weight that applies to the relevant securitisation exposure, including STS securitisations, in the non-trading book in accordance with the hierarchy of approaches set out in the Credit Risk: Standardised Approach (CRR) Part and irrespective of the type of counterparty.

2.

An institution shall apply a maturity of one year to all tranches, where risk weights are calculated in accordance with Article 259 or Article 263 of CRR.

3.

An institution shall cap the risk-weighted JTD amounts for individual cash securitisation exposures at the fair value of the position.

4.

An institution shall assign risk-weighted net JTD amounts to the following buckets:

1. (a) one common bucket for all corporates, regardless of the region;
2. (b) 44 different buckets corresponding to one bucket per region for each of the 11 asset classes defined in the second and third sub-paragraphs;

For the purposes of the first sub-paragraph, the 11 asset classes are:

1. (i) asset-backed commercial paper;
2. (ii) auto loans/leases;
3. (iii) residential mortgage-backed securities;
4. (iv) credit cards;
5. (v) commercial mortgage-backed securities;
6. (vi) collateralised loan obligations;
7. (vii) collateralised debt obligations squared;
8. (viii) small and medium-sized enterprises;
9. (ix) student loans;
10. (x) other retail; and
11. (xi) other wholesale.

For the purposes of the first sub-paragraph, the four regions are:

1. (A) Asia;
2. (B) Europe;
3. (C) North America; and
4. (D) the rest of the world.

5.

In order to assign a securitisation exposure to a bucket, an institution shall rely on a classification commonly used in the market. An institution shall assign each securitisation exposure to only one of the buckets referred to in paragraph 4. Any securitisation exposure that an institution cannot assign to a bucket for an asset class or region shall be assigned to the asset class ‘other retail’ or ‘other wholesale’ or to the region ‘rest of the world’, respectively.

6.

An institution shall aggregate weighted net JTD amounts within each bucket in the same manner as for default risk of non-securitisation exposures, using the formula in paragraph 4 of Article 325y, resulting in the own funds requirement for the default risk for each bucket.

7.

The final own funds requirement for the default risk for securitisations not included in the ACTP shall be calculated as the simple sum of the bucket-level own funds requirements.

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

1.

For the ACTP, an institution shall ensure that the own funds requirements includes the default risk for securitisation exposures and for non-securitisation hedges. Those hedges shall be removed from the default risk calculations for non-securitisation. There shall be no diversification benefit between the own funds requirements for the default risk for non-securitisations, the own funds requirements for the default risk for securitisations not included in the ACTP and own funds requirements for the default risk for securitisations included in the ACTP.

2.

For traded non-securitisation credit and equity derivatives, an institution shall determine JTD amounts by individual constituents applying a look-through approach.

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

1.

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

1. (a) ‘decomposition using a valuation model’ means that a single name constituent of a securitisation is valued as the difference between the unconditional value of the securitisation and the conditional value of the securitisation assuming that single name defaults with an LGD of 100%;
2. (b) ‘replication’ means that the combination of individual securitisation index tranches are combined to replicate another tranche of the same index series, or to replicate an untranched position in the index series; and
3. (c) ‘decomposition’ means replicating an index by a securitisation of which the underlying exposures in the pool are identical to the single name exposures that compose the index.

2.

The gross JTD amounts for securitisation exposures and non-securitisation exposures in the ACTP shall be their market value or, if their market value is not available, their fair value determined in accordance with the applicable accounting framework.

3.

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

1. (a) attachment point = (N – 1) / Total Names;
2. (b) detachment point = N / Total Names,

where ‘Total Names’ shall be the total number of names in the underlying basket or pool.

4.

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

1. (a) for indices, index tranches and bespoke tranches, offsetting shall be possible across maturities within the same index family, series and tranche, subject to the provisions on exposures of less than one year laid down in Article 325x; long gross JTD amounts and short gross JTD amounts that perfectly replicate each other may be offset through decomposition into single name equivalent exposures using a valuation model; in such cases, the sum of the gross JTD amounts of the single name equivalent exposures obtained through decomposition shall be equal to the gross JTD amount of the undecomposed exposure;
2. (b) offsetting through decomposition as set out in point (a) shall not be allowed for resecuritisations or derivatives on securitisation;
3. (c) for indices and index tranches, offsetting shall be possible across maturities within the same index family, series and tranche by replication or by decomposition; where the long exposures and short exposures are otherwise equivalent, apart from one residual component, offsetting shall be allowed and the net JTD amount shall reflect the residual exposure;
4. (d) different tranches of the same index series, different series of the same index and different index families may not be used to offset each other.

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

1.

An institution shall multiply net JTD amounts by:

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

2.

Risk-weighted net JTD amounts shall be assigned to buckets that correspond to an index.

3.

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

\[DRC_{b}=max\left\{\left ( \sum\nolimits _{i\in long}RW_{i}\cdot net\ JTD_{i}\right ) - WtS_{ACTP}\cdot\left (\sum\nolimits _{i\in short}RW_{i}\cdot \left|net\ JTD_{i}\right| \right );0 \right\}\]

where:

DRC_b = the own funds requirement for the default risk for bucket b;

i = an instrument belonging to bucket b;

WtS_ACTP = the ratio recognising a benefit for hedging relationships within a bucket, which shall be calculated in accordance with the WtS formula set out in paragraph 4 of Article 325y, but using long positions and short positions across the entire ACTP and not just the positions in the particular bucket.

4.

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

\[DRC_{ACTP}=max\left\{\sum_{b}{max\left\{DRC_b,\ 0\right\}+0.5\cdot\left(min\left\{DRC_b,0\right\}\right)};0\right\}\]

where:

DRC_ACTP = the own funds requirement for the default risk for the ACTP;

DRC_b = the own funds requirement for the default risk for bucket b.

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

1.

For currencies not included in the most liquid currency sub-category as referred to in point (a) of paragraph 8 of Market Risk: Internal Model Approach (CRR) Part Article 325bd, the risk weights of the sensitivities to the risk-free rate risk factors shall be the following for each sub-bucket in Table 3.

2.

An institution shall apply a risk weight of 1.6% to all sensitivities of inflation and to cross currency basis risk factors.

3.

The risk weights of all risk factors relating to the currencies included in the most liquid currency sub-category as referred to in point (a) of paragraph 8 of Market Risk: Internal Model Approach (CRR) Part Article 325bd and to the domestic currency of the institution shall be the risk weights referred to in Table 3 and paragraph 2 divided by \[\sqrt{2}\].

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

1.

Between two weighted sensitivities of GIRR factors WS_k and WS_l within the same bucket, and with the same assigned maturity but corresponding to different curves, an institution shall set correlation \[\rho _{kl}\] at 99.90%.

2.

Between two weighted sensitivities of GIRR factors WS_k and WS_l within the same bucket, corresponding to the same curve, but having different maturities, an institution shall set correlation in accordance with the following formula:

\[max\left[e^{\left(-\theta.\frac{\left| T_k-T_l \right|}{min\left\{T_k;\ T_l \right\}}\right)};40\%\right]\]

where:

T_k (respectively T_l) = the maturity that relates to the risk free rate;

\[\theta\] = 3%.

3.

Between two weighted sensitivities of GIRR factors WS_k and WS_l within the same bucket, corresponding to different curves and having different maturities, an institution shall set the correlation \[\rho _{kl}\] as equal to the correlation parameter specified in paragraph 2, multiplied by 99.90%.

4.

Between any given weighted sensitivity of GIRR factors WS_k and any given weighted sensitivity of inflation risk factors WS_l, an institution shall set the correlation at 40%.

5.

Between any given weighted sensitivity of cross-currency basis risk factors WS_k and any given weighted sensitivity of GIRR factors WS_l, including another cross-currency basis risk factor, the correlation shall be set at 0%.

6.

Between any given weighted sensitivity of inflation risk factor WS_k and any given weighted sensitivity of a different inflation risk factor in the same currency WS_l, an institution shall set the correlation at 99.90%.

[Note: Paragraphs 1 to 5 of this rule correspond to paragraphs 1 to 5 of Article 325af of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall use the parameter \[\gamma_{bc}\] = 50% to aggregate risk factors belonging to different buckets.

2.

[Note: Provision left blank]

[Note: Paragraph 1 of this rule corresponds to paragraph 1 of Article 325ag of CRR as it applied immediately before revocation by the Treasury]

1.

Risk weights for the sensitivities to CSR factors for non-securitisations shall be the same for all maturities (0.5 years, one year, three years, five years, 10 years) within each bucket in Table 4:

2.

To assign a risk exposure to a sector, an institution shall rely on a classification that is commonly used in the market for grouping issuers by sector. An institution shall assign each issuer to only one of the sector buckets in Table 4. Risk exposures from any issuer that an institution cannot assign to a sector in such a manner shall be assigned to bucket 16 in Table 4.

3.

The assignment of a risk exposure to investment grade or non-investment grade and unrated shall be on the basis of an external credit assessment by a nominated ECAI of the corresponding issuer. For an individual issuer for which a credit assessment by a nominated ECAI is not available, an institution using the approach referred to in the Credit Risk: Internal Ratings Based Approach (CRR) Part shall map the internal rating of the issuer to one of the external credit assessments.

4.

An institution shall assign an exposure to any non-tranched mortgage-backed security issued by an entity established or chartered by a government to serve public purposes specified by the legislative body of a country, but whose debt obligations are not explicitly guaranteed by the credit of that government (also known as a ‘government sponsored enterprise’) to bucket 2 in Table 4.

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

1.

An institution shall set the correlation parameter P_kl between two sensitivities WS_k and WS_t within the same bucket as follows:

\[\rho _{kl}= \rho {_{kl}}^{(name)}\cdot {\rho_{kl}}^{(tenor)}\cdot \rho {_{kl}}^{(basis)}\]

where:

\[\rho {_{kl}}^{(name)}\] = 1 where the two names of sensitivities k and l are identical;

35% where the two names of sensitivities k and l are assigned to buckets 1 to 15 in Table 4 of paragraph 1 of Article 325ah; and

80% where the two names of sensitivities k and l are assigned to buckets 17 to 18 in Table 4 of paragraph 1 of Article 325ah;

\[{\rho_{kl}}^{(tenor)}\] = 1 where the two vertices of the sensitivities k and l are identical, otherwise it shall be equal to 65%;

\[\rho {_{kl}}^{(basis)}\] = 1 where the two sensitivities are related to the same curves, otherwise it shall be equal to 99.90%.

2.

The correlation parameters referred to in paragraph 1 shall not apply to bucket 16 in Table 4 of paragraph 1 of Article 325ah. The own funds requirement for the delta risk aggregation formula within bucket 16 in Table 4 of paragraph 1 of Article 325ah shall be equal to the sum of the absolute values of the net weighted sensitivities allocated to that bucket:

\[K_{b^{(bucket\ 16)}} = \sum_{k}\left| WS_{k}\right|\]

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

An institution shall set the correlation parameter \[\gamma_{bc}\] that applies to the aggregation of sensitivities between different buckets as follows:

\[\gamma _{bc}= \gamma _{bc}^{(rating)}\cdot \gamma _{bc}^{(sector)}\]

where:

\[\gamma { _{bc}}^{(rating)}\] = 1 where the two buckets have the same rating category (either investment grade, non-investment grade or unrated), otherwise it shall be equal to 50%;

\[\gamma _{bc}^{(sector)}\] = 1 where the two buckets belong to the same sector, and otherwise shall be equal to the corresponding percentage set out in Table 5:

Table 5

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

1.

Risk weights for the sensitivities to CSR factors for securitisations included in the ACTP risk factors shall be the same for all maturities (0.5 years, one year, three years, five years, 10 years) within each bucket and shall be specified for each bucket in Table 6:

Table 6

2.

The assignment of a risk exposure to investment grade or non-investment grade and unrated shall be on the basis of an external credit assessment by a nominated ECAI of the corresponding issuer. For an individual issuer for which a credit assessment by a nominated ECAI is not available, an institution using the approach referred to in the Credit Risk: Internal Ratings Based Approach (CRR) Part shall map the internal rating of the issuer to one of the external credit assessments.

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

1.

An institution shall derive the delta risk correlation ρ_kl in accordance with Article 325ai, except that, for the purposes of this paragraph, ρ_kl^(basis) shall be equal to 1 where the two sensitivities are related to the same curves, otherwise it shall be equal to 99.00%.

2.

An institution shall derive \[\gamma_{bc}\] in accordance with Article 325aj.

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

1.

Risk weights for the sensitivities to CSR factors for securitisation not included in the ACTP shall be the same for all maturities (0.5 years, one year, three years, five years, 10 years) within each bucket in Table 7 as follows:

Table 7

2.

To assign a risk exposure to a sector, an institution shall rely on a classification that is commonly used in the market for grouping tranches by sector. An institution shall assign each tranche to one of the sector buckets in Table 7. Risk exposures from any tranche that an institution cannot assign to a sector in such a manner shall be assigned to bucket 25 of Table 7.

3.

The assignment of a risk exposure to investment grade or non-investment grade and unrated shall be on the basis of an external credit assessment by a nominated ECAI of the corresponding tranche. For an individual tranche for which a credit assessment by a nominated ECAI is not available, an institution using the approach referred to in the Credit Risk: Internal Ratings Based Approach (CRR) Part shall map the internal rating of the tranche to one of the external credit assessments.

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

1.

An institution shall set the correlation parameter ρ_kl between two sensitivities WS_k and WS_l within the same bucket as follows:

ρ_kl = ρ_kl^(tranche) · ρ_kl^(tenor) · ρ_kl^(basis)

where:

ρ_kl^(tranche) = 1 where the two names of sensitivities k and l are within the same bucket and are related to the same securitisation tranche (more than 80% overlap in notional terms), otherwise it shall be equal to 40%;

ρ_kl^(tenor) = 1 where the two vertices of the sensitivities k and l are identical, otherwise it shall be equal to 80%;

ρ_kl^(basis) = 1 where the two sensitivities are related to the same curves, otherwise it shall be equal to 99.90%.

2.

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

\[K_{b^{(bucket\ 25)}} = \sum_{k}\left| WS_{k}\right|\]

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

1.

An institution shall apply the correlation parameter \[\gamma_{bc}\] to the aggregation of sensitivities between different buckets at 0%.

2.

An institution shall add the own funds requirement for bucket 25 of Table 7 to the overall risk class level capital, with no diversification or hedging effects recognised with any other bucket.

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

1.

Risk weights for the sensitivities to equity and equity repo rate risk factors shall be specified for each bucket in Table 8 as follows:

Table 8

2.

For the purposes of this Article, what constitutes a small and a large market capitalisation shall be as specified in paragraph 9 of Market Risk: Internal Model Approach (CRR) Part Article 325bd.

3.

For the purpose of applying risk weights for equity risk in this Article, the following countries shall constitute advanced economies:

1. (a) Australia;
2. (b) Canada;
3. (c) Countries that are member states of the European Union and have adopted the Euro as their currency;
4. (d) Denmark;
5. (e) Hong Kong SAR;
6. (f) Japan;
7. (g) Mexico;
8. (h) New Zealand;
9. (i) Norway;
10. (j) Singapore;
11. (k) Sweden;
12. (l) Switzerland;
13. (m) The United Kingdom; and
14. (n) The United States.

Countries not included in the first sub-paragraph shall constitute emerging markets.

4.

When assigning a risk exposure to a sector, an institution shall rely on a classification that is commonly used in the market for grouping issuers by sector. An institution shall assign each issuer to one of the sector buckets in Table 8 and shall assign all issuers from the same industry to the same sector. Risk exposures from any issuer that an institution cannot assign to a sector in such a manner shall be assigned to bucket 11 in Table 8. Multinational or multi-sector equity issuers shall be assigned to a particular bucket on the basis of the most material region and sector in which the equity issuer operates.

[Note: This rule corresponds to Article 325ap(1), (2) and (4) of CRR as it applied immediately before revocation by the Treasury]

1.

An institution shall set the delta risk correlation parameter ρ_kl between two sensitivities WS_k and WS_l within the same bucket at 99.90% where one is a sensitivity to an equity spot price and the other is a sensitivity to an equity repo rate and where both sensitivities are related to the same equity issuer name.

2.

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

1. (a) 15% between two sensitivities within the same bucket that fall under the category large market capitalisation, emerging market economy (bucket number 1, 2, 3 or 4 in Table 8);
2. (b) 25% between two sensitivities within the same bucket that fall under the category large market capitalisation, advanced economy (bucket number 5, 6, 7 or 8 in Table 8);
3. (c) 7.5% between two sensitivities within the same bucket that fall under the category small market capitalisation, emerging market economy (bucket number 9 in Table 8);
4. (d) 12.5% between two sensitivities within the same bucket that fall under the category small market capitalisation, advanced economy (bucket number 10 in Table 8); and
5. (e) 80% between two sensitivities within the same bucket that fall under either index bucket (bucket number 12 or 13 in Table 8).

3.

An institution shall set the correlation parameter ρ_kl between two sensitivities WS_k and WS_l to equity repo rate within the same bucket in accordance with points (a) to (e) in paragraph 2.

4.

Between two sensitivities WS_k and WS_l within the same bucket where one is a sensitivity to an equity spot price and the other a sensitivity to an equity repo rate and both sensitivities relate to a different equity issuer name, an institution shall set the correlation parameter ρ_kl to the correlation parameters specified in paragraph 2, multiplied by 99.90%.

5.

The correlation parameters specified in paragraphs 1 to 4 shall not apply to bucket 11 in Table 8. An institution shall ensure the own funds requirement for the delta risk aggregation formula within bucket 11 shall be equal to the sum of the absolute values of the net weighted sensitivities allocated to that bucket:

\[K_{b^{(bucket\ 11)}} = \sum_{k}\left| WS_{k}\right|\]

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

An institution shall apply the correlation parameter \[\gamma_{bc}\] to the aggregation of sensitivities between different buckets.

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

1. (a) 15% where the two buckets fall within buckets 1 to 10;
2. (b) 0% where either of the two buckets fall within bucket number 11;
3. (c) 75% where the two buckets fall within bucket number 12 and 13; and
4. (d) 45% otherwise.

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

1.

Risk weights for sensitivities to commodity risk factors shall be specified for each bucket in Table 9:

Table 9

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

1.

For the purposes of this Article, any two commodities shall be considered distinct commodities where there exist in the market two contracts that are differentiated only by the underlying commodity to be delivered against each contract.

2.

In respect of bucket 3b in Table 10, an institution shall set the correlation parameter ρ_kl between two sensitivities WS_k and WS_l within the same bucket as follows:

\[\rho _{kl}= \rho {_{kl}}^{(commodity)}\cdot {\rho_{kl}}^{(tenor)}\cdot \rho {_{kl}}^{(basis)}\]

where:

ρ_kl^(commodity) = 1 where the two commodities of sensitivities k and l are identical, otherwise it shall be equal to the intra-bucket correlations in Table 10;

ρ_kl^(tenor) = 1 where the two vertices of the sensitivities k and l are identical, otherwise it shall be equal to 99%;

ρ_kl^(basis) = 1 where the two sensitivities are identical in the delivery location of a commodity, otherwise it shall be equal to 99.90%.

2A.

In respect of all other buckets in Table 10 (other than bucket 3b), an institution shall set the correlation parameter ρ_kl between two sensitivities WS_k and WS_l within the same bucket as follows:

\[\rho _{kl}= \rho {_{kl}}^{(commodity)}\cdot {\rho_{kl}}^{(tenor)}\cdot \rho {_{kl}}^{(basis)}\]

where:

ρ_kl^(commodity) = 1 where the two commodities of sensitivities k and l are identical, otherwise it shall be equal to the intra-bucket correlations in Table 10;

ρ_kl^(tenor) = 1 where the two vertices of the sensitivities k and l are identical, otherwise it shall be equal to 99%;

ρ_kl^(basis) = 1 where the two sensitivities are identical in the delivery location of a commodity, otherwise it shall be equal to 99.90%.

3.

The intra-bucket correlations \[{\rho_{kl}}^{(commodity)}\] are:

Table 10

4.

Notwithstanding paragraph 1, the following provisions apply:

1. (a) two risk factors that are allocated to bucket 3a in Table 10 and that concern electricity which is generated in different regions or is delivered at different periods under the contractual agreement shall be considered distinct commodity risk factors; and
2. (b) two risk factors that are allocated to bucket 4 in Table 10 and that concern freight where the freight route or week of delivery differ shall be considered distinct commodity risk factors.

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

1.

An institution shall set the correlation parameter \[\gamma_{bc}\] applying to the aggregation of sensitivities between different buckets at:

1. (a) 20% where the two buckets fall within bucket numbers 1 to 10 in Table 10; and
2. (b) 0% where either of the two buckets is bucket number 11 in Table 10.

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

1.

An institution shall apply a risk weight of 15% to all sensitivities of foreign exchange risk factors.

2.

[Note: Provision left blank]

3.

[Note: Provision left blank]

4.

The risk weight of the foreign exchange risk factors included in the most liquid currency pairs sub-category as referred to in point (b) of Market Risk: Internal Model Approach (CRR) Part Article 325bd(8) shall be the risk weight referred to in paragraph 1 divided by √2.

5.

[Note: Provision left blank]

[Note: Paragraph 1 and paragraph 4 of this rule correspond to paragraph 1 and paragraph 4 of Article 325av of CRR as it applied immediately before revocation by the Treasury]

1.

An institution must ensure a uniform correlation parameter \[\gamma_{bc}\] equal to 60% is applied to the aggregation of sensitivities to foreign exchange risk factors.

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

1.

Vega risk factors shall use the delta buckets referred to in Sub-section 1 of Section 3, other than in respect of foreign exchange risk, where the buckets shall be as set out in paragraph 2 of Article 325q of this Part.

2.

Risk weights for sensitivities to vega risk factors shall be assigned in accordance with the following table:

3.

An institution shall use buckets in the context of delta risk in Sub-section 1 in the curvature risk context, unless specified otherwise in this Part.

4.

For foreign exchange and equity curvature risk factors, the curvature risk weights shall be relative shifts equal to the delta risk weights referred to in Sub-section 1.

5.

For GIRR, CSR and commodity curvature risk factors, the curvature risk weight shall be the parallel shift of all the vertices for each curve on the basis of the highest prescribed delta risk weight referred to in Sub-section 1 for the relevant bucket.

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

1.

Between vega risk sensitivities within the same bucket of the GIRR class, an institution shall set the correlation parameter \[\rho_{kl}\] as follows:

\[\rho _{kl}= min\left\{\rho{_{kl}}^{(option\ maturity)}\cdot {\rho_{kl}}^{(underlying\ maturity)};1\right\}\]

where:

\[\rho {_{kl}}^{(option\ maturity)}= e^{-\alpha \cdot \frac{\left ( \left|T_{k}-T_{l}\right| \right)}{\left ( min\left\{T_{k};T_{l}\right\} \right )}}\] where \[\alpha\] shall be set at 1%, \[T_k\] and \[T_l\] shall be equal to the maturities of the options for which the vega sensitivities are derived, expressed as a number of years;

\[\rho {_{kl}}^{(underlying\ maturity)}= e^{-\alpha \cdot \frac{\left ( \left|T{^{U}}_{k}-T{^{U}}_{l}\right| \right)}{\left ( min\left\{T{^{U}}_{k};T{^{U}}_{l}\right\} \right )}}\] where \[\alpha\] is set at 1%, \[{T^U}_k\] and \[{T^U}_l\] shall be equal to the maturities of the underlyings of the options for which the vega sensitivities are derived, minus the maturities of the corresponding options, expressed in both cases as a number of years.

2.

Between vega risk sensitivities within a bucket of the other risk classes, an institution shall set the correlation parameter \[\rho_{kl}\] as follows:

\[\rho{_{kl}} = min \left\{ \rho {_{kl}}^{(DELTA)} \cdot \rho {_{kl}}^{(option \ maturity)};1 \right\}\]

where:

\[{\rho_{kl}}^{(DELTA)}\] = the delta intra-bucket correlation corresponding to the bucket to which vega risk factors k and l would be allocated;

\[{\rho_{kl}}^{(option\ maturity)}\] shall be set in accordance with paragraph 1.

3.

With regard to vega risk sensitivities between buckets within a risk class (GIRR and non-GIRR), the same correlation parameters for \[\gamma_{bc}\], as specified for delta correlations for each risk class in Section 4, shall be used in the vega risk context.

4.

There shall be no diversification or hedging benefit recognised in the standardised approach between vega risk factors and delta risk factors. Vega risk charges and delta risk charges shall be aggregated by simple summation.

5.

The curvature risk correlations shall be the square of corresponding delta risk correlations \[\rho_{kl}\] and \[\gamma_{bc}\] referred to in Sub-section 1.

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