Prudential Regulation Authority Rulebook

9.1

A firm must implement systems to identify, evaluate and manage the risk arising from potential changes in interest rates that affect a firm’s non-trading activities including the risks of such changes impacting either or both of the following:

1. (1) the economic value of the firm's non-trading activities;
2. (2) the earnings in respect of the firm's non-trading activities.

[Note: Art 84 of the CRD]

9.1A

A firm must in addition implement systems to monitor and assess credit spread risk in respect of its non-trading activities.

9.1B

As an alternative to implementing internal systems under 9.1(1), and only where appropriate to its nature, size and complexity as well as business activities and overall risk profile, a firm may elect to implement the standardised framework set out in 9.13 to 9.43 to identify, evaluate and manage the risk arising from potential changes in interest rates that affect the economic value of the firm’s non-trading activities.

9.1C

A firm shall notify the PRA prior to any implementation of the standardised framework pursuant to 9.1B or, if it elects to cease implementing the standardised framework, prior to doing so.

9.2

9.3

9.4

[Deleted.]

9.4A

A firm must regularly carry out an evaluation in respect of the interest rate shock scenarios in 9.7 and immediately notify the PRA if any evaluation under this rule indicates that, as a result of the application of the interest rate scenarios in 9.7, the EVE would decline by more than 15% of the sum of its common equity tier one capital and its additional tier one capital.

9.5

A firm must carry out the evaluation under 9.2 as frequently as necessary for it to be reasonably satisfied that it has at all times a sufficient understanding of the degree to which it is exposed to the risks referred to in 9.2 and the nature of that exposure. In any case it must carry out those evaluations no less frequently than once a year.

[Note: Art 98(5) of the CRD]

9.6

A firm’s management body must oversee and approve the firm’s risk appetite and risk management framework for managing interest rate risk from non-trading book activities.

9.7

For the purposes of the evaluation in 9.4A, a firm must apply the following prescribed interest rate scenarios to all material currencies as determined in 9.8:

scenario 0: current interest rates;

scenario 1: parallel shock up;

scenario 2: parallel shock down;

scenario 3: steepener shock (short rates down and long rates up);

scenario 4: flattener shock (short rates up and long rates down);

scenario 5: short rates shock up; and

scenario 6: short rates shock down.

9.8

For the purposes of 9.7 and 9.15, a firm shall determine which currencies are material currencies using the following tests:

1. (1) each currency that has non-trading book assets in that currency more than 5% of total non-trading book assets shall be a material currency;
2. (2) where the sum of non-trading book assets in material currencies as identified under (1) does not exceed 90% of total non-trading book assets, a firm must select additional currencies to be deemed material currencies such that the sum of non-trading book assets in material currencies as identified under (1) and (2) is at least 90% of total nontrading book assets;
3. (3) each currency that has non-trading book liabilities in that currency more than 5% of total non-trading book liabilities shall be a material currency; and
4. (4) where the sum of non-trading book liabilities in material currencies as identified under (3) does not exceed 90% of total non-trading book liabilities, a firm must select additional currencies to be deemed material currencies such that the sum of nontrading book liabilities in material currencies as identified under (3) and (4) is at least 90% of total non-trading book liabilities.

9.9

For the interest rate scenarios specified in 9.7, a firm shall determine the change to interest rates in accordance with the following formulae:

for scenario 0:	ΔRc(tk)	=	0
for scenario 1:	ΔRc(tk)	=	+
for scenario 2:	ΔRc(tk)	=	—
for scenario 3:	ΔRc(tk)	=	—0.65 . |ΔRshort,c(tk)| + 0.9 . |ΔRlong,c(tk)|
for scenario 4:	ΔRc(tk)	=	+0.8 . |ΔRshort,c(tk)| — 0.6 . |ΔRlong,c(tk)|
for scenario 5:	ΔRc(tk)	=	+ΔRshort,c(tk)
for scenario 6:	ΔRc(tk)	=	—ΔRshort,c(tk)

Where:

c = the index that denotes currency;

k = the index that denotes the buckets in accordance with Table 2 in 9.17 below;

t_k = the bucket midpoint of bucket k, measured in years;

ΔR_c(t_k) = the change in interest rate at the point t_k for currency c;

= the prescribed parallel interest rate shock for currency c determined in accordance with column two of Table 1 in 9.11;

ΔR_short,c(t_k) = the change in short interest rate at the point t_k for currency c determined in accordance with the formulae in 9.10; and

ΔR_long,c(t_k) = the change in long interest rate at the point t_k for currency c determined in accordance with the formulae in 9.10.

9.10

For the purposes of 9.9, a firm shall determine the value of ΔR_short(t_k) and ΔR_long(t_k) in accordance with the following formulae:

1. (1) for ΔR_short,c(t_k): ΔR_short,c(t_k) = +R_short,c_ ^. e
2. (2) for ΔR_long,c(t_k): ΔR_long,c(t_k) = +R_long,c ^. (1 – e )
3. Where:
1. c = the index that denotes currency;
2. k = the index that denotes the buckets in accordance with Table 2 in 9.17 below;
3. e = the mathematical constant that is the base of the natural logarithm;
4. x = 4;
5. t_k = the bucket midpoint of bucket k, measured in years;
6. ΔR_short,c(t_k) = the change in short interest rate at the point t_k for currency c;
7. ΔR_long,c(t_k) = the change in long interest rate at the point t_k for currency c;
8. = the prescribed short interest rate shock for currency c determined in accordance with column three of Table 1 in 9.11; and
9. = the prescribed long interest rate shock for currency c determined in accordance with column four of Table 1 in 9.11.

9.11

For the purposes of 9.9, the interest rate shock scenarios for individual currencies are those in Table 1 below:

Table 1. Specified size of interest rate shocks for each currency (bps)

9.12

For material positions in currencies not listed in 9.11, a firm must use appropriate shocks for the scenarios listed in 9.7.

9.13

Using the standardised framework, a firm shall carry out the evaluation in 9.1(1) by calculating the loss in EVE (EV E_loss) in accordance with the following formula:

Where:

i = the index that denotes the interest rate shock scenarios in accordance with 9.15;

c = the index that denotes the material currencies in accordance with 9.15; and

ΔEV E_i,c = the change in economic value in currency c for interest rate scenario i as calculated in accordance with 9.14.

9.14

For the purposes of 9.13, a firm must calculate the change in economic value in a given currency for a given interest rate scenario in accordance with the following formula:

ΔEV E_i,c = NA0_i,c + KA0_i,c

Where:

i = the index that denotes the interest rate shock scenarios in accordance with 9.15;

c = the index that denotes the material currencies in accordance with 9.15;

ΔEV E_i,c = the change in economic value in currency c for interest rate scenario i;

NA0_i,c = the non-automatic option risk in currency c for interest rate scenario i as calculated in accordance with 9.16; and

KA0_i,c = the automatic option risk in currency c for interest rate scenario i as calculated in accordance with 9.41.

9.15

For the purposes of 9.13 and 9.14, a firm must calculate the change in economic value in a given currency for a given interest rate scenario, ΔEV E_i,c, for every possible pair of:

1. (1) interest rate scenarios, i in 9.7; and
2. (2) each material currency, c as determined in 9.8.

9.16

For the purposes of 9.14, a firm must calculate the non-automatic option risk in currency c for interest rate scenario i (NA0_i,c) in accordance with the following formula:

Where:

i = the index that denotes the interest rate shock scenarios in accordance with 9.15;

c = the index that denotes the material currencies in accordance with 9.15;

k = the index that denotes the buckets in accordance with Table 2 in 9.17;

DF_i,c(t_k) (respectively DF_0,c(t_k)) = the discount factor for bucket k in currency c for interest rate scenario i (respectively for interest rate scenario 0), calculated in accordance with 9.18; and

CF_i,c(k) (respectively CF_0,c(k)) = the net repricing cash flow for bucket k in currency c for interest rate scenario i (respectively for interest rate scenario 0), calculated in accordance with 9.19 to 9.40.

9.17

For the calculation of discount factors and notional repricing cash flows in 9.18 and 9.19, a firm must project all notional repricing cashflows on to the following bucket intervals or bucket midpoints:

Table 2

9.18

1. (1) For the purposes of 9.16, a firm must calculate the discount factor for bucket k in currency c for interest rate scenario i (DF_i,c(t_k)) in accordance with the following formula:
2. 
1. Where:
2. i = the index that denotes the interest rate shock scenarios in accordance with 9.15;
3. c = the index that denotes the material currencies in accordance with 9.15;
4. k = the index that denotes the buckets in accordance with Table 2 in 9.17;
5. e = the mathematical constant that is the base of the natural logarithm;
6. t_k = the bucket midpoint of bucket k in accordance with Table 2 in 9.17; and
7. R_i,c(t_k)= subject to (2), the risk-free zero coupon rate at bucket midpoint t_k in currency c for interest rate scenario i, including any commercial margin and other spread components.
3. (2) A firm may elect to use the risk-free zero coupon rate R_i,c(t_k) excluding commercial margin and other spread components, provided the firm either (i) implements a prudent and transparent methodology for deducting commercial margins and other spread components from the initial repricing cash flows CF^α in 9.26 or (ii) determines that the effect of deducting commercial margins and other spread components is not material.

9.19

In accordance with 9.21, 9.22, 9.23 and 9.24, a firm must assign each interest rate risk position arising from non-trading activities to one of the following categories:

category 1: automatic interest rate options;
category 2: non-maturing deposits;
category 3: fixed rate loans with retail borrowers that are subject to prepayment risk;
category 4: term deposits by retail depositors subject to early redemption risk; and
category 5: other positions.

9.20

A firm must perform the allocation in 9.19 for all interest rate-sensitive non-trading book:

1. (1) assets, excluding assets that are:
1. (a) deducted from common equity tier one capital;
2. (b) fixed assets, including real estate and intangible assets; or
3. (c) equity exposures in the non-trading book;
2. (2) liabilities, including all non-remunerated deposits and excluding common equity tier one capital; and
3. (3) off-balance sheet items.

9.21

Under 9.19, term deposits that satisfy either of the following conditions may be treated as other positions in 9.19:

1. (1) the depositor has no legal right to withdraw the deposit; or
2. (2) an early withdrawal results in a significant penalty that at least compensates for the loss of interest between the date of withdrawal and the contractual maturity date and the economic cost of breaking the contract.

9.22

For the purposes of 9.19, and subject to 9.23, a firm must bifurcate any position with an embedded automatic interest rate option into two positions:

1. (1) a position excluding the embedded automatic interest rate option, which must be allocated to the other positions category in 9.19; and
2. (2) the embedded automatic interest rate option, which must be allocated to the category of automatic interest rate options in 9.19.

9.23

Where a firm is able to demonstrate that the embedded optionality is not material, the firm may choose not to perform the bifurcation in 9.22 and may directly allocate the position to the other positions category in 9.19.

9.24

For the purposes of 9.19, automatic interest rate options include:

1. (1) term deposits by wholesale depositors that do not meet the conditions in 9.21;
2. (2) wholesale fixed rate loans subject to prepayment risk; and
3. (3) mortgage loans with embedded caps and/or floors.

9.25

For each position allocated to the categories 2 to 5 in 9.19, a firm must determine a set of initial repricing cash flows, CF^α, per currency, in accordance with 9.26 and 9.27.

9.26

For each position, a firm must determine a set of initial repricing cash flows CF^α as:

1. (1) any repayment of principal;
2. (2) any repricing of principal; and
3. (3) any interest payment on a tranche of principal that has not yet been repaid or repriced.

9.27

A firm must determine the set of initial repricing cash flows CF^α for floating rate positions as:

1. (1) a series of coupon payments until the next repricing; and
2. (2) a par notional cash flow at the point of the next repricing.

9.28

In accordance with 9.32 to 9.40 for each material currency c identified in accordance with 9.15 and for interest rate scenario i, a firm must allocate each notional repricing cash flow CF_i,c to one of the buckets in Table 2 in 9.17 based on the repricing date, where repricing date means the date of each repayment, repricing or interest payment.

9.29

A firm may first choose to split an initial repricing cash flow determined in 9.25, CF^α , into two cash flows with tenors equal to the two bucket mid-point tenors in column 4 of Table 2 in 9.17 that are adjacent to the tenor of the initial repricing cash flow CF^α.

9.30

Where a firm chooses to apply the methodology in 9.29, that firm must:

1. (1) split each initial repricing cash flow determined in 9.25, CF^α such that:
1. (a) the sum of the resulting two cash flows is equal to the initial repricing cash flow, CF^α; and
2. (b) the weighted average maturity of the resulting two cash flows equals the initial repricing cash flows’ maturity; and
2. (2) document the methodology that the firm implements to split cash flows.

9.31

For 9.16, the net repricing cash flow for bucket k in currency c for interest rate scenario i, (CF_i,c(k)) shall be determined as the sum of CF_i,c as determined in 9.28 which:

1. (1) are derived from initial repricing cash flows CF^α that are allocated to currency c for interest rate scenario i in accordance with 9.28; and
2. (2) allocated to bucket k in accordance with Table 2 in 9.17.

9.32

For non-maturing deposits as determined in 9.19, a firm must allocate each position into one of the following categories:

1. (1) retail deposits defined as deposits placed with a firm by a natural person and where either regular transactions are carried out or the deposits are non-interest bearing;
2. (2) any other deposits with a firm by a natural person which are not covered in (1); or
3. (3) other deposits.

9.33

For the purposes of 9.32(1) deposits made by small businesses, legal entities, sole proprietorships or partnerships managed as retail exposures provided the total aggregated liabilities are less than £877,000 may also be treated as retail deposits.

9.34

For each category in 9.32, a firm must allocate each position to the following categories:

1. (1) the core portion, consisting of deposits that are found to remain undrawn with a high degree of likelihood using data history of an appropriate length, and unlikely to reprice even under significant changes in the interest rate environment; and
2. (2) the non-core portion, consisting of deposits not allocated to the core portion.

9.35

For non-maturing deposits as determined in 9.34, the notional repricing cash flows in currency c for each interest rate scenario i, CF_i,c, must be:

1. (1) for the core portion, the initial notional repricing cash flows in currency c for interest rate scenario i with the firm’s own estimates of tenors; and
2. (2) for the non-core portion, the initial notional repricing cash flows in currency c for interest rate scenario i with an overnight tenor.

9.36

For the allocation in 9.34 and the calculation of CF_i in 9.35, a firm must ensure that the proportion and average repricing date of core deposits is no greater than the caps in Table 3:

Table 3: Caps on core deposits

9.37

For fixed rate loans with borrowers that are subject to prepayment risk as determined in 9.19, a firm must:

1. (1) allocate each position to a single portfolio of homogeneous positions p denominated in a single currency c;
2. (2) for each portfolio of homogeneous positions, determine and notify the PRA a baseline monthly conditional prepayment rate () in currency c under the current term structure of interest rates;
3. (3) for each portfolio of homogeneous positions, determine the conditional prepayment rate in currency c for interest rate scenario i, (CPR_i,c) in accordance with the following formula:

1. where γ_i refers to the prescribed scalar multiplier for each interest rate shock scenarios given in Table 4 below.

Table 4

1. (4) for each portfolio of homogeneous positions, determine the notional repricing cash flows CF_i,c allocated to bucket 1 in accordance with Table 2 in 9.17, CF_i,c(1), in accordance with the following formula:

1. Where:
1. (1) = the initial repricing cash flows CF^α for interest rate scenario i with tenor that corresponds to bucket 1 in accordance with Table 2 in 9.17; and
2. Ni(0)= the notional currently outstanding before any repayments.

1. (5) for each portfolio of homogeneous positions, determine the notional repricing cash flows CF_i,c allocated to each bucket k in Table 2 where k > 1, CF_i,c(k), in accordance with the following recursive formula:

1. Where:
2. k = the index that denotes the buckets in accordance with Table 2 in 9.17;
3. W(k) = the width of bucket k measured in months and capped at 1200;
4. = the initial repricing cash flows CF^α in currency c for interest rate scenario i with tenor that corresponds to bucket k;
5. N(k – 1) = the notional outstanding after notional repricing cash flows in bucket k− 1 have transpired; and
6. = the sum of CF_i determined for preceding buckets 1 to k − 1 .

9.38

For the purpose of 9.37, firms may adjust the formulas in 9.37 (4) and (5) to reflect a base monthly conditional prepayment rate that varies over the life of each loan in the portfolio. In that case, it is denoted as for each time bucket k or time bucket midpoint tk in accordance with Table 2 in 9.17.

9.39

For term deposits by depositors subject to early redemption risk as determined in 9.19, a firm must:

1. (1) allocate each position to a single portfolio of homogeneous positions p denominated in each material currency c;
2. (2) for each portfolio of homogeneous positions, determine and notify the PRA a baseline term deposit redemption ratio in currency c under the current term structure of interest rates;
3. (3) for each portfolio of homogeneous loans, determine the conditional term deposit redemption ratio in currency c for interest rate scenario i, in accordance with the following formula:

1. where u_i refers to the prescribed scalar multiplier for each interest rate shock scenarios given in Table 5 below.

Table 5.

1. (4) for each portfolio of homogeneous positions, determine the notional repricing cash flows CF_i,c allocated to bucket 1 in Table 2 in 9.17, CF_i,c(1), in accordance with the following formula:
3. 
4. Where:
1. = the initial repricing cash flows in currency c for interest rate scenario i with tenor that corresponds to bucket 1 in accordance with Table 2 in 9.17; and
2. TD_c = the total term deposits subject to early redemption for currency c.
6. (5) for each portfolio of homogeneous positions, determine the notional repricing cash flows CF_i allocated to bucket k in Table 2 other than bucket CF_i(k), in accordance with the following formula:

1. Where:
1. k = the index that denotes the buckets in accordance with Table 2 in 9.17; and
2. = the initial repricing cash flows in currency c for interest rate scenario i with tenor that corresponds to bucket k.

9.40

For other positions as determined in 9.19, a firm must determine the notional repricing cash flows CF_i,c allocated to bucket k in Table 2 other than bucket 1, CF_i(k), in accordance with the following formula:

Where:

k = the index that denotes the buckets in accordance with Table 2 in 9.17; and

= the initial repricing cash flows in currency c for interest rate scenario i with tenor that corresponds to bucket k.

9.41

For 9.14, and subject to 9.42, a firm must determine the automatic option risk in currency c for interest rate scenario i (KA0_i,c) for all automatic interest rate options as determined in 9.19 and 9.22 in accordance with the following formula:

Where:

n_c = the index that denotes the number of all sold automatic options in currency c;

m_c = the index that denotes the number of all bought automatic options in currency c;

= the change in value of sold automatic option p for interest rate scenario i, calculated in accordance with 9.43; and

= the change in value of bought automatic option q for interest rate scenario i, calculated in accordance with 9.43.

9.42

A firm may choose to include in the calculation of only bought automatic options that are used for hedging sold automatic interest rate options, provided that the firm must add to KA0_i,c in 9.41 the value of bought automatic options that are not for hedging sold automatic interest rate options that is included in the firm’s own funds.

9.43

1. (1) For 9.41, a firm must calculate the change in value of sold automatic option p (respectively bought automatic option q) for interest rate scenario i other than interest rate scenario (respectively ), as the increase in value of the option to the option holder:
1. (a) from the value of the option for interest rate scenario 0; and
2. (b) to the value of the option for interest rate shock scenario i with a relative increase in implied volatility of 25%.
2. (2) For 9.41, a firm must set the change in value of sold automatic option p (respectively bought automatic option q) for interest rate scenario (respectively), as 0.
3. (3) A firm must notify the PRA of the methodology used to estimate the value of automatic options in (1).