Prudential Regulation Authority Rulebook

7.1

1. (1) A firm may use a simplified calculation for a specific sub-module or risk module where the nature, scale and complexity of the risks it faces justifies it.
2. (2) A firm must calibrate its simplified calculation in accordance with Solvency Capital Requirement – General Provisions 3.3 to 3.4.

[Note: Art. 109 of the Solvency II Directive]

7.2

1. (1) For the purposes of 7.1(1), a firm must determine whether the simplified calculation is proportionate to the nature, scale and complexity of the risks by carrying out an assessment which must include all of the following:
   1. (a) an assessment of the nature, scale and complexity of the risks of the firm covered in the relevant module or sub-module;
   2. (b) an evaluation in qualitative or quantitative terms, as appropriate, of the error introduced in the results of the simplified calculation due to any deviation between the following:
      1. (i) the assumptions underlying the simplified calculation in relation to the risk;
      2. (ii) the results of the assessment referred to in (a).
2. (2) Where the error referred to in 1(b) would lead to a misstatement of the SCR that could influence the decision-making or judgement of the user of the information relating to the SCR, the use of a simplified calculation by a firm will not be proportionate to the nature, scale and complexity of the risks that the firm faces and the firm must not use that simplified calculation, unless it produces an SCR which exceeds the SCR; that results from the standard calculation.

7.3

A firm that is a captive insurer or captive reinsurer may use the simplified calculations set out in 7.4, 7.23, 7.25 and 7.27, where 7.2 is complied with and all of the following requirements are met:

1. (1) in relation to the insurance obligations of the firm, all insured persons and beneficiaries are legal entities of the group of which the firm is part;
2. (2) in relation to the reinsurance obligations of the firm, all insured persons and beneficiaries of the contracts of insurance underlying the reinsurance obligations are legal entities of the group of which the firm is part; and
3. (3) the insurance obligations and the contracts of insurance underlying the reinsurance obligations of the firm do not relate to any compulsory third-party liability insurance.

7.4

1. (1) Subject to 7.2 and 7.3, a firm that is a captive insurer or captive reinsurer may calculate the capital requirement for non-life premium and reserve risk in accordance with the following formula:

$$SC{R}_{nlpremres}=\sqrt{0.65\cdot {\mathrm{\Sigma }}_{s}N{L}_{(pr,s)}^2+0.35\cdot {\left({\mathrm{\Sigma }}_{s}N{L}_{(pr,s)}\right)}^2}$$

where s covers all segments set out in 3A3.

1. (2) For the purposes of (1), a firm must calculate the capital requirement for non-life premium and reserve risk of a particular segment s set out in 3A3 in accordance with the following formula:

$${NL}_{pr,s}=0.6\cdot \sqrt{{V^2}_{(prem,s)}+V_{(prem,s)}\cdot V_{(res,s)}+{V^2}_{(res,s)}}$$

where:

1. (a) V_(prem,s) denotes the volume measure for premium risk of segment s calculated in accordance with 3A2.3; and
2. (b) V_(res,s) denotes the volume measure for reserve risk of a segment calculated in accordance with 3A2.6.

7.5

For the purposes of 3A6.1(1), subject to 7.2, a firm may determine the insurance policies for which discontinuance would result in an increase in technical provisions without the risk margin on the basis of groups of policies, provided that the grouping complies with the requirements set out in Technical Provisions – Further Requirements 20.1(2).

7.6

Subject to 7.2, a firm may calculate: 

1. (1) the sum insured for windstorm risk referred to in 3A9.6(2) and 3A9.8 on the basis of groups of risk zones provided that:
   1. (a) each of the risk zones within a group must be situated within the same particular region set out in Annex V; and
   2. (b) where the sum insured for windstorm risk referred to in 3A9.6(2) is calculated on the basis of a group of risk zones, the risk weight for windstorm risk referred to in 3A9.6(1) must be the risk weight for windstorm risk in the risk zone within that group with the highest risk weight for windstorm risk set out in Annex X;
2. (2) the sum insured for earthquake risk referred to 3A11.3(2) and 3A11.5 on the basis of groups of risk zones, provided that: 
   1. (a) each of the risk zones within a group must be situated within the same particular region set out in Annex VI; and 
   2. (b) where the sum insured for earthquake risk referred to in 3A11.3(2) is calculated on the basis of a group of risk zones, the risk weight for earthquake risk referred to in 3A11.3(1) must be the risk weight for earthquake risk in the risk zone within that group with the highest risk weight for earthquake risk as set out in Annex X; 
3. (3) the sum insured for flood risk referred to in 3A12.6(2) and 3A12.8 on the basis of groups of risk zones, provided that:
   1. (a) each of the risk zones within a group must be situated within the same particular region set out in Annex VII; and
   2. (b) where the sum insured for flood risk referred to in 3A12.6(2) is calculated on the basis of a group of risk zones, the risk weight for flood risk referred to in 3A12.6(1) must be the risk weight for flood risk in the risk zone within that group with the highest risk weight for flood risk as set out in Annex X;
4. (4) the sum insured for hail risk referred to in 3A13.6(2) and 3A13.8 on the basis of groups of risk zones, provided that: 
   1. (a) each of the risk zones within a group must be situated within the same particular region set out in Annex VIII; and
   2. (b) where the sum insured for hail risk referred to in 3A13.6(2) is calculated on the basis of a group of risk zones, the risk weight for hail risk referred to in 3A13.6(1) must be the risk weight for hail risk in the risk zone within that group with the highest risk weight for hail risk as set out in Annex X; and
5. (5) the weighted sum insured for subsidence risk referred to in 3A14.2 on the basis of groups of risk zones, provided that where the weighted sum insured referred to in 3A14.2 is calculated on the basis of a group of risk zones, the risk weight for subsidence risk referred to in 3A14.2(1) must be the risk weight for subsidence risk in the risk zone within that group with the highest risk weight for subsidence risk as set out in Annex X.

7.7

1. (1) Subject to 7.2, a firm may calculate the capital requirement for fire risk referred to in 3A21.1 in accordance with the following formula:

$$SC{R}_{fire}=\text{max}(SC{R}_{firei};SC{R}_{firec};SC{R}_{firer})$$

where:

1. (a) SCR _firei denotes the largest industrial fire risk concentration;
2. (b) SCR _firec denotes the largest commercial fire risk concentration; and
3. (c) SCR _firer denotes the largest residential fire risk concentration.

1. (2) A firm must calculate its largest industrial fire risk concentration in accordance with the following formula:

$$SC{R}_{firei}=\text{max}(E_{1,i};E_{2,i};E_{3,i};E_{4,i};E_{5,i})$$

where E _k,I denotes the total exposure within the perimeter of the k-th largest industrial fire risk exposure.

1. (3) A firm must calculate its largest commercial fire risk concentration in accordance with the following formula:

$${\mathrm{S}\mathrm{C}\mathrm{R}}_{firec}=\text{max}(E_{1,c};E_{2,c};E_{3,c};E_{4,c};E_{5,c})$$

where E _k,c denotes the total exposure within the perimeter of the k-th largest commercial fire risk exposure.

1. (4) A firm must calculate its largest residential fire risk concentration in accordance with the following formula:

$${\mathrm{S}\mathrm{C}\mathrm{R}}_{firer}=max(E_{1,r};E_{2,r};E_{3,r};E_{4,r};E_{5,r};\theta )$$

where:

1. (a) E _k,r  denotes the total exposure within the perimeter of the k-th largest residential fire risk exposure; and
2. (b) θ denotes the market share based residential fire risk exposure.

1. (5) For the purposes of (2), (3) and (4), the total exposure within the perimeter of the k-th largest industrial, commercial or residential fire risk exposure of a firm is the sum insured by the firm with respect to a set of buildings that meets all of the following requirements:
   1. (a) in relation to each building, the firm has obligations in lines of business 7 and 19 which cover damage due to fire or explosion, including as a result of terrorist attacks; and
   2. (b) each building is partly or fully located within a radius of 200 metres around the industrial, commercial or residential building with the k-th highest sum insured after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles.
   3. For the purposes of determining the sum insured with respect to a building, a firm must take into account all reinsurance contracts and special purpose vehicles that would pay out in case of insurance claims related to that building, other than reinsurance contracts and special purpose vehicles that are subject to conditions not related to that building, which must not be taken into account.
2. (6) A firm must calculate the market share based residential fire risk exposure in accordance with the following formula:

$$\theta ={SI}_{av}\cdot 500\cdot max(0.05;{max}_c({MarketShare}_c))$$

where:

1. (a) SI_av is the average sum insured by the firm with respect to residential property;
2. (b) c denotes all countries where the firm has obligations in lines of business 7 and 19 covering residential property; and
3. (c) MarketShare_c  is the market share of the firm in country c related to obligations in those lines of business covering residential property.

7.8

Subject to 7.2, a firm may calculate the capital requirement for life mortality risk in accordance with the following formula:

$${SCR}_{mortality}=0.15\cdot q\cdot \sum {}_{k=1}^n{CAR}_k\cdot \frac{{(1-q)}^{k-1}}{{(1+i_k)}^{k-0.5}}$$

where, with respect to insurance and reinsurance policies with a positive capital at risk:

1. (a) CAR_k denotes the total capital at risk in year k, meaning the sum over all contracts of insurance of the higher of zero and the difference, in relation to each contracts of insurance between the following amounts:
   1. (i) the sum of:
      1. A. the amount that the firm would pay in year k in the event of the death of the persons insured under the contracts of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
      2. B. the expected present value of amounts not covered in A. that the firm would pay after year k in the event of the immediate death of the persons insured under the contracts of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
   2. (ii) the best estimate of the corresponding insurance and reinsurance obligations in year k after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles;
2. (b) q denotes the expected average mortality rate over all the insured persons and over all future years weighted by the sum insured;
3. (c) n denotes the modified duration in years of payments payable on death included in the best estimate; and
4. (d) i_k denotes the annualised spot rate for maturity k of the relevant risk-free interest rate term structure.

7.9

Subject to 7.2, a firm may calculate the capital requirement for life longevity risk in accordance with the following formula:

$${SCR}_{longevity}=0.2\cdot q\cdot n\cdot {1.1}^{(n-1)/2}\cdot {BE}_{long}$$

where, with respect to the policies referred to in 3B2.2:

1. (a) q denotes the expected average mortality rate of the insured persons during the following 12 months weighted by the sum insured;
2. (b) n denotes the modified duration in years of the payments to beneficiaries included in the best estimate; and
3. (c) BE_long denotes the best estimate of the insurance and reinsurance obligations subject to longevity risk.

7.10

Subject to 7.2, a firm may calculate the capital requirement for life disability-morbidity risk in accordance with the following formula:

$${SCR}_{disability-morbidity}=0.35\cdot {CAR}_1\cdot d_1+0.25\cdot {1.1}^{(n-3)/2}\cdot (n-1)\cdot {CAR}_2\cdot d_2+0.2\cdot {1.1}^{(n-1)/2}\cdot t\cdot n\cdot {BE}_{dis}$$

where, with respect to insurance and reinsurance policies with a positive capital at risk:

1. (a) CAR₁ denotes the total capital at risk, meaning the sum over all contracts of insurance of the higher of zero and the difference between the following amounts:
   1. (i) the sum of:
      1. A. the amount that the firm would currently pay in the event of the death or disability of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
      2. B. the expected present value of amounts not covered in A. that the firm would pay in the future in the event of the immediate death or disability of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
   2. (ii) the best estimate of the corresponding insurance and reinsurance obligations after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles;
2. (b) CAR₂ denotes the total capital at risk as defined in (a) after 12 months;
3. (c) d₁ denotes the expected average disability-morbidity rate during the following 12 months weighted by the sum insured;
4. (d) d₂ denotes the expected average disability-morbidity rate in the 12 months after the following 12 months weighted by the sum insured;
5. (e) n denotes the modified duration of the payments on disability-morbidity included in the best estimate;
6. (f) t denotes the expected termination rates during the following 12 months; and
7. (g) BE_dis denotes the best estimate of insurance and reinsurance obligations subject to disability-morbidity risk.

7.11

Subject to 7.2, a firm may calculate the capital requirement for life expense risk in accordance with the following formula:

$${\mathrm{S}\mathrm{C}\mathrm{R}}_{expenses}=0.1\cdot EI\cdot n+EI\cdot (\left(\frac{1}{i+0.01}\right)\cdot ((1+i+{0.01)}^n-1)-\frac{1}{i}{((1+i)}^{\mathcal{n}}-1))$$

where:

1. (a) EI denotes the amount of expenses incurred in servicing long-term insurance or reinsurance obligations other than health insurance obligations and health reinsurance obligations during the last year;
2. (b) n denotes the modified duration in years of the cash-flows included in the best estimate of those obligations; and
3. (c) i denotes the weighted average inflation rate included in the calculation of the best estimate of those obligations, where the weights are based on the present value of expenses included in the calculation of the best estimate for servicing existing long-term insurance and reinsurance obligations.

7.12

1. (1) Subject to 7.2, a firm may calculate the capital requirement for the risk of a permanent increase in lapse rates in accordance with the following formula:

$${\mathrm{L}\mathrm{a}\mathrm{p}\mathrm{s}\mathrm{e}}_{up}=0.5\cdot l_{up}\cdot n_{up}\cdot S_{up}$$

where:

1. (a) l_up denotes the higher of the average lapse rate of the policies with positive surrender strains and 67%;
2. (b) n_up denotes the average period in years over which the policies with positive surrender strains run off; and
3. (c) S_up denotes the sum of positive surrender strains referred to in (3).

1. (2) Subject to 7.2, a firm may calculate the capital requirement for the risk of a permanent decrease in lapse rates in accordance with the following formula:

$${\mathrm{L}\mathrm{a}\mathrm{p}\mathrm{s}\mathrm{e}}_{down}=0.5\cdot l_{down}\cdot n_{down}\cdot S_{down}$$

where:

1. (a) l_down denotes the higher of the average lapse rate of the policies with negative surrender strains and 40%;
2. (b) n_down denotes the average period in years over which the policies with negative surrender strains run off; and
3. (c) S_down denotes the sum of negative surrender strains referred to in (3).

1. (3) The surrender strain of an insurance policy is the difference between the following:
   1. (a) the amount currently payable by the firm on discontinuance by the policyholder, net of any amounts recoverable from policyholders or intermediaries; and
   2. (b) the amount of technical provisions without the risk margin.

7.13

Subject to 7.2, a firm may calculate each of the following capital requirements on the basis of groups of policies, provided that the grouping complies with the requirements set out in Technical Provisions – Further Requirements 20.1(2):

1. (1) the capital requirement for the risk of a permanent increase in lapse rates referred to in 3B6.2;
2. (2) the capital requirement for the risk of a permanent decrease in lapse rates referred to in 3B6.3; and
3. (3) the capital requirement for mass lapse risk referred to in 3B6.6.

7.14

Subject to 7.2, a firm may calculate the capital requirement for life-catastrophe risk in accordance with the following formula:

$${\mathrm{S}\mathrm{C}\mathrm{R}}_{life-catastrophe}=\sum _{i}0.0015\cdot {\mathrm{C}\mathrm{A}\mathrm{R}}_i$$

1. where:
2. (a) the sum includes all policies with a positive capital at risk; and
3. (b) CAR_i denotes the capital at risk of the policy i, meaning the higher of zero and the difference between the following amounts:
   1. (i) the sum of:
      1. A. the amount that the firm would currently pay in the event of the death of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
      2. B. the expected present value of amounts not covered in A. that the firm would pay in the future in the event of the immediate death of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
   2. (ii) the best estimate of the corresponding insurance and reinsurance obligations after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles.

7.15

For the purposes of 3C7.1(1), subject to 7.2, a firm may determine the insurance policies for which discontinuance would result in an increase in technical provisions without the risk margin on the basis of groups of policies, provided that the grouping complies with the requirements set out in Technical Provisions – Further Requirements 20.1(2).

7.16

Subject to 7.2, a firm may calculate the capital requirement for health mortality risk in accordance with the following formula:

$${SCR}_{health-mortality}=0.15\cdot q\cdot \sum {}_{k=1}^n{CAR}_k\cdot \frac{{(1-q)}^{k-1}}{{\left({1+i}_k\right)}^{k-0.5}}$$

where, with respect to insurance and reinsurance policies with a positive capital at risk:

1. (a) CAR _k denotes the total capital at risk in year k, meaning the sum over all contracts of insurance of the higher of zero and the difference, in relation to each contract of insurance, between the following amounts:
   1. (i) the sum of:
      1. A. the amount that the firm would pay in year k in the event of the death of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
      2. B. the expected present value of amounts not covered in A. that the firm would pay after year k in the event of the immediate death of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
   2. (ii) the best estimate of the corresponding insurance and reinsurance obligations in year k after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles;
2. (b) q denotes the expected average mortality rate over all insured persons and over all future years weighted by the sum insured;
3. (c) n denotes the modified duration in years of payments payable on death included in the best estimate; and
4. (d) i_k denotes the annualised spot rate for maturity k of the relevant risk-free interest rate term structure.

7.17

Subject to 7.2, a firm may calculate the capital requirement for health longevity risk in accordance with the following formula:

$${\mathrm{S}\mathrm{C}\mathrm{R}}_{health-longevity}=0.2\cdot q\cdot n\cdot {1.1}^{(n-1)/2}\cdot {\mathrm{B}\mathrm{E}}_{long}$$

where, with respect to the policies referred to in 3C10.2:

1. (a) q denotes the expected average mortality rate of the insured persons during the following 12 months weighted by the sum insured;
2. (b) n denotes the modified duration in years of the payments to beneficiaries included in the best estimate; and
3. (c) BE_long denotes the best estimate of the obligations subject to health longevity risk .
   

7.18

Subject to 7.2, a firm may calculate the capital requirement for medical expense disability-morbidity risk in accordance with the following formula:

$${\mathrm{S}\mathrm{C}\mathrm{R}}_{medicalexpense}=0.05\cdot MP\cdot n+MP\cdot (\left(\frac{1}{i+0.01}\right)({(1+i+0.01)}^n-1)-\frac{1}{i}({(1+i)}^n-1))$$

where:

1. (a) MP denotes the amount of medical payments on medical expense insurance obligations or medical expense reinsurance obligations during the last year;
2. (b) n denotes the modified duration in years of the cash-flows included in the best estimate of those obligations; and
3. (c) i denotes the average rate of inflation on medical payments included in the calculation of the best estimate of those obligations, where the weights are based on the present
4.      value of medical payments included in the calculation of the best estimate of those obligations.

7.19

Subject to 7.2, a firm may calculate the capital requirement for income protection disability-morbidity risk in accordance with the following formula:

$${SCR}_{income-protection-disability-morbidity}=0.35\cdot {CAR}_1\cdot d_1+0.25\cdot {1.1}^{(n-3)/2}\cdot (n-1)\cdot {CAR}_2\cdot d_2+0.2\cdot {1.1}^{(n-1)/2}\cdot t\cdot n\cdot {BE}_{dis}$$

where, with respect to insurance and reinsurance policies with a positive capital at risk:

1. (a) CAR₁ denotes the total capital at risk, meaning the sum over all contracts of insurance of the higher of zero and the difference between the following amounts:
   1. (i) the sum of:
      1. A. the amount that the firm would currently pay in the event of the death or disability of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles; and
      2. B. the expected present value of amounts not covered in A. that the firm would pay in the future in the event of the immediate death or disability of the persons insured under the contract of insurance after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles;
   2. (ii) the best estimate of the corresponding insurance and reinsurance obligations after deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles;
2. (b) CAR₂ denotes the total capital at risk as defined in (a) after 12 months;
3. (c) d₁ denotes the expected average disability-morbidity rate during the following 12 months weighted by the sum insured;
4. (d) d₂ denotes the expected average disability-morbidity rate in the 12 months after the following 12 months weighted by the sum insured;
5. (e) n denotes the modified duration of the payments on disability-morbidity included in the best estimate;
6. (f) t denotes the expected termination rates during the following 12 months; and
7. (g) BE_dis denotes the best estimate of obligations subject to disability-morbidity risk.

7.20

Subject to 7.2, a firm may calculate the capital requirement for health expense risk in accordance with the following formula:

$${SCR}_{health-expense}=0.1\cdot EI\cdot n+EI\cdot (\left(\frac{1}{i+0.01}\right)\cdot ({(1+i+0.01)}^n-1)-\frac{1}{i}({(1+i)}^n-1))$$

where:

1. (a) EI denotes the amount of expenses incurred in servicing health insurance obligations and health reinsurance obligations during the last year;
2. (b) n denotes the modified duration in years of the cash-flows included in the best estimate of those obligations; and
3. (c) i denotes the weighted average inflation rate included in the calculation of the best estimate of those obligations, weighted by the present value of expenses included in the calculation of the best estimate for servicing existing health insurance obligations and health reinsurance obligations.

7.21

1. (1) Subject to 7.2, a firm may calculate the capital requirement for the risk of a permanent increase in lapse rates referred to in 3C16.1(1) in accordance with the following formula:

$${Lapse}_{up}=0.5\cdot l_{up}\cdot n_{up}\cdot S_{up}$$

1. where:
   1. (a) l_up denotes the higher of the average lapse rate of the policies with positive surrender strains and 83%;
   2. (b) n_up denotes the average period in years over which the policies with positive surrender strains run off; and
   3. (c) Su_p denotes the sum of positive surrender strains referred to in (3).
2. (2) Subject to 7.2, a firm may calculate the capital requirement for the risk of a permanent decrease in lapse rates referred to in 3C16.1(2) in accordance with the following formula:

$${Lapse}_{down}=0.5\cdot l_{down}\cdot n_{down}\cdot S_{down}$$

1. where:
   1. (a) l_down denotes the average lapse rate of the policies with negative surrender strains;
   2. (b) n_down denotes the average period in years over which the policies with negative surrender strains run off; and
   3. (c) S_down denotes the sum of negative surrender strains referred to in (3).
2. (3) The surrender strain of an insurance policy is the difference between the following:
   1. (a) the amount currently payable by the firm on discontinuance by the policyholder, net of any amounts recoverable from policyholders or intermediaries; and
   2. (b) the amount of technical provisions without the risk margin.

7.22

Subject to 7.2, a firm may calculate each of the following capital requirements on the basis of groups of policies, provided that the grouping complies with the requirements set out in Technical Provisions – Further Requirements 20.1(2):

1. (1) the capital requirement for the risk of a permanent increase in SLT health lapse rates referred to in 3C16.2;
2. (2) the capital requirement for the risk of a permanent decrease in SLT health lapse rates referred to in 3C16.3; and
3. (3) the capital requirement for SLT health mass lapse risk referred to in 3C16.6.

7.23

1. (1) Subject to 7.2 and 7.3, a firm that is a captive insurer or captive reinsurer may calculate the capital requirement for interest-rate risk referred to in 3D4 as follows:
   1. (a) the sum, for each currency, of the capital requirements for the risk of an increase in the term structure of interest rates as set out in (2); and
   2. (b) the sum, for each currency, of the capital requirements for the risk of a decrease in the term structure of interest rates as set out in (3).
2. (2) For the purposes of (1)(a), a firm must calculate the capital requirement for the risk of an increase in the term structure of interest rates for a given currency in accordance with the following formula:

$${IR}_{up}=\sum _i{MVAL}_i\cdot {dur}_i\cdot {rate}_i\cdot {stress}_{(i,up)}-\sum _{lob}{BE}_{lob}\cdot {dur}_{lob}\cdot {rate}_{lob}\cdot {stress}_{(lob,up)}$$

where:

1. (a) the first sum covers all maturity intervals i set out in (4);
2. (b) MVAL_i denotes the value in accordance with Valuation 2.1 to 2.2 of assets less liabilities other than technical provisions for maturity interval i;
3. (c) dur_i denotes the simplified duration of maturity interval i;
4. (d) rate_i denotes the relevant risk-free rate for the simplified duration of maturity interval i;
5. (e) stress_(i,up) denotes the relative upward stress of the interest rate for simplified duration of maturity interval i;
6. (f) the second sum covers all lines of business;
7. (g) BE_lob denotes the best estimate for line of business lob;
8. (h) dur_lob denotes the modified duration of the best estimate in line of business lob;
9. (i) rate_lob denotes the relevant risk-free rate for modified duration in line of business lob; and
10. (j) stress_(lob,up) denotes the relative upward stress of the interest rate for the modified duration dur_lob.

1. (3) For the purposes of (1)(b), a firm must calculate the capital requirement for the risk of a decrease in the term structure of interest rates for a given currency in accordance with the following formula:

$${IR}_{down}=\sum _i{MVAL}_i\cdot {dur}_i\cdot {rate}_i\cdot {stress}_{(i,down)}-\sum _{lob}{BE}_{lob}\cdot {dur}_{lob}\cdot {rate}_{lob}\cdot {stress}_{(lob,down)}$$

where:

1. (a) the first sum covers all maturity intervals i set out in (4);
2. (b) MVALi denotes the value in accordance with Valuation 2.1 to 2.2 of assets less liabilities other than technical provisions for maturity interval i;
3. (c) dur_i denotes the simplified duration of maturity interval i;
4. (d) rate_i denotes the relevant risk-free rate for the simplified duration of maturity interval i;
5. (e) stress(i,down) denotes the relative downward stress of the interest rate for simplified duration of maturity interval i;
6. (f) the second sum covers all lines of business;
7. (g) BE_lob denotes the best estimate for line of business lob;
8. (h) dur_lob denotes the modified duration of the best estimate in line of business lob;
9. (i) rate_lob denotes the relevant risk-free rate for modified duration in line of business lob; and(j) stress(_{lob, down)} denotes the relative downward stress of the interest rate for modified duration durlob.

1. (4) The maturity intervals i and the simplified duration duri referred to in (2)(a), 2(c), (3)(a) and 3(c) must be as follows:
   1. (a) up to the maturity of one year, the simplified duration must be 0.5 years;
   2. (b) between maturities of one and three years, the simplified duration must be two years;
   3. (c) between maturities of three and five years, the simplified duration must be four years;
   4. (d) between maturities of five and 10 years, the simplified duration must be seven years; and
   5. (e) from the maturity of 10 years onwards, the simplified duration must be 12 years.

7.24

1. (1) Subject to 7.2, a firm may calculate the capital requirement for spread risk referred to in 3D17 in accordance with the following formula:

$${SCR}_{bonds}={MV}^{bonds}\cdot (\sum _i{\mathrm{\%}MV}_i^{bonds}\cdot {stress}_i+{\mathrm{\%}MV}_{norating}^{bonds}\cdot min[{dur}_{norating}\cdot 0.03;1])+∆Lia{b}_{ul}$$

where:

1. (a) SCR_bonds denotes the capital requirement for spread risk on bonds and loans;
2. (b) MV^bonds denotes the value in accordance with Valuation 2.1 to 2.2 of the assets subject to capital requirements for spread risk on bonds and loans;
3. (c) %MV_i ^bonds denotes the proportion of the portfolio of the assets subject to a capital requirement for spread risk on bonds and loans with credit quality step i, where a credit assessment by a nominated external credit assessment institution is available for those assets;
4. (d) %MV^bonds _norating denotes the proportion of the portfolio of the assets subject to a capital requirement for spread risk on bonds and loans for which no credit assessment by a nominated external credit assessment institution is available;
5. (e) dur_i and dur_norating denote the modified duration denominated in years of the assets subject to a capital requirement for spread risk on bonds and loans where no credit assessment by a nominated external credit assessment institution is available;
6. (f) stress_i denotes a function of the credit quality step i and of the modified duration denominated in years of the assets subject to a capital requirement for spread risk on bonds and loans with credit quality step i, set out in (2); and
7. (g) ΔLiab_ul denotes the increase in the technical provisions without risk margin for policies where the policyholders bear the investment risk with embedded options and guarantees that would result from an instantaneous decrease in the value of the assets subject to the capital requirement for spread risk on bonds of:

$${MV}^{bonds}\cdot (\sum _i{\mathrm{\%}MV}_i^{bonds}\cdot {stress}_i+{\mathrm{\%}MV}_{norating}^{bonds}\cdot min[{dur}_{norating}\cdot 0.03;1])$$

1. (2) stress_i referred to in (1)(f), for each credit quality step i, must be equal to: dur_i ∙ b_i where dur_i is the modified duration denominated in years of the assets subject to a capital requirement for spread risk on bonds and loans with credit quality step i, and b_i is determined in accordance with the following table:

Credit quality step i	0	1	2	3	4	5	6
bi	0.9%	1.1%	1.4%	2.5%	4.5%	7.5%	7.5%

1. (3) dur_norating referred to in (1)(e) and dur_i referred to in (2) must not be lower than one year.

7.25

Subject to 7.2 and 7.3, a firm that is a captive insurer or captive reinsurer may base the calculation of the capital requirement for spread risk referred to in 3D17 on the assumption that all assets are assigned to credit quality step 3.

7.26

Subject to 7.2, a firm may assign a bond other than those to be included in the calculations under paragraphs 3D24.2 to 3D24.21 a risk factor stress_i equivalent to that for credit quality step 3 for the purposes of 3D17.3 and assign the bond to credit quality step 3 for the purpose of calculating the weighted average credit quality step in accordance with 3D26.4, provided that all of the following requirements are met:

1. (1) credit assessments from a nominated external credit assessment institution are available for at least 80% of the total value of the bonds other than those to be included in the calculations under 3D24.2 to 3D24.21;
2. (2) a credit assessment by a nominated external credit assessment institution is not available for the bond in question;
3. (3) the bond in question provides a fixed redemption payment on or before the date of maturity, in addition to regular fixed or floating rate interest payments;
4. (4) the bond in question is not a structured note or collateralised security as referred to in the CIC table set out in the Section IR.06.02 instructions referred to in Reporting 10; and
5. (5) the bond in question does not cover liabilities that provide long-term insurance obligations with profit participation, nor does it cover unit-linked liabilities or index-linked liabilities, nor liabilities where a matching adjustment is applied.

7.27

Subject to 7.2 and 7.3, a firm that is a captive insurer or captive reinsurer may use all of the following assumptions for the calculation of the capital requirement for concentration risk:

1. (1) Intra-group asset pooling arrangements of the firm may be exempted from the calculation base referred to in 3D28.2 to the extent that there exist legally enforceable contractual terms which ensure that the liabilities of the firm will be offset by the intra-group exposures it holds against other entities of the group.
2. (2) The relative excess exposure threshold referred to in 3D28.1(c) must be equal to 15% for the following single name exposures:
   1. (a) exposures to credit institutions that do not belong to the same group and that have been assigned to the credit quality step 2; and
   2. (b) exposures to entities of the group that manage the cash of the firm that have been assigned to the credit quality step 2.

7.28

1. (1) Subject to 7.2 and where the best estimate of amounts recoverable from a reinsurance arrangement or securitisation and the corresponding debtors is not negative, a firm may calculate the risk-mitigating effect on underwriting risk of that reinsurance arrangement or securitisation referred to in 3E9 in accordance with the following formula:

$${RM}_{re,all}\cdot \frac{{Recoverables}_i}{{Recoverables}_{all}}$$

where:

1. (a) RM_re,all denotes the risk-mitigating effect on underwriting risk of the reinsurance arrangements and securitisations for all counterparties calculated in accordance with (2); and
2. (b) Recoverables_i denotes the best estimate of amounts recoverable from the reinsurance arrangement or securitisation and the corresponding debtors for counterparty i and Recoverables_all denotes the best estimate of amounts recoverable from the reinsurance arrangements and securitisations and the corresponding debtors for all counterparties.

1. (2) A firm may calculate the risk-mitigating effect on underwriting risk of the reinsurance arrangements and securitisations for all counterparties referred to in (1) as the difference between the following capital requirements:
   1. (a) the hypothetical capital requirement for underwriting risk of the firm if none of the reinsurance arrangements and securitisations exist; and
   2. (b) the capital requirement for underwriting risk of the firm.

7.29

Subject to 7.2 and where the best estimate of amounts recoverable from a proportional reinsurance arrangement and the corresponding debtors for a counterparty i is not negative, a firm may calculate the risk-mitigating effect on underwriting risk j of the proportional reinsurance arrangement for counterparty i referred to 3E9 in accordance with the following formula:

$$\frac{{Recoverables}_i}{{BE-Recoverables}_{all}}\cdot {SCR}_j$$

where:

1. (1) BE denotes the best estimate of obligations gross of the amounts recoverable;
2. (2) Recoverables_i denotes the best estimate of amounts recoverable from the proportional reinsurance arrangement and the corresponding debtors for counterparty i;
3. (3) Recoverablesa_ll denotes the best estimate of amounts recoverable from the proportional reinsurance arrangements and the corresponding debtors for all counterparties; and
4. (4) SCR_j denotes the capital requirement for underwriting risk j of the firm.

7.30

Subject to 7.2, a firm may use the following simplified calculations for the purposes of 3E6, 3E7 and 3E8:

1. (1) The best estimate referred to in 3E7.1(d) may be calculated in accordance with the following formula:

$${BE}_C=\frac{P_C}{P_U}\cdot {BE}_U$$

where:

1. (a) BE_U denotes the best estimate of the liability ceded to the pooling arrangement by the firm, net of any amounts reinsured with counterparties external to the pooling arrangement;
2. (b) P_C denotes the counterparty member’s share of the risk according to the terms of the pooling arrangement; and
3. (c) P_U denotes the firm’s share of the risk according to the terms of the pooling arrangement.

1. (2) The best estimate referred to in 3E8.1(c) may be calculated in accordance with the following formula:

$${BE}_{CE}=\frac{1}{P_U}\cdot {BE}_{CEP}$$

where:

1. (a) BE_CEP denotes the best estimate of the liability ceded to the external counterparty by the pooling arrangement, in relation to risk ceded to the pooling arrangement by the firm; and
2. (b) P_U denotes the firm’s share of the risk according to the terms of the pooling arrangement.
3. (3) A firm may calculate the risk-mitigating effect referred to in 3E8.1(d) in accordance with the following formula:

$$\mathrm{\Delta }R{M}_{CE}=\frac{B{E}_{CE}}{{\mathrm{\Sigma }}_{CE}B{E}_{CE}}\cdot \mathrm{\Delta }R{M}_{CEP}$$

where:

1. (a) BE_CE denotes the best estimate of the liability ceded to the external counterparty by the pooling arrangement as a whole; and
2. (b) ΔRM_CEP denotes the contribution of all external counterparties to the risk-mitigating effect of the pooling arrangement on the underwriting risk of the firm.

1. (4) The counterparty pool members and the counterparties external to the pooling arrangement may be grouped according to the credit assessment by a nominated external credit assessment institution, provided there are separate groupings for pool exposure of type A, pool exposure of type B and pool exposure of type C.

7.31

Subject to 7.2, a firm may calculate the loss-given-default set out in 3E4, including the risk-mitigating effect on underwriting risk and market risk and the risk-adjusted value of collateral provided by way of a collateral arrangement, for a group of single name exposures provided that the group of single name exposures are assigned the highest probability of default assigned to single name exposures included in the group in accordance with 3E12.

7.32

Subject to 7.2, a firm may calculate the risk-mitigating effect on underwriting risk and market risk of a reinsurance arrangement, securitisation or derivative referred to in 3E9 as the difference between the following capital requirements:

1. (1) the sum of the hypothetical capital requirement for the sub-modules of the underwriting risk and market risk modules of the firm, calculated in accordance with this Part but as if the reinsurance arrangement, securitisation or derivative did not exist; and
2. (2) the sum of the capital requirements for the sub-modules of the underwriting risk and market risk  modules of the firm.

7.33

For the purposes of 3E9, subject to 7.2 and where the reinsurance arrangement, securitisation or derivative covers obligations from only one of the segments (segment s) set out in 3A3 or, as applicable, 3C4, a firm may calculate the risk-mitigating effect of that reinsurance arrangement, securitisation or derivative on its underwriting risk in accordance with the following formula:

$$\sqrt{{({SCR}_{CAT}^{hyp}-{SCR}_{CAT}^{without})}^2+{(3\cdot {\sigma }_s\cdot (P_s^{hyp}-P_s^{without}+Recoverables))}^2+1.5\cdot {\sigma }_s\cdot (P_s^{hyp}-P_s^{without}+Recoverables)\cdot ({SCR}_{CAT}^{hyp}-{SCR}_{CAT}^{without})}$$

1. where:
2. (1) SCR_CAT^hyp denotes the hypothetical capital requirement for the non-life catastrophe risk sub-module referred to in 3A7.2 or, as applicable, the hypothetical capital requirement for the health catastrophe risk sub-module referred to in 3C17, that would apply if the reinsurance arrangement, securitisation or derivative did not exist;
3. (2) SCRCAT^without denotes the capital requirement for the non-life catastrophe risk sub-module referred to in 3A7.2 or, as applicable, the capital requirement for the health catastrophe risk sub-module referred to in 3C17;
4. (3) σ_s denotes the standard deviation for non-life premium risk of segment s determined in accordance with 3A4.3 and 3A4.4 or, as applicable, the standard deviation for the NSLT health premium risk of segment s determined in accordance with 3C5.3;
5. (4) Ps^hyp denotes the hypothetical volume measure for premium risk of segment s determined in accordance with 3A2.3 or 3A2.4 or, as applicable, 3C3.3 or 3C3.4 that would apply if the reinsurance arrangement, securitisation or derivative did not exist;
6. (5) Ps^without denotes the volume measure for premium risk of segment s determined in accordance with 3A2.3 or 3A2.4 or, as applicable, 3C3.3 or 3C3.4; and
7. (6) Recoverables denotes the best estimate of amounts recoverable from the reinsurance arrangement, securitisation or derivative and the corresponding debtors.

7.34

1. (1) Subject to 7.2, and where the counterparty requirement and the third party requirement referred to in 3E10.1 are both met, a firm may, for the purposes of 3E10, calculate the risk-adjusted value of a collateral provided by way of a collateral arrangement under which collateral is provided by way of security, as 85% of the value of the assets held as collateral, valued in accordance with Valuation 2.1 to 2.2.
2. (2) Subject to 7.2 and 3G8, and where the counterparty requirement referred to in 3E10.1 is met and the third party requirement referred to in 3E10.1 is not met, a firm may, for the purposes of 3E10, calculate the risk-adjusted value of a collateral provided by way of a collateral arrangement  under which collateral is provided by way of security, as 75% of the value of the assets held as collateral, valued in accordance with Valuation 2.1 to 2.2.

7.35

Subject to 7.2, a firm may calculate the loss-given-default on a reinsurance arrangement or insurance securitisation referred to in 3E4.3 in accordance with the following formula:

$$LGD=max[90\mathrm{\%}\cdot (Recoverables+50\mathrm{\%}\cdot {RM}_{re})-F\cdot Collateral;0]$$

1. where:
2. (1) Recoverables denotes the best estimate of amounts recoverable from the reinsurance arrangement or insurance securitisation and the corresponding debtors;
3. (2) RM_re  denotes the risk-mitigating effect on underwriting risk of the reinsurance arrangement or securitisation;
4. (3) Collateral denotes the risk-adjusted value of collateral provided by way of a collateral arrangement in relation to the reinsurance arrangement or securitisation; and
5. (4) F denotes a factor to take into account the economic effect of the collateral arrangement in relation to the reinsurance arrangement or securitisation in case of any credit event related to the counterparty, determined in accordance with 3E10.7.

7.36

Subject to 7.2 and where the standard deviation of the loss distribution of type 1 exposures, as determined in accordance with 3E13.4 is lower than or equal to 20% of the total loss-given default on all type 1 exposures referred to in 3.13 to 3.19, a firm may calculate the capital requirement for counterparty default risk referred to in 3E13.1 in accordance with the following formula:

$${SCR}_{def,1}=5\cdot \sigma$$

where σ denotes the standard deviation of the loss distribution of type 1 exposures as determined in accordance with 3E13.4.