Prudential Regulation Authority Rulebook

16E.1

The basic SCR must be equal to the following:

$$\mathrm{B}\mathrm{S}\mathrm{C}\mathrm{R}=\sqrt{\sum _{i,j}{S}_S^2+2S_S({\omega }_1\cdot P_C+{\omega }_2\cdot P_S)+P^2}+{\mathrm{S}\mathrm{C}\mathrm{R}}_{\mathrm{i}\mathrm{n}\mathrm{t}}$$

where:

1. (1) S_s denotes the capital requirement derived by applying the standard formula for the basic SCR only to the risks not covered by the partial internal model;
2. (2) ω₁ denotes the first implied correlation parameter as set out in 16E.2;
3. (3) P_c denotes the capital requirement reflecting the risks that are both within the scope of the standard formula and the scope of the partial internal model, generated by the partial internal model;
4. (4) ω₂ denotes the second implied correlation parameter as set out in 16E.3;
5. (5) P_s is the capital requirement reflecting the risks within the scope of the partial internal model but not within the scope of the standard formula, generated by the partial internal model;
6. (6) P denotes the capital requirement reflecting the risks that are within the scope of the partial internal model, generated by the partial internal model;
7. (7) SCR_int denotes the capital requirement for intangible asset risk as set out in Solvency Capital Requirement - Standard Formula 3F1.

16E.2

The first implied correlation parameter must be equal to the following:

$${\omega }_1=\frac{S^2-S_S^2-S_C^2}{d_1+2\cdot S_S\cdot S_C}$$

where:

1. (1) S denotes the capital requirement calculated in the same way as the basic SCR by means of the standard formula, but where capital requirements for modules or sub-modules are replaced by capital requirements for those modules or sub-modules that are generated by the partial internal model, where possible;
2. (2) S_c denotes the capital requirement derived by applying the standard formula for the basic SCR only to the risks that are within the scope of the standard formula and the scope of the partial internal model, but where the capital requirements for the modules and sub-modules are replaced by capital requirements for those modules or sub-modules that are generated by the partial internal model;
3. (3) S_s is defined as in 16E.1(1);
4. (4) d₁ is equal to 1 where S_s or S_c are zero and equal to zero where S_s and S_c are different from zero.

16E.3

The second implied correlation parameter must be equal to the following:

$${\omega }_2={\omega }_1\cdot {\omega }_3+\frac{1}{2}\sqrt{(1-{\omega }_1^2)(1-{\omega }_3^2)}$$

where ω₁ is as defined in 16E.2 and ω₃ is the third implied correlation parameter as set out in 16E.4.

16E.4

The third implied correlation parameter must be equal to the following:

$${\omega }_3=\frac{P^2-P_S^2-P_C^2}{d_2+2\cdot P_S\cdot P_C}$$

where:

1. (1) P, P_s and P_c are as defined in 16E.1;
2. (2) d₂ is equal to 1 where P_s or P_c are zero and equal to zero where P_s and P_c are different from zero.