Prudential Regulation Authority Rulebook

16D.1

The basic SCR must be equal to the following:

\[\mathrm{BSCR}=\sqrt{\sum_{i,j}{{\mathrm{Corr}}_{(i,j)}\cdot{\mathrm{SCR}}_\mathrm{i}\cdot{\mathrm{SCR}}_\mathrm{j}}}+{\mathrm{SCR}}_{\mathrm{int}}\]

where:

1. (1) the sum covers all possible combinations (i,j) of the aggregation list set out in 16D.2;
2. (2) Corr_(i,j) denotes the correlation parameter for items i and j of the aggregation list;
3. (3) SCR_i and SCR_j denote the capital requirements for items i and j of the aggregation list, respectively;
4. (4) SCR_int denotes the capital requirement for intangible asset risk as set out in Solvency Capital Requirement - Standard Formula 3F1.

16D.2

The items on the aggregation list must meet the following requirements:

1. (1) they must cover each of the units of the partial internal model;
2. (2) they must include each of the following sub-modules of the standard formula excluding those within the scope of the partial internal model:
   1. (a) the sub-modules of the non-life underwriting risk module set out in Solvency Capital Requirement - Standard Formula 3.6;
   2. (b) the sub-modules of the life underwriting risk module set out in Solvency Capital Requirement – Standard Formula 3.7 – 3.9;
   3. (c) the sub-modules of the health underwriting risk module set out in Solvency Capital Requirement - Standard Formula 3C8.1; and
   4. (d) the sub-modules of the market risk module set out in Solvency Capital Requirement – Standard Formula 3.11;
3. (3) they must include the counterparty default risk module of the standard formula unless it is within the scope of the partial internal model.

However, where none of the sub-modules of a module of the standard formula are within the scope of the partial internal model, the aggregation list must include that module instead of its sub-modules.

16D.3

The correlation parameters referred to in 16D.1(2) must comply with the following requirements:

1. (1) for all items i and j from the aggregation list the correlation parameter Corr_(i,j) must not be less than -1 and must not exceed 1;
2. (2) for all items i and j from the aggregation list the correlation parameters Corr_(i,j) and Corr_(j,i) must be equal;
3. (3) for all items i from the aggregation list the correlation parameter Corr_(i,i) must be equal to 1;
4. (4) for any assignment of real numbers to the items of the aggregation list the following must hold:

\[\sum_{i,j}{{\mathrm{Corr}}_{(i,j)}\cdot x_i\cdot x_\mathrm{j}\geq0}\]

where:

1. (a) the sum covers all possible combinations (i,j) of the aggregation list; and
2. (b) x_i and x_j are the numbers assigned to the items i and j, respectively, of the aggregation list;

1. (5) where the items i and j from the aggregation list are modules of the standard formula, the correlation parameter Corr_(i,j) must be equal to the correlation parameter of the standard formula that is used to aggregate those two modules;
2. (6) where the items i and j from the aggregation list are sub-modules of the same module of the standard formula, then the correlation parameter Corr_(i,j) must be equal to the correlation parameter of the standard formula that is used to aggregate those two sub-modules;

(7) for all items i and j from the aggregation list the correlation parameter \[{\mathrm{Corr}}_{(i,j)}\] must not be less than \[{\mathrm{Corr}}_{(i,j)}^{\mathrm{min}}\] and must not exceed \[{\mathrm{Corr}}_{(i,j)}^{\mathrm{max}}\], where \[{\mathrm{Corr}}_{(i,j)}^{\mathrm{min}}\] and \[{\mathrm{Corr}}_{(i,j)}^{\mathrm{max}}\] are appropriate lower and upper bounds selected by the firm.

A firm must choose the correlation parameters referred to in 16D.1(2) in such a way that no other set of correlation parameters that meets the requirements set out in (1) to (7) results in a higher basic SCR, calculated in accordance with 16D.1.