Commission Delegated Regulation (EU) 2015/35Show full title

ANNEX XVIII INTEGRATION TECHNIQUES FOR PARTIAL INTERNAL MODELS

A. General provisions

(1) For the purposes of this Annex, the following definitions shall apply:

(a)

‘unit of the partial internal model’ is a component of the partial internal model that is separately calculated and not aggregated within the partial internal model;

(2) Where insurance and reinsurance undertakings apply integration techniques 1 to 5, their Solvency Capital Requirement shall be the sum of the following items:

(a)

the Basic Solvency Capital Requirements as laid down in sections C to F;

(b)

the capital requirement for operational risk as laid down in Article 107 of Directive 2009/138/EC, where that capital requirement is not within the scope of the partial internal model, and calculated with the partial internal model, where that capital requirement is within the scope of the partial internal model;

(c)

the adjustment for the loss-absorbing capacity of technical provisions and deferred taxes, as laid down in paragraph 3, where that adjustment is not within the scope of the partial internal model, and calculated with the partial internal model where that adjustment is within the scope of the partial internal model.

(3) Where the adjustment for the loss-absorbing capacity of technical provisions and deferred taxes is not within the scope of the partial internal model, it shall be calculated as laid down in Articles 205 to 207, but with the following changes:

(a)

the Basic Solvency Capital Requirement referred to in Articles 206(1) and (2) and 207(1) is calculated in accordance with sections B to F;

(b)

points (a) to (d) of Article 206(2) apply only to calculations with the standard formula;

(c)

for the purposes of Article 206(2) the capital requirements used in the calculation of the Basic Solvency Capital Requirement that are calculated with the partial internal take into account the risk-mitigating effect provided by future discretionary benefits of insurance contracts;

(d)

the capital requirement for operational risk referred to in Article 207(1)(c) is calculated in accordance with paragraph 2(b).

B. Integration technique 1

The Basic Solvency Capital Requirement shall be equal to the sum of the capital requirements for the units of the partial internal model, the capital requirement derived by applying the standard formula for the Basic Solvency Capital Requirement only to the risks that are out of the scope of the partial internal model and the capital requirement for intangible asset risk as set out in Article 203.

C. Integration technique 2

(1) The Basic Solvency Capital Requirement shall be equal to the following:

where:

(a)

the sum covers all possible combinations (i,j) of the aggregation list set out in paragraph 2;

(b)

Corr_(i,j) denotes the correlation parameter, for items i and j of the aggregation list;

(c)

SCR_i and SCR_j denote the capital requirements for the items i and j of the aggregation list respectively;

(d)

SCR_int denotes the capital requirement for intangible asset risk as set out in Article 203.

(2) The items on the aggregation list shall meet the following requirements:

(a)

they shall cover each of the units of the partial internal model;

(b)

none of the following sub-modules of the standard formula shall be within the scope of the partial internal model:

i.

the sub-modules of the non-life underwriting risk module set out in Article 114(1);

ii.

the sub-modules of the life underwriting risk module set out in Article 105(3) of Directive 2009/138/EC;

iii.

the sub-modules of the health underwriting risk module set out in Article 151(1);

iv.

the sub-modules of the market risk module set out in Article 105(5) of Directive 2009/138/EC;

(c)

the counterparty default risk module of the standard formula shall not be 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 module, the aggregation list shall include that module instead of its sub-modules.

(3) The correlation parameters referred to in point (b) of paragraph 1 shall comply with the following requirements:

(a)

for all items i and j from the aggregation list the correlation parameter Corr_(i,j) shall not be less than – 1 and shall not exceed 1;

(b)

for all items i and j from the aggregation list the correlation parameters Corr_(i,j) and Corr_(j,i) shall be equal;

(c)

for all items i from the aggregation list the correlation parameter Corr_(i,i) shall be equal to 1;

(d)

for any assignment of real numbers to the items of the aggregation list the following shall hold:

where:

i.

the sum covers all possible combinations (i,j) of the aggregation list;

ii.

x_i and x_j are the numbers assigned to the items i and j, respectively, of the aggregation list;

(e)

where the items i and j from the aggregation list are modules of the standard formula, the correlation parameter Corr_(i,j) shall be equal to the correlation parameter of the standard formula that is used to aggregate those two modules;

(f)

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) shall be equal to the correlation parameter of the standard formula that is used to aggregate those two sub-modules;

(g)

for all items i and j from the aggregation list the correlation parameter Corr_(i,j) shall not be less than Corr^min _(i,j) and shall not exceed Corr^max _(i,j) , where Corr^min _(i,j) and Corr^max _(i,j) are appropriate lower and upper bounds selected by the undertaking.

Insurance and reinsurance undertakings shall choose the correlation parameters referred to in point (b) of paragraph 1 in such a way that no other set of correlation parameters that meets the requirements set out in points (a) to (g) results in a higher Solvency Capital Requirement, calculated in accordance with paragraph 1.

D. Integration technique 3

(1) The Basic Solvency Capital Requirement shall be equal to the following:

where:

(a)

S_S denotes the capital requirement derived by applying the standard formula for the Basic Solvency Capital Requirement only to the risks not covered by the partial internal model;

(b)

ω ₁ denotes the first implied correlation parameter as set out in paragraph 2;

(c)

P_c denotes the capital requirement reflecting the risks that are both within the scope of the standard formula and the partial internal model, calculated with the partial internal model;

(d)

ω ₂ denotes the second implied correlation parameter as set out in paragraph 3;

(e)

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, calculated with the partial internal model;

(f)

P denotes the capital requirement reflecting the risks that are within the scope of the partial internal model, calculated with the partial internal model.

(g)

SCR_int denotes the capital requirement for intangible asset risk as set out in Article 203.

(2) The first implied correlation parameter shall be equal to the following:

where:

(a)

S denotes the capital requirement calculated in the same way as the Basic Solvency Capital Requirement 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 calculated with the partial internal model where possible;

(b)

S_C denotes the capital requirement derived by applying the standard formula for the Basic Solvency Capital Requirement only to the risks that are within the scope of the standard formula and 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 calculated with the partial internal model;

(c)

S_S is defined as in paragraph 1(a);

(d)

d ₁ 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.

(3) The second implied correlation parameter shall be equal to the following:

where ω ₁ is as defined in paragraph 2 and ω ₃ is the third implied correlation parameter as set out in paragraph 4.

(4) The third implied correlation parameter shall be equal to the following:

where:

(a)

P, P_s and P_c are as defined in paragraph 1;

(b)

d ₂ 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.

E. Integration technique 4

(1) The Basic Solvency Capital Requirement shall be equal to the following:

where:

(a)

P denotes the capital requirement reflecting the risks that are within the scope of the partial internal model, calculated with the partial internal model;

(b)

S_S denotes the capital requirement derived by applying the standard formula for the Basic Solvency Capital Requirement only to the risks not covered by the partial internal model;

(c)

k denotes the number of modules of the standard formula that are within the scope of the partial internal model;

(d)

n denotes the number of modules of the standard formula;

(e)

l denotes the number of modules of the standard formula for each of which the capital requirement can be calculated with the partial internal model;

(f)

Corr_(i,j) denotes the correlation parameter of the standard formula for the aggregation of modules i and j;

(g)

P_i denotes the capital requirement for the module i of the standard formula, calculated with the partial internal model;

(h)

S_i and S_j denote the capital requirement for modules i and j of the standard formula respectively which are calculated in the following way:

i.

the module is calculated with the standard formula provided that the module does not consists of sub-modules;

ii.

the module is calculated in accordance with paragraph 2 provided that the module consist of sub-modules.

(i)

SCR_int denotes the capital requirement for intangible asset risk as set out in Article 203.

(2) For all modules of the standard formula referred to in paragraph 1(h)(ii), the capital requirement of a particular module shall be calculated with the formula set out in paragraph 1, applying the following denominations:

(a)

P denotes the capital requirement reflecting the risks of the sub-modules of that particular module which are within the scope of the partial internal model, calculated with the partial internal model;

(b)

S_S denotes the capital requirement derived by applying that particular module only to the risks not covered by the partial internal model;

(c)

k denotes the number of sub-modules of that particular module that are within the scope of the partial internal model;

(d)

n denotes the number of sub-modules of that particular module;

(e)

l denotes the number of sub-modules of that particular module for each of which the capital requirement can be calculated with the partial internal model;

(f)

Corr_(i,j) denotes the correlation parameter of the standard formula for the aggregation of sub-modules i and j of that particular module;

(g)

P_i denotes the capital requirement for the sub-module i of that particular module, calculated with the partial internal model;

(h)

S_i and S_j denote the capital requirement for sub-modules i and j of that particular module respectively which are calculated in the following way:

i.

the sub-module is calculated with the standard formula provided that the sub-module does not consists of other sub-modules;

ii.

the sub-module is calculated in accordance with paragraph 3 provided that the sub-module consist of other sub-modules.

(i)

SCR_int shall be set to zero.

(3) For all sub-modules of the standard formula referred to in paragraph 2(h)(ii), the capital requirement of a particular sub-module shall be calculated with the formula set out in paragraph 1, applying the following denominations:

(a)

P denotes the capital requirement reflecting the risks of the sub-modules of that particular sub-module which are within the scope of the partial internal model, calculated with the partial internal model;

(b)

S_S denotes the capital requirement derived by applying that particular sub-module only to the risks not covered by the partial internal model;

(c)

k denotes the number of sub-modules of that particular sub-module that are within the scope of the partial internal model;

(d)

n denotes the number of sub-modules of that particular sub-module;

(e)

l denotes the number of sub-modules of that particular sub-module for each of which the a capital requirement can be calculated with the partial internal model;

(f)

Corr_(i,j) denotes the correlation parameter of the standard formula for the aggregation of sub-modules i and j of that particular sub-module;

(g)

P_i denotes the capital requirement for the sub-module i of that particular sub-module, calculated with the partial internal model;

(h)

S_i and S_j denote the capital requirement for sub-modules i and j of that particular sub-module respectively which are calculated in the following way:

i.

the sub-module is calculated with the standard formula provided that the sub-module does not consists of other sub-modules;

ii.

the sub-module is calculated in accordance with this paragraph provided that the sub-module consist of other sub-modules.

(i)

SCR_int shall be set to zero.

F. Integration technique 5

(1) The Basic Solvency Capital Requirement shall be equal to the following:

where:

(a)

P, S_S , k, n, Corr_(i,j) and SCR_int are defined as in paragraph 1 of section E;

(b)

S_i and S_j denote the capital requirement for modules i and j respectively of the standard formula which are calculated in the following way:

i.

the module is calculated with the standard formula provided that the module does not consists of sub-modules;

ii.

the module is calculated in accordance with paragraph 2 provided that the module consist of sub-modules.

(2) For all modules of the standard formula referred to in paragraph 1(b)(ii), the capital requirement of a particular module shall be calculated with the formula set out in paragraph 1, applying the following denominations:

(a)

P, S_S , k, n, Corr_(i,j) and SCR_int are defined as in paragraph 2 of section E;

(b)

S_i and S_j denote the capital requirement for sub-modules i and j of that particular module respectively which are calculated in the following way:

i.

the sub-module is calculated with the standard formula provided that the sub-module does not consists of other sub-modules;

ii.

the sub-module is calculated in accordance with paragraph 3 provided that the sub-module consist of other sub-modules.

(3) For all modules of the standard formula referred to in paragraph 2(b)(ii), the capital requirement of a particular module shall be calculated with the formula set out in paragraph 1, applying the following denominations:

(a)

P, S_S , k, n, Corr_(i,j) and SCR_int are defined as in paragraph 3 of section E;

(b)

S_i and S_j denote the capital requirement for sub-modules i and j of that particular module respectively which are calculated in the following way:

i.

the sub-module is calculated with the standard formula provided that the sub-module does not consists of other sub-modules;

ii.

the sub-module is calculated in accordance with this paragraph provided that the sub-module consist of other sub-modules.