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

B. Premium risk method

Input data and method-specific data requirements

(1) The data for estimating the undertaking-specific standard deviation of segment s shall consist of the following:

(a)

the payments made and the best estimates of the provision for claims outstanding in segment s after the first development year of the accident year of those claims (aggregated losses);

(b)

the premiums earned in segment s;

Those aggregated losses and earned premiums shall be available separately for each accident year of the insurance and reinsurance claims in segment s.

(2) The following method-specific data requirements shall apply:

(a)

the data are representative for the premium risk that the insurance or reinsurance undertaking is exposed to during the following twelve months;

(b)

data are available for at least five consecutive accident years;

(c)

where the premium risk method is applied to replace the standard parameters referred to in Article 218(1)(a)(i) and (c)(i), the aggregated losses and earned premiums are not adjusted for recoverable from reinsurance contracts and special purpose vehicles or reinsurance premiums;

(d)

where the premium risk method is applied to replace the standard parameters referred to in Article 218(1)(a)(ii) and (c)(ii):

i.

the aggregated losses are adjusted for amounts recoverable from reinsurance contracts and special purpose vehicles which are consistent with the reinsurance contracts and special purpose vehicles that are in place to provide cover for the following twelve months;

ii.

the earned premiums are adjusted for reinsurance premiums which are consistent with the reinsurance contracts and special purpose vehicles that are in place to provide cover for the following twelve months;

(e)

the aggregated losses are adjusted for catastrophe claims to the extent that the risk of those claims is reflected in the non-life or health catastrophe risk sub-modules;

(f)

the aggregated losses include the expenses incurred in servicing the insurance and reinsurance obligations;

(g)

the data fit the following assumptions:

i.

expected aggregated losses in a particular segment and accident year are linear proportional in premiums earned in a particular accident year;

ii.

the variance of aggregated losses in a particular segment and accident year is quadratic in premiums earned in a particular accident year;

iii.

aggregated losses follow a lognormal distribution;

iv.

maximum likelihood estimation is appropriate.

Method specification

(3) For the purpose of paragraphs 4-6, the following notation shall apply:

(a)

accident years are denoted by consecutive numbers starting with 1 for the first accident year for which data are available;

(b)

T denotes the latest accident year for which data are available;

(c)

for all accident years, the aggregated losses in segment s in a particular accident year t are denoted by y_t ;

(d)

for all accident years, the premiums earned in segment s in a particular accident year t are denoted by x_t .

(4) The undertaking-specific standard deviation of segment s shall be equal to the following:

where:

(a)

c denotes the credibility factor set out in section G;

(b)

denotes the standard deviation function set out in paragraph 5;

(c)

denotes the mixing parameter set out in paragraph 6;

(d)

denotes the logarithmic variation coefficient set out in paragraph 6.

(e)

σ_(prem,s) denotes the standard parameter that should be replaced by the undertaking-specific parameter.

(5) The standard deviation function shall be equal to the following function of two variables:

where:

(a)

and are defined in point (c) and (d) of paragraph 4;

(b)

exp denotes the exponential function;

(c)

ln denotes the natural logarithm;

(d)

π_t denotes the following function of two variables:

where:

i.

and are defined in point (c) and (d) of paragraph 4;

ii.

denotes the following amount:

(6) The mixing parameter and the logarithmic variation coefficient shall be the values and respectively for which the following amount becomes minimal:

where:

(a)

ln denotes the natural logarithm;

(b)

π_t denotes the function set out in point (d) of paragraph 5;

(c)

denotes the standard deviation function set out in paragraph 5;

(d)

denotes the following amount:

For the determination of the minimal amount, no values for the mixing parameter less than zero or exceeding 1 shall be considered.