Answers to the European Commission on the ... - Eiopa - Europa

B.61 The second alternative was chosen in <strong>the</strong> Swiss Solvency Test. Here,
<strong>the</strong> insurer has <strong>to</strong> estimate <strong>the</strong> variance of <strong>the</strong> run-off result RunOff.
On <strong>the</strong> basis of this estimation, and assuming a lognormal distribution,
<strong>the</strong> capital charge is calculated. This approach would make a high
demand on <strong>the</strong> insurer as far as his actuarial skills are concerned, and
may be <strong>to</strong>o ambitious for <strong>the</strong> standard formula.
B.62 The third alternative is an intermediate approach that uses limited
portfolio specific data <strong>to</strong> measure <strong>the</strong> portfolio specific risk in a reliable
and practicable way. For example, <strong>the</strong> variance of <strong>the</strong> distribution may
be regarded as a function of <strong>the</strong> size of <strong>the</strong> portfolio:
2
%
σ ( RunOff ) = f ( n)
.
B.63 The function f would be provided by <strong>the</strong> supervisor and <strong>the</strong> size n of
<strong>the</strong> portfolio would be determined individually by <strong>the</strong> insurer. The size
of <strong>the</strong> portfolio could be measured, for example, by <strong>the</strong> number of risks
in <strong>the</strong> portfolio at <strong>the</strong> beginning of <strong>the</strong> time horizon. This approach
would combine an assumption on <strong>the</strong> volatility of <strong>the</strong> distribution which
is specific <strong>to</strong> <strong>the</strong> business line and independent of <strong>the</strong> single company
with <strong>the</strong> diversification effects caused by <strong>the</strong> size of <strong>the</strong> portfolio which
is specific <strong>to</strong> <strong>the</strong> company. This approach has been chosen by <strong>the</strong>
Dutch supervisory authority for <strong>the</strong> Financial Assessment Framework 152
and by <strong>the</strong> IAA in <strong>the</strong> ultimate loss approach.
- premium risk
B.64 Using <strong>the</strong> notation introduced in CEIOPS’ ma<strong>the</strong>matical framework, it
can be seen that on an abstract level one needs <strong>to</strong> choose <strong>the</strong>
coefficient γ applicable <strong>to</strong> CEIOPS’ volume measure P CY as
CY
γ = ρ − ( 1−
CR ) ,
1 α
where ρ is a given risk measure and α is <strong>the</strong> ruin probability.
B.65 Similar <strong>to</strong> <strong>the</strong> case of reserve risk, <strong>the</strong> coefficient γ depends on <strong>the</strong>
s<strong>to</strong>chastic properties of <strong>the</strong> random variable CR CY . Again assuming, on
a practical level, that this distribution is of a type that is completely
specified by its first two moments, γ may be determined once <strong>the</strong>
following has been specified:
• <strong>the</strong> type of <strong>the</strong> distribution;
• its expected value µ; and
• its variance σ 2 .
This specification can differ in <strong>the</strong> degree of company-specific
information that is evaluated.
152 Cf. Financial Assessment Framework Consultation Paper, section B4.54.
249