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

technical
technical
technical
technical
RC ρ UR ) = VaR ( UR ) = q ( −UR
) .
= 1−α ( 99%
99%
So in this case <strong>the</strong> risk capital charge is <strong>the</strong> 99 th -quantile of <strong>the</strong>
distribution –UR technical , or <strong>the</strong> smallest value of RC that satisfies <strong>the</strong>
inequality –UR technical ≤ RC with a probability of at least 99%.
B.53 Considering premium and reserve risk separately, risk capital charges
can be defined as
RC
premium
RC reserve
where:
RC premium
CY CY CY
ρ1 ( P − ( E + IL )) and
= −α
= 1 ( RunOff ) ,
ρ −α
= <strong>the</strong> risk capital charge for premium risk;
RC reserve = <strong>the</strong> risk capital charge for reserve risk.
B.54 Expressing <strong>the</strong>se charges in terms of <strong>the</strong> volume measures P CY and
PCO0 (<strong>the</strong> provision for claims outstanding at <strong>the</strong> beginning of <strong>the</strong>
current year), one has that
premium
CY CY
RC = ρ 1−α ( 1−
CR ) × P and
RC
where
reserve
= 1−α
CY CY
CR = ( E +
%
ρ ( RunOff ) × PCO ,
IL
CY
) /
P
CY
0
is <strong>the</strong> combined loss ration of <strong>the</strong> insurer in <strong>the</strong> current year and
RunOff RunOff
% =
/ PCO0
is <strong>the</strong> (relative) run-off result, expressed in percentage of <strong>the</strong>
outstanding provision at <strong>the</strong> beginning of <strong>the</strong> current year.
B.55 Translating <strong>the</strong>se <strong>the</strong>oretical equations in<strong>to</strong> a fac<strong>to</strong>r-based,
standardised formula requires:
• analysis at <strong>the</strong> level of individual undertakings; and
• generalised analysis that can be applied across <strong>the</strong> industry.
In <strong>the</strong> following paragraphs, <strong>the</strong>se two steps are analysed fur<strong>the</strong>r,
considering reserve risk and premium risk separately.
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