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

Degree of personalisation
B.24 Translating <strong>the</strong>se <strong>the</strong>oretical equations in<strong>to</strong> a fac<strong>to</strong>r-based,
standardised formula requires:
- Mortality risk
• 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, are fur<strong>the</strong>r analysed <strong>the</strong>se two steps
fur<strong>the</strong>r, considering mortality, lapse and expense risk separately.
B.25 Defining UR% mortality as <strong>the</strong> quotient of UR mortality and <strong>the</strong> corresponding
volume measure TP0 or CR0, it can be seen that on an abstract level
one needs <strong>to</strong> choose <strong>the</strong> coefficient β or γ applicable <strong>to</strong> CEIOPS’ volume
measure as
β 1−α
( %
mortality
mortality
= ρ UR ) or = ρ UR )
γ 1−α
( %
respectively, where ρ is a given risk measure and α is <strong>the</strong> ruin
probability.
B.26 In general terms, <strong>to</strong> be able <strong>to</strong> compute <strong>the</strong> coefficient β according <strong>to</strong>
<strong>the</strong> formula in <strong>the</strong> preceding paragraph, one needs <strong>to</strong> know <strong>the</strong>
probability distribution of <strong>the</strong> random variable UR% mortality . On a practical
level, it may be assumed that this distribution is of a type that is
completely specified by its first two moments. Then β 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 .
B.27 Assuming that <strong>the</strong> type of distribution of UR% mortality is set by <strong>the</strong>
supervisor, <strong>the</strong> determination of its expected value and variance allows
for a wide range of approaches, which vary in <strong>the</strong>ir degree of
personalisation:
• all parameters are set by <strong>the</strong> supervisor; <strong>the</strong> result would be a
table of industry-wide fac<strong>to</strong>rs β and γ for mortality risk that can
be applied <strong>to</strong> <strong>the</strong> insurers’ provisions in each segment; or
• <strong>the</strong> expected value and/or variance of <strong>the</strong> distribution are
computed using company-specific data; or
• <strong>the</strong> expected value and/or variance of <strong>the</strong> distribution are
computed using a mixture of company-specific data and data
which is set by <strong>the</strong> supervisor.
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