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

- Aggregation
10.62 Mortality, lapse and expense risk may be analysed on <strong>the</strong> basis of
homogenous segments of <strong>the</strong> portfolio <strong>to</strong> take <strong>the</strong> particularities of <strong>the</strong>
single segments in<strong>to</strong> account. Such a segmented approach <strong>to</strong>
underwriting risk would present <strong>the</strong> problem of how <strong>to</strong> aggregate
individual risk charges. Simply adding up <strong>the</strong> individual charges would
neglect diversification effects between different homogenous risk
groups. This may lead <strong>to</strong> an overestimation of <strong>the</strong> required risk capital.
10.63 Two potential approaches <strong>to</strong> deal with this problem for fur<strong>the</strong>r
consideration are:
• determining mortality (or lapse/expense) risk capital charges for
each segment and calculate <strong>the</strong> overall mortality (or
lapse/expense) risk capital charge using capital aggregation
methods; or
• determining only <strong>the</strong> first two moments of <strong>the</strong> distribution of <strong>the</strong>
mortality (or lapse/expense) risk for each segment and calculate
<strong>the</strong> first two moments of <strong>the</strong> overall mortality (or lapse/expense)
risk using a correlation matrix for <strong>the</strong> second moments. Assuming
<strong>the</strong> overall mortality (or lapse/expense) risk <strong>to</strong> have a specific
two-parametric probability distribution, one may <strong>the</strong>n calculate
<strong>the</strong> overall mortality (or lapse/expense) risk capital charge.
10.64 The Dutch Financial Assessment Framework 88 and <strong>the</strong> IAA, for
example, follows <strong>the</strong> first approach. The advantage of this approach is
that for <strong>the</strong> calculation of <strong>the</strong> capital charges of <strong>the</strong> single segments
<strong>the</strong> underlying probability distribution of <strong>the</strong> risk can be chosen
according <strong>to</strong> <strong>the</strong> particularities of <strong>the</strong> segment. The disadvantage of
this approach is that a standardised aggregation of <strong>the</strong> risk capital
charges of <strong>the</strong> segments may cause certain problems. To be in a
position <strong>to</strong> aggregate <strong>the</strong>m in a ma<strong>the</strong>matically precise manner, <strong>the</strong>
complete dependence structure of <strong>the</strong> risks has <strong>to</strong> be known. This is
rarely <strong>the</strong> case.
10.65 According <strong>to</strong> <strong>the</strong> second alternative, it is not necessary for <strong>the</strong>
supervisor <strong>to</strong> set a probability distribution for <strong>the</strong> risk on <strong>the</strong> level of
<strong>the</strong> individual segment. This may help <strong>to</strong> reduce <strong>the</strong> model error of <strong>the</strong>
determination of <strong>the</strong> risk capital, since <strong>the</strong> moments of <strong>the</strong> risks can be
aggregated precisely once <strong>the</strong> linear correlations between those risks
are known. Moreover, it may be easier <strong>to</strong> make an adequate
assumption on <strong>the</strong> type of <strong>the</strong> distribution on <strong>the</strong> level of <strong>the</strong> diversified
overall risk than on <strong>the</strong> level of <strong>the</strong> segment risk. On <strong>the</strong> o<strong>the</strong>r hand,
this approach takes only <strong>the</strong> first two moments of <strong>the</strong> probability
distribution on <strong>the</strong> segment level in<strong>to</strong> account.
88 De Nederlandsche Bank (2004) – Consultatiedocument Financieel Toetsingskader (FTK).
94