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

E.11 Ano<strong>the</strong>r aspect of <strong>the</strong> non-linearity issues concerns
“<strong>the</strong> fact that many reinsurance contracts do not bear a linear
relationship with <strong>the</strong> underlying risks. […] In fact, <strong>the</strong> contracts
transforming <strong>the</strong> overall risk in<strong>to</strong> a 'narrower' risk profile typically are
exactly of this nature. The magnitude of <strong>the</strong> leverage effect depends on
<strong>the</strong> sizes of <strong>the</strong> retention (attachment point or priority) and <strong>the</strong> limit.”
E.12 A simple example of this aspect of non-linearity may be an excess-ofloss
cover with retention (attachment point) M and limit L. In this case
<strong>the</strong> single claim amount net of reinsurance (YNet) is given by:
YNet = min(YGross, M) + max(0, YGross – L).
E.13 In a context of non-negligible claims inflation <strong>the</strong> risk sharing effect of
this reinsurance cover may vary considerably depending on <strong>the</strong> delay
between <strong>the</strong> occurrence and final settlement of <strong>the</strong> individual claims –
unless <strong>the</strong> retention (M) and <strong>the</strong> limit (L) are adjusted according <strong>to</strong> an
index reflecting <strong>the</strong> claims inflation.
E.14 Similar effects may apply for o<strong>the</strong>r types of reinsurance cover
(including s<strong>to</strong>p-loss covers) where aggregate deductibles and
aggregate limits are stipulated in nominal terms.
E.15 A considerably more technical aspect of <strong>the</strong> concept 'non-linearity'
concerns e.g. <strong>the</strong> non-linear correlation effects between <strong>the</strong> individual
LOBs. However, this aspect is briefly commented upon in conjunction
with <strong>the</strong> discussion below regarding correlation effects.
E.16 It seems reasonable that <strong>the</strong> various aspects regarding non-linearity
referred <strong>to</strong> above should impact on <strong>the</strong> standard model for stipulating
<strong>the</strong> SCR. Some initial considerations on this issue is given in <strong>the</strong> last
section of this annex.
Tail behaviour and <strong>the</strong> efficiency of reinsurance covers
E.17 As with <strong>the</strong> concept 'non-linearity', <strong>the</strong> concept 'tail behaviour' is
applied in different contexts regarding <strong>the</strong> (statistical) modelling of
insurance risk processes and again it will be referred only <strong>to</strong> some
aspects that may be relevant for analysing <strong>the</strong> impact of various
reinsurance arrangements on <strong>the</strong> stipulation of <strong>the</strong> SCR (or more
precisely on <strong>the</strong> stipulation of <strong>the</strong> risk capital charge related <strong>to</strong>
underwriting risk).
E.18 The analysis of 'tail behaviour' will be of special interest in cases of
(heavily) skewed probability distributions or probability distributions
with heavy ('fat') tails – both for <strong>the</strong> individual and <strong>the</strong> <strong>to</strong>tal claim
amounts.
E.19 It <strong>the</strong> present context it seems likely that standard measures of tail
behaviour as e.g. <strong>the</strong> failure rate (<strong>the</strong> hazard rate) 160 would not
160 For a definition of <strong>the</strong> failure rate or hazard rate (as a standard measure of <strong>the</strong> tail behaviour of a
distribution function) it may be referred <strong>to</strong> Cf. Klugman et. al. (1998): “Loss Models” (Wiley), pages 86ff.
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