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

“While proportional reinsurance typically reduces <strong>the</strong> overall (nominal)
risk in a linear way, non-proportional covers typically address <strong>the</strong> large
losses, <strong>the</strong>reby reducing <strong>the</strong> company’s net exposure <strong>to</strong> large
loss/catastrophic events. Technically speaking, non-proportional
reinsurance eliminates part or all of <strong>the</strong> volatility coming from <strong>the</strong> tail
of <strong>the</strong> distribution.”
E.6 By taking a simple quota share cover as an example, <strong>the</strong> single claim
amount net of reinsurance (YNet) may be expressed as a linear function
of <strong>the</strong> claim amount gross of reinsurance (YGross), that is
YNet = Q × YGross
where Q represents <strong>the</strong> (cedant’s) retention ratio for <strong>the</strong> quota share
cover in question.
E.7 If <strong>the</strong> quota share cover is <strong>the</strong> only reinsurance cover applied for <strong>the</strong>
line of business (LOB) in question, a similar relation holds for <strong>the</strong> <strong>to</strong>tal
claim amounts related <strong>to</strong> that LOB (for a given financial year) – at least
as long as all claim amounts on a gross basis are less than <strong>the</strong> limit of
<strong>the</strong> quota share cover. However, in general this simple linear relation
will not hold for <strong>the</strong> <strong>to</strong>tal claim amounts related <strong>to</strong> <strong>the</strong> company’s
overall business – unless <strong>the</strong> reinsurance arrangements in all LOBs
consist of similar quota share covers. 158
E.8 For all o<strong>the</strong>r reinsurance covers – whe<strong>the</strong>r proportional or non–
proportional or combinations of <strong>the</strong>m – <strong>the</strong>re is in general a non-linear
relationship between <strong>the</strong> claim amounts on a net basis and <strong>the</strong> claim
amounts on a gross basis. This fact concerns both <strong>the</strong> single claim
amounts and <strong>the</strong> <strong>to</strong>tal claim amounts (ei<strong>the</strong>r within a LOB or for <strong>the</strong>
overall portfolio of <strong>the</strong> company in question).
E.9 Examples of more complex reinsurance covers that would support <strong>the</strong>
relevance of <strong>the</strong> aspect of non-linearity sketched above may be <strong>the</strong>
combination of quota share and excess-of-loss covers or <strong>the</strong>
combination of surplus and excess-of-loss covers. In both cases <strong>the</strong>
presence of aggregate deductibles and aggregate limits as well as calls
for reinstatement premiums adds <strong>to</strong> <strong>the</strong> complexity. As a fur<strong>the</strong>r
example one may refer <strong>to</strong> 'umbrella arrangements' covering several
LOBs. 159
E.10 It may be argued that <strong>the</strong> non-linear effects should have an impact on
<strong>the</strong> design of <strong>the</strong> standard formula for <strong>the</strong> SCR. This is especially <strong>the</strong>
case if <strong>the</strong> non-linearity (<strong>the</strong> non-linear reduction of <strong>the</strong> nominal risk)
has an effect on <strong>the</strong> volatility as indicated in <strong>the</strong> IAA report.
158 Even in this simple case where <strong>the</strong> reinsurance arrangement in all LOB consists of quota share covers with
retention ratios that are specific for <strong>the</strong> individual LOB, <strong>the</strong> simple linear relationship between <strong>the</strong> <strong>to</strong>tal
claim amounts on a net basis and gross basis, respectively, may break down. In fact <strong>the</strong> overall (or
average) retention ratio will depend on <strong>the</strong> distribution of <strong>the</strong> <strong>to</strong>tal claim amounts between <strong>the</strong> individual
LOBs.
159 Cf. <strong>the</strong> IAA Solvency Report (2004), page 71, where it is referred <strong>to</strong> complexities stemming from “<strong>the</strong>
tremendous diversity in <strong>the</strong> types of insurance contracts”.
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