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

Annex E (Call for Advice No. 12)
Non-linearity, tail behaviour and correlation
effects
E.1 A large variety of reinsurance covers and combinations of such covers
are available. However, <strong>the</strong> impact of <strong>the</strong> combinations of reinsurance
covers on individual claim amounts as well as <strong>to</strong>tal claim amounts –
within a specific line of business or for <strong>the</strong> insurance company’s overall
portfolio – may vary substantially, depending on <strong>the</strong> characteristics of
<strong>the</strong> actual reinsurance cover or combination of such covers.
E.2 The present part comments briefly on some of <strong>the</strong> more technical
aspects related <strong>to</strong> <strong>the</strong> various types of reinsurance covers and <strong>the</strong>ir
impact on both individual and <strong>to</strong>tal claim amounts, i.e. non-linearity of
reinsurance covers, tail behaviour and <strong>the</strong> efficiency of reinsurance
covers and correlation effects. As will be seen from <strong>the</strong> discussion
below, <strong>the</strong>se aspects are – at least <strong>to</strong> some extent – interlinked.
E.3 In general terms it may be stated that all <strong>the</strong> abovementioned
technical aspects may have an impact on <strong>the</strong> ability of a reinsurance
cover – or combination of covers – <strong>to</strong> reduce <strong>the</strong> volatility and
uncertainty of insurance operations and especially <strong>the</strong> consequences of
extreme events. Accordingly, <strong>the</strong>se aspects should be taken in<strong>to</strong>
consideration when stipulating <strong>the</strong> solvency capital requirement (SCR).
Some general comments on how this might potentially be done in
practice – especially in <strong>the</strong> context of <strong>the</strong> standard model for <strong>the</strong> SCR –
are given in <strong>the</strong> last section. 157
Non-linearity of reinsurance covers
E.4 It should be noticed that <strong>the</strong> concept 'non-linearity' is applied in several
different contexts when it comes <strong>to</strong> <strong>the</strong> modelling of relevant risk
processes (in a wide sense) for stipulating requirements for technical
provisions and solvency capital in insurance. However, in this section it
is focussed only on a few aspects that may be of importance when
considering <strong>to</strong> what extent <strong>the</strong> impact of reinsurance covers should be
taken in<strong>to</strong> account when designing <strong>the</strong> standard formula for <strong>the</strong> SCR.
E.5 As a first example of <strong>the</strong> non-linear aspects concerning <strong>the</strong> impact of
reinsurance covers on <strong>the</strong> claim amounts, one may refer <strong>to</strong> <strong>the</strong>
distinction between proportional reinsurance (typically quota share and
surplus covers) and non-proportional (typically excess-of-loss and s<strong>to</strong>ploss
covers). In <strong>the</strong> IAA Solvency Report <strong>the</strong> issue at stake has been
briefly described as follows:
157 With respect <strong>to</strong> internal models, it seems reasonable <strong>to</strong> include an adequate treatment of non-linearity,
tail behaviour and correlation effects among <strong>the</strong> minimum design criteria for such models. With respect <strong>to</strong>
<strong>the</strong> stipulation of technical provisions – and especially <strong>the</strong> risk margin – <strong>the</strong> relevant issues regarding <strong>the</strong>
impact on reinsurance covers are discussed in <strong>the</strong> context of CfA 7 and CfA 8.
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