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

on <strong>the</strong> 'fatness' of <strong>the</strong> tail of <strong>the</strong> distribution function for <strong>the</strong> <strong>to</strong>tal claim
amounts.
E.24 With respect <strong>to</strong> both approaches sketched above it should be noticed
that <strong>the</strong> analysis of <strong>the</strong> impact of a given reinsurance arrangement
(consisting of both proportional and non-proportional covers) on <strong>the</strong>
tail behaviour of <strong>the</strong> distribution function of <strong>the</strong> <strong>to</strong>tal claim amount –
and accordingly on <strong>the</strong> volatility of <strong>the</strong> underwriting result – is a
complex issue. In order <strong>to</strong> find an answer <strong>to</strong> <strong>the</strong> question on how such
complex reinsurance arrangements should impact on <strong>the</strong> capital charge
related <strong>to</strong> <strong>the</strong> underwriting risk, it seems necessary <strong>to</strong> turn <strong>to</strong>
approximate methods and simulation techniques.
E.25 However, it should in any case be stressed that non-proportional
reinsurance covers are in general more 'efficient' than proportional
reinsurance covers with respect <strong>to</strong> reducing <strong>the</strong> 'fatness' of <strong>the</strong> tail of
<strong>the</strong> distribution function (of both individual and <strong>to</strong>tal claim amounts)
and accordingly <strong>the</strong> volatility of <strong>the</strong> underwriting result. In <strong>the</strong> IAA
Solvency Report this aspect is briefly summarised as follows:
“[r]einsurance, in particular <strong>the</strong> non-proportional type, can greatly
reduce, or even eliminate, <strong>the</strong> extreme tail of <strong>the</strong> cedant’s loss
distribution. This effect can be assessed ma<strong>the</strong>matically if <strong>the</strong> TVar risk
measure is being used. […] If applied properly in a solvency or
management context, reinsurance is a very efficient means of reducing
risk (particularly if measured by TVar) and <strong>the</strong>refore risk-bearing
capital.”
E.26 This aspect should be taken in<strong>to</strong> account when stipulating <strong>the</strong> part of
<strong>the</strong> SCR representing <strong>the</strong> capital charge for underwriting risk, cf. also
<strong>the</strong> last section of <strong>the</strong> present part.
Correlation effects
E.27 The main purpose of this section is <strong>to</strong> discuss <strong>the</strong> possible impact of
various reinsurance covers on <strong>the</strong> tail correlation or tail dependence
between two or several lines of business (LOBs).
E.28 In general terms it may be stated that 'tail correlation' or 'tail
dependence' occurs if two or more LOBs apparently operate
independently in 'normal times' but deteriorate <strong>to</strong>ge<strong>the</strong>r if <strong>the</strong>
'insurance environment' (in some sense) deteriorates. A more precise
explanation may be <strong>to</strong> describe tail dependence as “<strong>the</strong> phenomenon
whereby certain loss distributions show dependence only in <strong>the</strong>
extreme tail.” 161 In <strong>the</strong> presence of this phenomenon it should be
noticed that standard correlation analysis will not be able <strong>to</strong> capture
“<strong>the</strong> fact that certain areas of <strong>the</strong> loss distributions may be highly
correlated while o<strong>the</strong>rs are less correlated or independent.”
161 Cf. Seamus Creedon et. al (2003): ”Risk and Capital Assessment and Supervision in Financial Firms”,
Working Report presented <strong>to</strong> <strong>the</strong> GIRO Convention 2003.
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