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

- reserve risk
B.56 Using <strong>the</strong> notation introduced in CEIOPS’ ma<strong>the</strong>matical framework, it
can be seen that on an abstract level one needs <strong>to</strong> choose <strong>the</strong>
coefficient β applicable <strong>to</strong> CEIOPS’ volume measure PCO0 as
β −α
%
= ρ1
( RunOff ) ,
where ρ is a given risk measure and α is <strong>the</strong> ruin probability.
B.57 In general terms, <strong>to</strong> be able <strong>to</strong> compute <strong>the</strong> coefficient β according <strong>to</strong>
<strong>the</strong> formula in <strong>the</strong> preceding paragraph, one needs <strong>to</strong> know <strong>the</strong>
probability distribution of <strong>the</strong> random variable RunOff % . On a practical
level, it may be assumed may assume that this distribution is of a type
that is completely specified by its first two moments. For example, one
may assume that RunOff % follows a shifted lognormal, or gamma,
distribution. Then β may be determined once <strong>the</strong> following has been
specified:
• <strong>the</strong> type of <strong>the</strong> distribution;
• its expected value µ; and
• its variance σ 2 .
B.58 Assuming that <strong>the</strong> type of distribution of RunOff % is set by <strong>the</strong>
supervisor, <strong>the</strong> determination of its expected value and variance allows
for a wide range of approaches, which vary in <strong>the</strong>ir degree of
personalisation:
• all parameters are set by <strong>the</strong> supervisor; <strong>the</strong> result would be a
table of industry-wide fac<strong>to</strong>rs β for reserve risk that can be
applied <strong>to</strong> <strong>the</strong> insurers’ provisions in each segment; or
• <strong>the</strong> expected value and/or variance of <strong>the</strong> distribution are
computed using company-specific data; or
• <strong>the</strong> expected value and/or variance of <strong>the</strong> distribution are
computed using a mixture of company-specific data and data
which is set by <strong>the</strong> supervisor.
B.59 The decision about <strong>the</strong> degree of personalisation requires a trade-off
between accuracy and practicability of <strong>the</strong> determination of <strong>the</strong> risk
within <strong>the</strong> limits of <strong>the</strong> standard formula.
B.60 The first alternative can be compared with <strong>the</strong> actuarial studies used <strong>to</strong>
calibrate <strong>the</strong> 'enhanced capital requirement' in <strong>the</strong> United Kingdom 150
and <strong>the</strong> NAIC's Risk Based Capital model in <strong>the</strong> United States 151 .
150
Watson Wyatt for <strong>the</strong> Financial Services Authority (2003) – Calibration of <strong>the</strong> general insurance risk based
capital model.
151
AAA Property/Casualty Risk Based Capital Task Force (1993) – Report on reserve and underwriting risk
fac<strong>to</strong>rs.
248