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

B.66 The level of premium risk strongly depends on <strong>the</strong> expected value of
CY
<strong>the</strong> combined ratio CR . An estimated combined ratio above one
increases <strong>the</strong> risk by <strong>the</strong> estimated loss, whereas an estimated
combined ratio below one decreases <strong>the</strong> risk by <strong>the</strong> estimated profit.
Since insurers tend <strong>to</strong> differ in <strong>the</strong> expected value of <strong>the</strong> combined ratio
of <strong>the</strong>ir business, it seems advisable <strong>to</strong> personalise this parameter of
CR CY . This could be achieved by estimating <strong>the</strong> expected value of <strong>the</strong>
combined ratio of <strong>the</strong> insurer by using <strong>the</strong> his<strong>to</strong>rical ratios.
B.67 As <strong>to</strong> <strong>the</strong> personalisation of <strong>the</strong> variance of <strong>the</strong> combined ratio, a
number of different approaches seem possible. The determination of
<strong>the</strong> variance may be left completely, partly or not at all <strong>to</strong> <strong>the</strong> insurer.
The decision requires a trade-off between accuracy and practicability of
<strong>the</strong> determination of <strong>the</strong> variance within <strong>the</strong> limits of <strong>the</strong> standard
formula.
B.68 A completely company-specific determination of <strong>the</strong> variance would
make a high demand on <strong>the</strong> insurer. It would require <strong>the</strong> insurer <strong>to</strong>
observe <strong>the</strong> volatility of <strong>the</strong> relevant business for a long period of time
and <strong>to</strong> make an actuarial analysis on those data. This approach may
not seem feasible for <strong>the</strong> standard formula.
B.69 The opposite approach would be <strong>to</strong> uniformly fix <strong>the</strong> assumed variance
of <strong>the</strong> combined ratio of a business line for all companies. This option
has been chosen in <strong>the</strong> UK solvency regime. It would not take in<strong>to</strong>
account <strong>the</strong> differences between <strong>the</strong> insurers in <strong>the</strong> volatility of <strong>the</strong>ir
combined ratios. In particular, <strong>the</strong> standard formula would not
differentiate between <strong>the</strong> volatility of large and of small portfolios.
B.70 An intermediate approach would be <strong>to</strong> determine <strong>the</strong> variance of <strong>the</strong>
combined ratio by referring <strong>to</strong> data which are partly specific <strong>to</strong> <strong>the</strong>
company and partly independent from <strong>the</strong> company. For example, <strong>the</strong>
Swiss Solvency Test assumes that <strong>the</strong> probability distribution of <strong>the</strong>
loss ratio follows a compound poisson distribution. Given a coefficient
of variation for <strong>the</strong> claim size, <strong>the</strong> insurer may calculate <strong>the</strong> coefficient
of variation of <strong>the</strong> loss ratio by estimating <strong>the</strong> expected number of
claims of its portfolio.
B.71 While this approach is quite ambitious, a more pragmatic attempt <strong>to</strong>
personalise <strong>the</strong> determination of <strong>the</strong> variance is <strong>to</strong> regard <strong>the</strong> variance
as a function of <strong>the</strong> size of <strong>the</strong> portfolio:
2
( CR ) f ( n)
CY σ = .
B.72 The function f would be provided by <strong>the</strong> supervisor and <strong>the</strong> size n of
<strong>the</strong> portfolio would be determined individually by <strong>the</strong> insurer. The size
of <strong>the</strong> portfolio could be measured by <strong>the</strong> number of risks in <strong>the</strong>
portfolio at <strong>the</strong> beginning of <strong>the</strong> time horizon. This approach would
combine an assumption on <strong>the</strong> volatility of <strong>the</strong> combined ratio which is
specific <strong>to</strong> <strong>the</strong> business line and independent of <strong>the</strong> single company
with <strong>the</strong> diversification effects caused by <strong>the</strong> size of <strong>the</strong> portfolio which
is specific <strong>to</strong> <strong>the</strong> company. This approach has been chosen by <strong>the</strong>
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