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

easonably simple manner. It would not naturally include <strong>the</strong> results of
scenario analyses, although <strong>the</strong>se could be incorporated at <strong>the</strong> expense
of greater complexity. However, <strong>the</strong> approach could be quite rigorous,
and <strong>the</strong> effect of approximations and uncertainties could be analysed in
some detail.
10.42 The bot<strong>to</strong>m-up method is simpler in principle, but it may be difficult <strong>to</strong>
combine different risks in anything more than an ad hoc manner. As a
result, it could be more difficult <strong>to</strong> understand <strong>the</strong> weaknesses of <strong>the</strong>
resulting formula. Important sources of risks may not be reflected in
<strong>the</strong> constituent parts of <strong>the</strong> standard formula, skewing <strong>the</strong> overall
result. In addition, it is not always possible (or sensible) <strong>to</strong> consider
risks in isolation.
10.43 In practice, <strong>the</strong> two methodologies should be seen as complementary
ra<strong>the</strong>r than contradic<strong>to</strong>ry, and both should be used in <strong>the</strong> development
of <strong>the</strong> standard formula.
Modelling approaches <strong>to</strong> <strong>the</strong> main risk categories
Risk dependencies
10.44 Generally, CEIOPS may assume that not all risks will occur at <strong>the</strong> same
time. Due <strong>to</strong> diversification effects, <strong>the</strong> overall capital requirement
might be smaller than <strong>the</strong> sum of <strong>the</strong> capital components for <strong>the</strong>
individual risks. Simple addition of <strong>the</strong> components could <strong>the</strong>refore
overstate <strong>the</strong> appropriate amount of capital.
10.45 A commonly used ma<strong>the</strong>matical <strong>to</strong>ol <strong>to</strong> analyse risk dependencies is
linear correlation. Linear correlation is based on <strong>the</strong> assumption of
linear dependency between risks and has <strong>the</strong> advantage of familiarity,
as well as being relatively easy <strong>to</strong> compute. However, its effectiveness
is limited, particularly as insurance risks are not generally subject <strong>to</strong> a
normal distribution. For risks that follow a heavily-skewed distribution,
or for risks where <strong>the</strong> dependency relationship is non-linear, a linear
correlation assumption may underestimate capital requirements 87 . In
addition, normally uncorrelated risks may become highly correlated in
extreme circumstances.
10.46 Notwithstanding its <strong>the</strong>oretical deficiencies, linear correlation, <strong>to</strong>ge<strong>the</strong>r
with a simplified form of tail correlation, may provide a starting point
(and practical expedient) for <strong>the</strong> standard formula. However, it would
be important <strong>to</strong> keep note of any dependencies that would not be
addressed properly by this treatment.
10.47 An important associated question is <strong>the</strong> degree of granularity in <strong>the</strong>
analysis. Breaking down risks in<strong>to</strong> many categories and <strong>the</strong>n assuming
independence may underestimate <strong>the</strong> capital needs if, in reality, some
of <strong>the</strong> categories turn out <strong>to</strong> be positively correlated. Conversely, using
87
See Embrechts, McNeil, Straumann, Correlation and Dependency in Risk Management: Properties and
Pitfalls,
90