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

features. 81 TailVaR is an example of a coherent risk measure. 82 One
desirable feature is 'subadditivity', which means <strong>the</strong> aggregation of
risks does not lead <strong>to</strong> an increase in overall risk. 83 VaR, by contrast,
does not enjoy this property, except in <strong>the</strong> case of normally-distributed
risks.
10.8 For <strong>the</strong>se reasons, TailVaR is <strong>the</strong> risk measure that <strong>the</strong> IAA Insurer
Solvency Assessment Working Party 84 has suggested <strong>to</strong> use for <strong>the</strong>
purpose of setting solvency requirements.
10.9 While <strong>the</strong> standard formula would be calibrated <strong>to</strong> simulate <strong>the</strong> effects
of a particular risk measure, undertakings operating under this
approach would not be expected <strong>to</strong> perform a VaR or TailVaR
calculation <strong>the</strong>mselves. The effects could be simulated using a prespecified,
formulaic calculation. Internal models could deliver
requirements that are closer <strong>to</strong> an undertaking's 'true' VaR/TailVaR
result.
10.10 The most significant disadvantage associated with TailVaR is <strong>the</strong>
scarcity of data, which could lead <strong>to</strong> increased modelling error. A
formula based on TailVaR might be difficult <strong>to</strong> generalise in such a way
as <strong>to</strong> provide a good fit for <strong>the</strong> majority of insurance undertakings (i.e.
<strong>the</strong> standard formula would over- or under-estimate capital
requirements in many cases because it would be calibrated using tail
data that may not be representative).
10.11 Following changes <strong>to</strong> <strong>the</strong> Framework for Consultation, CEIOPS 85 notes
that <strong>the</strong> <strong>Commission</strong> Services are proposing <strong>the</strong> use of VaR as a
general principle for calculating <strong>the</strong> SCR. For internal models, <strong>the</strong>
<strong>Commission</strong> Services acknowledge in CfA 11 that more advanced
modelling techniques could be used, including <strong>the</strong> use of TailVaR as a
risk measure. CEIOPS would stress <strong>the</strong> importance of a common
underlying philosophy for <strong>the</strong> SCR, applicable <strong>to</strong> both <strong>the</strong> standard
formula and internal models. Using different risk measures would
impact <strong>the</strong> incentives <strong>to</strong> move from <strong>the</strong> standard formula <strong>to</strong> internal
models and would lead <strong>to</strong> unpredictable results in <strong>the</strong> context of partial
models. Since internal models strive for a more accurate mapping of
<strong>the</strong> business and <strong>the</strong>refore are more likely <strong>to</strong> address also <strong>the</strong>
consequences of tail events, <strong>the</strong> use of TailVaR would smooth <strong>the</strong>
transition from <strong>the</strong> standard formula <strong>to</strong> internal models and facilitate
partial use.
81 Artzner, Ph. et al, 'Coherent Measures of Risk' (1999) – Ma<strong>the</strong>matical Finance 9.
82 International Actuarial Association (2004) – A Global Framework of Insurer Solvency Assessment.
83
Subadditivity means that ρ(A + B) ≤ ρ(A) + ρ(B), where ρ is a risk measure and A, B represent any two
portfolios.
84 IAA (2004) – A global framework for insurer solvency assessment.
85 MARKT/2506/04 (2005) – Amended Framework for Consultation.
83