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

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TVaR1-α for Tail Value-at-risk. In this c<strong>on</strong>text, 1-α or 1-α’ corresp<strong>on</strong>d <str<strong>on</strong>g>to</str<strong>on</strong>g><br />

<str<strong>on</strong>g>the</str<strong>on</strong>g> c<strong>on</strong>fidence level ensuring <str<strong>on</strong>g>the</str<strong>on</strong>g> degree of prudence, that CEIOPS<br />

wishes <str<strong>on</strong>g>to</str<strong>on</strong>g> achieve.<br />

B.18 The risk capital charge for underwriting risk is given by<br />

technical<br />

RC = ρ1−α ( UR<br />

technical<br />

)<br />

For example, a ruin probability of 0,5% and a VaR risk measure would<br />

corresp<strong>on</strong>d <str<strong>on</strong>g>to</str<strong>on</strong>g><br />

technical<br />

technical<br />

technical<br />

RC ρ UR ) = VaR ( UR ) = q ( −UR<br />

= 1−α<br />

( 99,<br />

5%<br />

99,<br />

5%<br />

technical<br />

so <str<strong>on</strong>g>the</str<strong>on</strong>g> risk capital charge is <str<strong>on</strong>g>the</str<strong>on</strong>g> 99.5 th -quantile of <str<strong>on</strong>g>the</str<strong>on</strong>g> distributi<strong>on</strong> –<br />

UR technical , or <str<strong>on</strong>g>the</str<strong>on</strong>g> smallest value of RC that satisfies <str<strong>on</strong>g>the</str<strong>on</strong>g> inequality –<br />

UR technical ≤ RC with a probability of at least 99.5%.<br />

In case of <str<strong>on</strong>g>the</str<strong>on</strong>g> risk measure TVaR and a ruin probability of, e.g. 0.8 %<br />

<str<strong>on</strong>g>the</str<strong>on</strong>g> risk charge for underwriting risk would be <str<strong>on</strong>g>the</str<strong>on</strong>g> average loss in <str<strong>on</strong>g>the</str<strong>on</strong>g><br />

worst 0.8 % cases:<br />

technical<br />

technical<br />

RC = ρ<br />

1−α<br />

' ( UR ) = TVaR99,<br />

2%<br />

( UR<br />

technical<br />

)<br />

)<br />

239

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