I have a question regarding the use of alternative vega sensitivities (bank system sensitivities) in the context of the Vega Risk Charge of the SBM. The article 325t.6 of the CRR allows banks to calculate vega sensitivities on the basis of a linear transformation of alternative definitions of sensitivities in the calculation of the own funds requirements of a trading book position: https://www.eba.europa.eu/regulation-and-policy/single-rulebook/interactive-single-rulebook/101249

To do so, one should demonstrate that the linear transformation reflects a vega risk sensitivity (point (b) of the cited article). I can't see how I should proceed to demonstrate that point. Having bank system sensitivities on a set of volatility term structure maturities, how to prove that linearly projecting these sensitivities on the regulatory set of volatility maturities makes sense? Has anyone researched this question before? I am more than happy to have your feedback.


  • $\begingroup$ IIRC: you may calculate the FRTB-Vegas based on your internal model‘s Vegas, eg by rebasing the sensitivities from your pillars to the FRTB pillars. But I have the feeling that’s not what you are after, no? $\endgroup$ Aug 17, 2021 at 18:17
  • $\begingroup$ Yes, that's the point. However, in order to rebash the sensitivity from your pillars to the FRTB pillars, the regularoty asks to prove first that this rebasing (linear projection) reflects the vega risk. My point is how to perform such demonstration? $\endgroup$
    – MI70
    Aug 17, 2021 at 19:54
  • $\begingroup$ you are talking FRTB SA, I understand. And I understand your point. In most (all?) shops I’ve seen, the vol surfaces have been set up with more, and with overlapping, pillars compared to the FRTB-SA pillars. What could be done is to calculate only the FRTB pillars as a (strict) subset of all available pillars and compare that result to a result with „all pillars, rebased to FRTB pillars“. In any case, the comparison might require a second risk setup on a test system, I think. $\endgroup$ Aug 18, 2021 at 18:42


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