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.