Before enthusiasm, it is crucial to recall that a proof of equivalence between sensitivities based on fixed points and those based on KKT conditions does not create them, but demonstrates them.
Our mandate for compliance, notably under the auspices of the ASIC in Australia, requires a clear distinction: proof is a validation, not a fabrication of existence.
Such jurisdiction does not tolerate confusion between what is postulated and what is proven; if a sensitivity model is applied, its equivalence must rest on an intrinsic validity, not an ad-hoc creation.
For example, an APRA regulation for risk management does not create the risk, it defines it and frames its mitigation.
Confusing these terms could lead to a mistaken perception of the robustness of models, which is forbidden in capital management.