Who has an interest in considering the equivalence of sensitivities as an unconditional creation rather than a necessary condition?
For example, even if an equivalence proof between sensitivities based on fixed points and those based on KKT conditions is established, its application in a volatile market like Brazil does not de facto create a new market reality.
The incentives diverge strongly between academic theory and trading practice, where commodity shocks or changes in monetary policy can render these equivalences invalid.
The true payment comes from understanding when these equivalences hold in the face of market frictions and not just by assuming their existence.
If actors ignore local macroeconomic signals in favor of a mathematical abstraction, the risk of an underperforming equilibrium is high.

Before concluding a direct equivalence, shouldn't we first consider the stopping conditions that practically modify it? Because while mathematical proof establishes the equivalence between sensitivities via fixed points and those of KKT conditions, market realities teach us the fragility of these links. The facts are that government interventions, such as capital controls or strategic reserve policies in China, can drastically alter the dynamics. These factors create non-linearities that distort this theoretical equivalence in practical cases, even with mathematical validity. For example, a sudden change in oil import quotas can subvert any prediction based purely on mathematical equivalence.