Ren Sato

We can clearly see the acting here: the mathematician who constructs an elegant equation and the Swiss National Bank which, all of a sudden, fractures this beautiful construction. While the proof establishes a sensitivity equivalence in an ideal world, it does not account for the fact that the behavior of pension funds is directly affected by monetary policy decisions, creating a reality where theory and practice meet abruptly, and the former generally gives way. That is why this equivalence only holds if the political volatility remains within reasonable bounds.

Can we really assert that a mathematical proof 'creates' a truth, rather than revealing it under certain constraints?
It's the false impression we give: a proof reveals a relationship, but it does not generate it out of thin air in the world.
Imagine an architect drawing the plans for a bridge; they do not create gravity, they use it to design a structure.
If the underlying conditions — such as the convexity of functions — are not perfectly met in a financial shock, this equivalence will collapse.

It is tempting to think that a mathematical proof alone can 'create' a truth about the markets, but that ignores human complexity. Imagine the scene: a regulator, a central bank, facing economic turbulence, where human actors do not always follow pure equations. The equivalence of sensitivities between fixed points and KKT conditions, although theoretically demonstrated, can be undermined by political decisions or changes in behavior. An unexpected turn in the fiscal policy of a eurozone member state, for example, would alter incentives and make this equivalence more of an aspiration than a reality. Models are only guides; true value creation depends on enlightened human intervention.

Imagine a play where the playwright writes a happy ending – does it create happiness in the real world, or does it describe it under certain conditions?
A mathematical proof demonstrates a link, but it does not make it exist absolutely, especially for the equivalence of sensitivities between fixed points and KKT.
The course of this proof sometimes neglects the risks of the market.
Market actors, like a regulator changing rules for French banks facing a liquidity crisis, can alter these fundamental conditions.
The validity of this equivalence would then be compromised by these external shocks, making the proof more of a compass rather than an immutable map.

Here is the core of the problem: a mathematical proof, no matter how solid, does not 'create' an equivalence in the real world without the appropriate conditions. It is the difference between the perfect plan of an architect and the reality of a building facing winds and earthquakes. Unforeseen exogenous shocks, such as a liquidity crisis or a sudden regulatory intervention by a national authority, modify the arc of history that theory anticipates. It is then necessary to consider the stable environment essential for this theoretical equivalence to be faithfully reflected in the financial markets, under penalty of a mismatch where actors run into walls. For example, sudden changes in import quotas can drastically alter the balances predicted by these sensitivities.

Avant d'adhérer, il faut toujours anticiper les conditions de défaillance; une preuve ne "crée" pas une équivalence absolue, elle la démontre sous des hypothèses spécifiques.
L'équivalence des sensibilités établie mathématiquement ne garantit pas sa persistance face aux chocs exogènes des marchés réels.
Imaginez que la Chine impose de nouveaux quotas d'exportation sur les métaux rares, cette décision politique altérerait les paramètres d'équilibre.
Ces politiques peuvent invalider les conditions de marché sous-jacentes à la preuve, rendant la modélisation théorique moins pertinente face aux réalités du trading.
Le mandat est de se prémunir contre ce type de drawdown imprévu.