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We study the performance of the euro/Swiss franc exchange rate in theextraordinary period from September 6, 2011 and January 15, 2015 when the SwissNational Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro.Based on the analogy between Brownian motion in finance and physics, thefirst-order effect of such a steric constraint would enter a priori in the formof a repulsive entropic force associated with the paths crossing the barrierthat are forbidden. Non-parametric empirical estimates of drift and volatilityshow that the predicted first-order analogy between economics and physics areincorrect. The clue is to realise that the random walk nature of financialprices results from the continuous anticipations of traders about futureopportunities, whose aggregate actions translate into an approximate efficientmarket with almost no arbitrage opportunities. With the Swiss National Bankstated commitment to enforce the barrier, traders's anticipation of this actionleads to a vanishing drift together with a volatility of the exchange rate thatdepends on the distance to the barrier. We give direct quantitative empiricalevidence that this effect is well described by Krugman's target zone model[P.R. Krugman. The Quarterly Journal of Economics, 106(3):669-682, 1991].Motivated by the insights from this economical model, we revise the initialeconomics-physics analogy and show that, within the context of hindereddiffusion, the two systems can be described with the same mathematics afterall. Using a recently proposed extended analogy in terms of a colloidalBrownian particle embedded in a fluid of molecules associated with theunderlying order book, we derive that, close to the restricting boundary, thedynamics of both systems is described by a stochastic differential equationwith a very small constant drift and a linear diffusion coefficient.

Currency target zone modeling: An interplay between physics and economics