Currency target-zone modeling: An interplay between physics and economics

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Sandro Claudio Lera, Didier Sornette

Abstract

We study the performance of the euro-Swiss franc exchange rate in the extraordinary period from September 6, 2011 to January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions and based on the analogy between Brownian motion in finance and physics, the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. Nonparametric empirical estimates of drift and volatility show that the predicted first-order analogy between economics and physics is incorrect. The clue is to realize that the random-walk nature of financial prices results from the continuous anticipation of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank's stated commitment to enforce the barrier, traders' anticipation of this action leads to a vanishing drift together with a volatility of the exchange rate that depends on the distance to the barrier. This effect is described by Krugman's model [P. R. Krugman, Tar...Continue Reading

References

Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A W C Lau, T C Lubensky
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Ruseckas, B Kaulakys
Mar 25, 2014·Physical Review Letters·Yoshihiro YuraMisako Takayasu
May 31, 2014·Reports on Progress in Physics·Didier Sornette
Oct 16, 2015·Journal of Mathematical Neuroscience·Sergej O VoronenkoBenjamin Lindner

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