Quantitative modelling of the EUR/CHF exchange rate during the target zone regime of September 2011 to January 2015

Krugman (1991)'s target zone model for exchange rate dynamics has become the reference of a large part of this literature. Despite its simplicity and elegance, empirical evidence has been lacking, not least because it is difficult to capture the predicted non-linear relationship between the observable exchange rate and the non-observable fundamental value. This is why we propose a different approach. By inverting locally the relation between exchange rate and fundamental value, we derive analytical expressions for the conditional volatility and the probability density as a function of the exchange rate. This allows us to examine Krugman's prediction directly from historical data, and, furthermore, enables us to test the smooth pasting condition, which is intimately related to the no-arbitrage condition. Concretely, 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. We show that the data are well explained by the theory and conclude that Krugman's target zone model holds after all, but apparently only under extreme and sustained pressure that pushes continuously the exchange rate very close to the boundary of the target zone.