In this paper we analyse the behaviour of the bilateral exchange rates that were converted into euros on 1 January 1999. Using a model of stochastic regime switching we study the effects of future conversion on current exchange-rate dynamics. We find that exchange rates are to a large extent determined by the discounted (expected) conversion value. The theoretical model is subsequently applied to the currencies that participate in the first wave of the European Monetary Union (EMU). Using a Kalman approach, we find that for most currencies the weight attached to the future conversion value was well over 95%. This pricing characteristic successfully insulated intra-European exchange rates from the turmoil generated by the ongoing crises in Asia, Russia and Latin America.