Euro was introduced around 1.17 dollar per euro which was at the time the historical average of basket of european currencies against USD (read: DEM). The lowest point of EUR against USD was at 0.8252, this is 1.42 times less the average (1.17 / 0.8252). If you assume symetry around the historical average, estimated maximum is 1.42 * 1.17 = 1.63 dollar per euro. This is of course back of the enveloppe, but at 1.33 there's still room for appreciation if the past is to predict the future :).