This paper proposes an arbitrage free trilateral model of a credible target zone regime with bands on each bilateral exchange rate. The no arbitrage condition reduces the system to only two dimensions. Any two rates must obey their own boundaries but, in addition, the free rein for movements is restricted by the band of the redundant rate. Therefore, target zone models defined in bilateral settings do not apply to general systems with a cobweb of bilateral bands, such as the European Monetary System. Since the model has no known analytical solution it is estimated by the method of simulated moments.