In the last decade, interest in exotic options has been growing, especially in the over-the-counter currency market. In this paper we consider Iookback currency options, which are path-dependent. We show that a one-state variable binomial model for currency Iookback options can be constructed with the same computational complexity, or should we say simplicity, as the standard binomial model. Furthermore, the model allows us to investigate a second very important feature of real-life lookback option contracts -- the observation frequency.