We construct models which enable a decision maker to analyse the implications of typical time series patterns of daily exchange rates for currency risk management. Our approach is Bayesian where extensive use is made of Markov chain Monte Carlo methods. The effects of several model characteristics (unit roots, GARCH, stochastic volatility, heavy-tailed disturbance densities) are investigated in relation to the hedging strategies. Consequently, we can make a distinction between statistical relevance of model specifications and the economic consequences from a risk management point of view. We compute payoffs and utilities from several alternative hedge strategies. The results indicate that modelling time-varying features of exchange rate returns may lead to improved hedge behaviour within currency overlay management. Copyright © 2000 John Wiley & Sons, Ltd.