Many asset prices, including exchange rates, exhibit periods of stability punctuated by infrequent, substantial, often one-sided adjustments. Statistically, this generates empirical distributions of exchange rate changes that exhibit high peaks, long tails, and skewness. This paper introduces a GARCH model, with a flexible parametric error distribution based on the exponential generalized beta (EGB) family of distributions. Applied to daily US dollar exchange rate data for six major currencies, evidence based on a comparison of actual and predicted higher-order moments and goodness-of-fit tests favours the GARCH-EGB2 model over more conventional GARCH-t and EGARCH-t model alternatives, particularly for exchange rate data characterized by skewness. Copyright © 2001 John Wiley & Sons, Ltd.