In this paper, we propose a bounded influence estimation (BIE) and outlier detection procedure for the ARCH and GARCH models of foreign exchange rates. It is known that due to outliers, exchange rates present heavy tails that are not explained by standard ARCH and GARCH models. The proposed BIE is robust against departure of the disturbances from normality, and its performance is compared with the MLE and semi-parametric models. A method of detection of additive outliers is developed. The economic events that lead to outliers in foreign exchange rates are identified and studied.