In the article we first introduce asymmetric response of equity volatility to return shock and then the effect of good and bad news to volatility for empirical time series of EUR/USD (EUR currency against US dollar) exchange rates in the pre-crisis period, during the crisis and the post-crisis period. We found that GARCH-class models with normal errors are not capable to capture fully the leptokurtosis in empirical time series, while Student´s t and GED errors provide better description for the conditional volatility. Then, we alternatively develop forecasting models based on the ARIMA/GARCH methodology and on the neural approach. In the direct comparison between statistical and neural models, the experiment shows that the neural approach clearly improve the forecast accuracy.