Purpose – The aim is to evaluate the performance of symmetric and asymmetric ARCH models in forecasting both the one-day-ahead Value-at-Risk (VaR) and the realized intra-day volatility of two equity indices in the Athens Stock Exchange. Design/methodology/approach – Two volatility specifications are estimated, the symmetric generalized autoregressive conditional heteroscedasticity (GARCH) and the asymmetric APARCH processes. The data set consisted of daily closing prices of the General and the Bank indices from 25 April 1994 to 19 December 2003 and their intra day quotation data from 8 May 2002 to 19 December 2003. Findings – Under the VaR framework, the most appropriate method for the Bank index is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one-step-ahead intra-day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index. Originality/value – As concerns the Greek stock market, there are adequate methods in predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.