The main aim of the paper is to examine if the stock market volatility exhibits a symmetric or an asymmetric response to past shocks, for certain CEE countries (Romania, Hungary, Bulgaria, Poland) over the period May 2004 - September 2014. For the stock markets from East Europe the results are in line with the symmetric volatility, i.e. volatility is similar affected by both positive and negative returns with the same magnitude. For the stock markets from Central Europe the results are consistent with the leverage hypothesis of the asymmetric volatility, i.e. negative and positive returns with the same magnitude have different impact on volatility. Furthermore the volatility is more sensitive to its lagged values in the market place than it is to new information. These results reinforce the diversification principle that has to be considered in portfolio and risk management process.