This study investigates the real estate stock market in Portugal, Italy, Ireland, Greece and Spain from the introduction of the REIT legislation in each country until April 2014. We examine their descriptive statistics and we use various GARCH and asymmetric EGARCH models to their daily returns. The results suggest that the general index of each stock market has a significant impact on real estate stock returns except of the Italian BNS REIT and the Irish GREEN REIT. Except Greece, the general indices tend to report lower standard deviations than the REIT companies. The asymmetry of the volatility response to news seems to be present due to the fact that Italian IGD and BNS, Irish HIBERNIA, Spanish AXIA, MERLIN and PROMORENT along with the Greek Grivalia and TRASTOR report asymmetric transition dynamics for positive and negative shocks.