In this paper, we used the GARCH (1,1) and GARCH-M (1,1) models to investigate volatility and persistence at daily frequency for European and US financial markets. In the study we included fourteen stock indices (twelve Europeans and two Americans), during March 2013 - January 2017. The results of the GARCH (1.1) show that the models are correctly specified for most of the analysed series (except for the WIG30 index). The study found that the BET-BK index recorded the lower persistence of volatility, meaning that the conditional volatility tends to revert faster to the long-term mean than the other stock indices analysed. In the case of the GARCH-M (1.1) model, the variance coefficient in the mean equation was statistically significant and positive (thus confirming the hypothesis that an increase in volatility leads an increase in future returns), only for six of the analysed series. The strongest relationship was recorded for the US index, S&P500. It is also recorded for the Romanian stock indices: BET and BET-BK. For the BET index, the conclusions are in line with the results of previous studies.