Global stock markets experienced a dual shock in 2020 due to the impact of the global health crisis, parallel to a simultaneous shock derived from the Saudi Arabia and Russia oil price war. The dual shock fueled oil market volatility with lasting effects as the global economy is immersed in an energy crisis combined with high inflationary pressures exacerbated by heightened energy costs. This research paper implemented GARCH and FIGARCH models on daily returns from 31 December 2015, to 9 December 2021, to examine volatility persistence and long memory processes. The world’s most prominent economies are represented by the G7, E7 and the GCC stock markets. Particular attention was devoted to the case of Kuwait as an example of a small oil-dependent economy. The research findings suggest evidence of volatility persistence across the markets, as reported by the GARCH (1,1) model. The FIGARCH (1,1) did not offer significant evidence of long memory processes except for the cases of FTSE 100, BIST 100, IDEX, BSE 100 and Bahrain.