This paper examines the frequency dynamics of volatility spillovers between Brent crude oil and stock markets in the US (S&P500 index), Europe (STOXX600 index), Asia (Dow Jones Asia index) and stock markets of five vulnerable European Union (EU) countries known as the GIPSI (Greece, Ireland, Portugal, Spain, and Italy). We use the methodologies developed by Diebold and Yilmaz (2012) and Baruník and Křehlík (2018) and the in-sample VaR performance to achieve our objectives. The results show that the spillover effect between the oil and the considered stock markets is time-varying, crisis-sensitive, and frequency-dependent. In addition, this effect had intensified during the onset of the 2008–2009 Global Financial Crisis, the plunge of oil prices that started in the mid-2014, and the occurrence of COVID-19. Furthermore, the results also demonstrate that oil is a net receiver of risk in the system, irrespective of the time horizon. Among the GIPSI markets, the larger and highly indebted EU economies of Italy and Spain are net contributors of risk, while the smaller EU economies of Greece, Ireland, and Portugal as well as Asia are net receivers of risk, also regardless of the time horizons. The US and European stock markets are net contributors of the spillovers, whereas the Asia equity index is a net receiver, irrespective of the frequencies. Finally, the AR(1)-FIGARCH model with the skewed Student-t distribution provides more accurate in-sample estimates in all markets. The hedging is more expensive in the long term than in the short term. The hedging is also more expensive during the ESDC period than the other turbulent periods considered in the study. The hedging effectiveness is also higher in the long term than in the short term, is crisis-sensitive, and depends on the time-investment horizon factor.