•Causal links in volatility between oil prices and several exchange rates are examined.•The analysis is carried out in the time-frequency space using the wavelet-Granger causality method of Olayeni (2016).•Possible asymmetries in volatility spillovers coming from good and bad volatility are analyzed.•Causal flows are more pronounced at longer time horizons and from currency markets to the crude oil market.•Bad volatility tends to predominate over good volatility. This paper investigates the causal linkages in volatility between crude oil prices and six major bilateral exchange rates against the U.S. dollar in the time-frequency space using high-frequency intraday data. Special attention is paid to the potential asymmetries in the causal effects between oil and forex markets. The wavelet-based Granger causality method proposed by Olayeni (2016) is applied to quantify the causal relations in the time and frequency domains simultaneously. Moreover, the realized semivariance approach of Barndoff-Nielsen et al. (2010) is used to account for possible asymmetries in the transmission of volatility shocks. The empirical results show that the significant causal links between oil prices and exchange rates are mainly concentrated in the long-run and during periods of increased economic and financial uncertainty such as the global financial crisis and the subsequent European sovereign debt crisis. Further, the causal effects from currency markets to the crude oil market are stronger than in the opposite direction, consistent with the forward-looking nature of exchange rates, the role of the U.S. dollar as the key invoicing currency for global oil trading and the expanding financialization of the oil market since the mid-2000s. In addition, significant asymmetries coming from good and bad volatility are found at longer horizons. Specifically, bad volatility seems to dominate good volatility in terms of the importance of transmission of volatility shocks.