The main aim of this paper is to investigate the volatility determinants of crude oil and foreign exchange markets and jump spillover between them. We consider currencies of two major oil-importing countries (India and China) over the sample period of January 1.2013 to October 31, 2019. We find evidence of positive return spillover from the oil to the foreign exchange market; however, there is a lack of return spillover in the other direction. Oil jumps appear to have a negative impact on exchange rate conditional volatility, and the latter responds asymmetrically to disentangled (positive and negative) oil price jumps. We also report disentangled exchange rate jumps significant impact on conditional oil price volatility. These results, however, are asymmetric based on the nature of jumps and alternative oil price series. Finally, we do not find evidence of co-jump between the oil and foreign exchange markets. These results have important implications for investors and policymakers. (C) 2020 Elsevier B.V. All rights reserved.