This paper investigates the cointegration between possible determinants of crude oil futures prices during the COVID-19 pandemic period. We perform comparative analysis of WTI and newly-launched Shanghai crude oil futures (SC) via the Autoregressive Distributed Lag (ARDL) model and Quantile Autoregressive Distributed Lag (QARDL) model. The empirical results confirm that economic policy uncertainty, stock markets, interest rates and coronavirus panic are important drivers of WTI futures prices. Our findings also suggest that the US and China's stock markets play vital roles in movements of SC futures prices. Meanwhile, CSI300 stock index has a significant positive short-run impact on SC futures prices while S\&P500 prices possess a positive nexus with SC futures prices both in long-run and short-run. Overall, these empirical evidences provide practical implications for investors and policymakers.