In light of current high and volatile energy and food prices, we examine the daily dynamics of the conditional variance-covariance matrix and price discovery in European vegetable oils. We find that energy prices chiefly influence vegetable oil trends, while stock-to-use ratios significantly impact variance-covariance dynamics when considering their specific cold filter plugging point (CFPP). This technical detail robustly demonstrates interplays among vegetable oils based on economic principles of complementarity and substitutability, even amid the pandemic and the Russian-Ukrainian conflict. Moreover, both marginal distributions and volatility dependence structures relate to distinct economic fundamentals, enhancing our understanding of the market's complexity.