Several drivers may generate market instability, but the partial contribution of different factors is still debated. We investigate how market-based drivers influence the global price volatility of three major grains: wheat, corn, barley. We adopt a Seemingly Unrelated Regression Equations model, in order to investigate potential common patterns. We compare inter-annual, intra-annual, and global volatility, to conclude on short-run and long-run dynamics of markets instability. We quantify the negative relationship linking (temporal) arbitrage and grain price volatility and conclude on the effects of supply movements on price volatility.