This paper investigates the dynamics of volatility and conditional correlations between corn and soybean prices in the spot and futures markets. Faced with price and production risks, farmers must use all information available in their risk management process, both in their product's spot and futures markets, and in related products' markets, either domestic or foreign. Dynamic conditional correlation specifications with a bivariate GARCH model are employed, with data for Brazilian and U.S. markets in the period 2004-2017, during which several structural changes and extreme climate phenomena have occurred. We find the highest correlations between the corn and soybean spot markets, and evidence of spillovers in both products in the spot and futures markets. We also find that the financial crisis have significantly affected the relationship between the corn and soybean markets. We also find that in periods of increased conditional correlation between the soybean and corn markets, there is an increase in the optimal hedge ratio for risk management strategies involving corn futures contracts at B3 and Chicago Mercantile Exchange.