Previous literature on volatility links between food and energy prices is scarce and mainly based on parametric approaches. We assess this issue by using a semiparametric GARCH model recently proposed by Long et al. (2009), which is essentially a nonparametric correction of the parametric conditional covariance function. We focus on price links between crude oil, ethanol and sugar prices in Brazil. Results suggest strong volatility links between the prices studied. They also suggest that parametric approximations of the conditional covariance matrix may lead to misleading results and can be improved using nonparametric techniques.