Prices of food crops, which depend on unpredictable factors like the weather, are naturally volatile. However, in recent years we have experienced bouts of extreme food price volatility. These can be a thread to world food security. Especially in developing countries, where households spend a large share of income on food items and about two billion people live off small farms, while often not having access to credit, savings, or storage facilities, large price fluctuations can have devastating and long-term repercussions. In order to be able to anticipate, prepare for, or even mitigate abnormally high price volatility, it is essential to better understand how the many factors suspected to affect volatility exert their impact. Which are the most relevant factors? Is the influence gradual? Or do we, for example, find evidence for the conjecture of a critical stocks-to-use threshold below which volatility increases drastically? We look at three basic food commodities to investigate these questions – wheat, maize, and soybeans. We formulate an exponential ARCH model with additional exogenous covariates and use component-wise gradient boosting to both select variables and estimate the model. While certain factors, e.g. the stocks-to-use ratio, turn out to be important for all three commodities, which variables are informative generally varies by crop. Their influence typically being non-linear, we quantify critical thresholds associated with changes in volatility levels.