The paper studies the return–volatility relationship in a range of commodities. We develop a commodity price model and show that the volatility of price changes can be positively or negatively related to demand shocks. An “inverse leverage effect”—the volatility is higher following positive price shocks—is found in more than half of the daily spot prices. The effect is weaker in the three-month futures market, the period after mid-2000s and monthly historical volatility measures. Only crude oil exhibits a “leverage effect”—higher volatility follows a negative shock—and the reason is explored in the context of its special market structure.

中文翻译：

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商品市场的不对称波动

该论文研究了一系列商品的收益-波动性关系。我们开发了一个商品价格模型，并表明价格变化的波动可能与需求冲击呈正相关或负相关。超过一半的每日现货价格都存在“反向杠杆效应”——价格受到积极冲击后波动性更高。三个月期期货市场、2000 年代中期之后的时期以及月度历史波动率指标的影响较弱。只有原油表现出“杠杆效应”——在负面冲击之后波动性更高——其原因是在其特殊的市场结构的背景下进行探讨的。