We develop a cobweb-type oil market model in which producers’ supply responds positively to the lagged oil price, while consumers’ demand responds negatively to the current oil price. In addition, speculators buy or sell oil to maintain a desired market position and to exploit basis-trade arbitrage opportunities. In the absence of speculators, the oil price, governed by a one-dimensional linear map, converges to its fundamental value when the slope of the consumers’ demand schedule exceeds that of the producers’ supply schedule. When speculators are present, the oil price is determined by a two-dimensional discontinuous piecewise linear map, and both regular and irregular price movements may occur regardless of the relationship between the slopes of the consumers’ demand and producers’ supply schedules. The model reproduces key stylized facts of oil markets, including their excessive volatility and pronounced boom–bust cycles. We also address questions related to regulatory policy.