We introduce tractable models for commodity derivatives pricing with inventory and volatility eects, and illustrate with applications to the oil market. We contribute to the existing literature in several respects. First, whereas the previous literature uses futures data for investigating the relationship between inventory and volatility, we use the information available in options traded on futures. Second, performance assessment in the previous literature has primarily evolved around explaining moments of data or forecasting prices of futures. Instead, we asses the performance of our model by considering both the ability of explaining prices in-sample and out-of-sample - assessing both the pricing-performance and the hedging-performance of the models. Third, we model the futures surface rather than the spot price process, and from the no-arbitrage relationship between spot and futures prices we limit the number of parameters to calibrate. We introduce a new, maturity-wise calibration method compatible with this modeling methodology. Fourth, we use actual data on inventories rather than a proxy. Fifth, our model is very exible and allows for testing several dierent types of relationships between inventory and volatility.