Abstract The potential presence of jumps and time-varying volatility in convenience yields can lead to abnormally fat tails, which has implications for investment in storage capacity, leasing and drilling for crude oil. In this paper we evaluate the potential for these features in convenience yields. To that end, we analyze the rate of change in convenience yields for five futures prices time horizons (1, 3-, 6-, 9- and 12-month ahead), allowing for the both jumps and time-varying volatility. We find that both features exert a statistically important effect on convenience yields, for each of the five time horizons. We also calculate the implied probability that at least one jump would occur on any date, which reveals a period of relative calm at the start of the fracking boom, when large stockpiles built up at the trading hub for West Texas Intermediate, and a period of considerable churn, after the ban on exporting crude oil was lifted. Both elements underscore a linkage between inventory holdings and convenience yields.