Crude futures in New York were near $40 a barrel, after advancing more than 10% at one point on Monday. It comes after early findings showed that a vaccine developed by Pfizer Inc. and BioNTech SE protects most people from the virus.

While headline prices are gaining, there have also been sharp moves in the structure of the futures curve. Brent for six months ahead was at its strongest versus 12 months out since March, a sign that traders are growing more positive on supply and demand balances for the second half of the year. In another sign of strength, the Middle Eastern Dubai benchmark was trading in a bullish backwardated structure.

Crude has mirrored a wider rally in equities markets on optimism that a vaccine will help mobility return to normal levels. In the near term, the market continues to wrestle with a mixed demand picture, with Europe still under new virus restrictions. Consumption is improving in China, while oil demand in Japan is roughly back to normal.

“For oil markets, the advent of vaccines could turn the focus from the short-term supply-demand question onto how the oil market might cope with a recovery in demand in 2021,” said Callum MacPherson, head of commodities at Investec Bank Plc. “It may help to embolden governments into easing lockdowns.”

Monday’s price rally came after a mammoth short position had built up in the oil market. That forced a buying spree as traders rushed to cover those bearish bets. It also triggered a rally in some refined products, most notably jet fuel.

See also: Goldman Sees Oil Hitting Covid-19 Speed Bump Before Tightening

There are reasons to remain cautious. Global oil demand still won’t get back to pre-virus levels until the end of next year, JPMorgan Chase & Co. analysts including Natasha Kaneva wrote in a report. The chief executive of Vitol Group also warned on Tuesday that there are difficult months ahead for the market.