Equity markets rallied Monday as governments across the world started to ease coronavirus lockdown measures, but oil prices tumbled as a supply glut overwhelmed output cuts.

US markets followed Asia and Europe higher after virus figures from some of the worst-hit countries provided hope that the peak of the crisis may have passed.

Stocks kicked off the week "in optimistic fashion," said Joshua Mahony, senior market analyst at IG trading group.

Ending lockdowns means one step towards the resumption of economic activity.

Germany on Monday said it had seen the slowest pace of infections and deaths since March 29.

In Italy, wholesale stores and restaurants will be allowed to resume business on May 4, Spain on Sunday let children play outside, and Swiss hairdressers, massage parlors, florists and garden centers are reopening.

Meanwhile, New York Governor Andrew Cuomo said that a first stage of a reopening would start on May 15 if hospitalizations decreased.

British Prime Minister Boris Johnson said Britain was beginning to "turn the tide" but it was too early to ease the lockdown.

Despite the gains, plenty of commentators are skeptical that the rally can continue.

"Ultimately the stock market is in a mode of blocking out bad news right now and is squeezing the 'worst is behind us' narrative for all it is worth," Briefing.com analyst Patrick O'Hare said, warning that the market had become "divorced from fundamental reality."

The Bank of Japan on Monday ramped up its emergency monetary easing, and forecast the economy could contract by up to five percent in the year to March 2021.

The stimulus move was "largely symbolic, but it's better than doing nothing", Taro Saito, senior economist at NLI Research Institute, told AFP.

The Federal Reserve and the European Central Bank meet this week, with announcements due on Wednesday and Thursday, respectively. The Fed on Monday expanded its crisis lending facility for states and cities to include dozens more smaller cities and counties across the country.

In the US, the calendar also includes the government's first assessment of US growth in the first quarter and earnings from Amazon, Boeing, Pfizer and other US giants.

On oil markets, WTI lost 25 percent, having already endured a hammering last week.

Worries about a lack of storage amid plunging demand for crude overshadowed signs that some countries -- including Kuwait and Algeria -- are starting to slash production in line with a deal hammered out this month.

With signs of an easing in coronavirus, governments are looking to ease some lockdown restrictions that have left cities like ghost towns and pummelled economies
With signs of an easing in coronavirus, governments are looking to ease some lockdown restrictions that have left cities like ghost towns and pummelled economies Agence France-Presse / Kena Betancur

New York - Dow: UP 1.5 percent at 24,133.78 (close)

New York - S&P 500: UP 1.5 percent at 2,879.57 (close)

New York - Nasdaq: Up 1.1 percent at 8,730.16 (close)

London - FTSE 100: UP 1.6 percent at 5,846.79 (close)

Frankfurt - DAX 30: UP 3.1 percent at 10,659.99 (close)

Paris - CAC 40: UP 2.6 percent at 4,505.26 (close)

EURO STOXX 50: UP 2.6 percent at 2,882.09 (close)

Tokyo - Nikkei 225: UP 2.7 percent at 19,783.22 (close)

Hong Kong - Hang Seng: UP 1.9 percent at 24,280.14 (close)

Shanghai - Composite: UP 0.3 percent at 2,815.49 (close)

West Texas Intermediate: DOWN 25 percent at $12.78 per barrel

Brent North Sea crude: DOWN 7 percent at $19.99 per barrel

Euro/dollar: UP at $1.0828 from $1.0823 at 2100 GMT on Friday

Dollar/yen: DOWN at 107.25 yen from 107.51 yen

Pound/dollar: UP at $1.2427 from $1.2367

Euro/pound: DOWN at 87.12 pence from 87.51 pence