Global stocks are extending gains on the news.

• UK’s FTSE 100 index up 2.14% to 6,352
• Germany’s Dax up 2.7% to 12,345
• France’s CAC 40 up 2.48% to 4,979
• Italy’s FTSE MiB up 2.99% to 19,537
• Dow Jones up 0.92% to 25,979
• Nasdaq up 0.57% to 9,663
• S&P 500 up 0.78% to 3,104

This compares with 41.8 in April. The UK and European services PMIs were also revised higher, even though they indicated further contraction, while China’s services index jumped to the highest in nearly 10 years and pointed to growth.

The US services business activity index from IHS Markit posted 37.5 in May, up from April’s record low of 26.7 and slightly higher than the flash estimate of 36.9. Any reading below 50 indicates contraction. This means the downturn in services eased last month as some businesses returned to work, but was still the second-biggest decline since data collection began in October 2009.

We are waiting for the more important ISM survey, out in four minutes.

The opening bell has rung on Wall Street.

• Dow Jones up 230 points, or 0.9%, at 25,973
• Nasdaq up 41 points, or 0.4%, at 9,649
• S&P 500 up 22 points, or 0.7%, at 3,102

The ADP figures come before Friday’s official non-farm payrolls numbers.

ADP says:

The National Employment Report uses the same time period the Bureau of Labor and Statistics uses for their survey. As such, the May NER does not reflect the full impact of Covid-19 on the overall employment situation.

Even so, the much smaller-than-expected rise in unemployment in May, by 2.76m, should cheer financial markets. It is another big number, but nowhere near April’s revised figure of 19.6m job losses.

European stock markets continue to march higher. The FTSE 100 index in London is now 1.2% ahead, while Germany’s Dax and Italy’s FTSE MiB have each gained 2.3% and France’s CAC 40 is 1.97% higher.

Large businesses (with 500 or more employees) accounted for the bulk of the job cuts, shedding 1.6m. The service sector was worst affected with almost 2m job losses, and 794,000 factory workers also lost their jobs. You can read the report here.

In other travel news, Spain is working on plans to open its borders to tourists from lower-risk Covid-19 countries, possibly as early as 21 or 22 June, according to its tourism ministry.

Spain is due to lift its state of emergency on Sunday, 21 June, and could reopen its borders around that time -- earlier than the previously targeted date of 1 July. Reuters reported a tourism ministry spokesman as saying:

We want to reactivate and accelerate international mobility but starting with areas in epidemiological situations.

Here is our story about Tui’s compensation deal with the US aircraft maker Boeing, Lufthansa’s first-quarter losses and Wizz Air’s full-year profit.

The global MSCI index, which tracks shares in 49 countries, is still trading at a three-month high, up 1.14%.

Stock markets are still pushing higher, lifted by economic optimism.

• UK’s FTSE 100 index up 63 points, or 1.02%
• Germany’s Dax up 2.23%
• France’s CAC 40 up 1.83%
• Italy’s FTSE MiB up 2.08%

US stock futures are pointing to a higher open on Wall Street later. The Dow Jones is seen opening 175 points higher, and the Nasdaq is expected to gain some 33 points at the open.

The Bank of England has issued a statement following the earlier Sky News report that governor Andrew Bailey has told banks to step up preparations for the possibility of a no-deal Brexit at the end of the transition period on 31 December.

The central bank said:

It is fundamental to the Bank of England’s remit that it prepares the UK financial system for all risks that it might face. In performing that role, the governor meets the leadership of UK banks on a very regular basis. As we have said previously, the possibility that negotiations between the UK and EU over a future trading relationship might not conclude in a deal is one of a number of outcomes that UK banks need to prepare for over the coming months.

Oil prices are now falling, after rallying to three-month highs earlier. Brent crude is down 1.62% at $38.93 a barrel after rising through $40 a barrel, while US crude has lost 1.77% to $36.16 a barrel.

Saudi Arabia, the world’s largest oil producer and the leader of the Opec oil cartel, and Russia, which is not in Opec, have reportedly reached a preliminary agreement to extend the existing record oil production cuts by one month.

Sources told Reuters:

Any agreement on extending the cuts is conditional on countries who have not fully complied in May deepening their cuts in upcoming months to offset their overproduction.

The Opec+ group, which includes Russia, agreed last month to cut output by a record 9.7m barrels a day, equivalent to about 10% of global output.

But there are now doubts as to whether an early meeting of Opec and its allies to extend the production cuts will take place tomorrow, pushing oil prices lower. Bloomberg reported that the meeting won’t happen unless problems around compliance are resolved.

Zoom, the booming video conferencing firm, reported its first-quarter results last night. My colleague Mark Sweney has taken a closer look.

Zoom may be booming as the global coronavirus lockdown moves work and social life to cyberspace but deep-pocketed rivals including Microsoft, Google and Facebook are taking aim as video conferencing becomes a staple of daily life.

On Tuesday, Zoom, which has been catapulted from a relatively unknown video service to a household name during the coronavirus pandemic, reported first-quarter results that were impressive on almost every measure.

Revenue surged by 169% to $328m (£261m) in the three months to the end of April, prompting the company to double revenue guidance for this year. The number of people attending meetings and gatherings on any one day peaked at 300 million in April. In December it was 10 million a day.

One analyst called Zoom’s results “one of, if not the greatest quarter in enterprise software history” and its share price enjoyed an initial bounce. However, Zoom’s stock dropped in after-hours trading on Tuesday as investors and analysts began to worry about its ability to cope with competitors aiming to muscle in on the video-conferencing boom.

In March, Microsoft, an aggressive competitor against Zoom for paying business customers with Microsoft Teams, announced it is to launch a version of its video-conferencing service for consumers.

The following month, Facebook, the world’s biggest social networking site, introduced a group video-calling feature called Messenger Rooms that prompted a dip in Zoom’s share price. In April, Google announced it was to make Meet, another Zoom competitor in the business video market, available for consumer use.

The hotel chain Travelodge is expected to launch insolvency proceedings in the form of a company voluntary arrangement (CVA) later today, allowing it to cut its rent by around 40% over the next 18 months, reports my colleague Joanna Partridge.

The 580-hotel chain is owned by investment firms include Goldman Sachs, Avenue Capital and GoldenTree and has £100m in cash reserves. It has been locked in a battle with its landlords since late March when it initially refused to pay rent for the second quarter of the year, and the company is now offering landlords a sweetened deal in a bid to win them over.

Travelodge’s shareholders have pledged to inject up to £40m in new equity, and to raise £100m in new debt. Unlike a traditional CVA, Travelodge’s plan does not propose any hotel closures or job cuts among its 10,000 staff, and the rent reduction will last until the end of 2021.

As reported earlier, Nissan warned again today that its Sunderland manufacturing plant is still under threat if the UK leaves the EU without a trade deal.

Sky News is reporting that the Bank of England’s governor, Andrew Bailey, has told banks to step up their plans for a no-deal Brexit. He held a conference call with the UK’s biggest lenders yesterday.

Britain left the EU on 31 January but is still in a transition period, until the end of December. Both sides began a fourth round of virtual negotiations yesterday to try and hammer out a trade agreement before the end of the year.

The UK wants binding commitments from the EU to secure its finance industry’s access to the bloc, but has met with rejection.

UK firms cut jobs at the second-fastest pace since the survey began in January 1998, according to Markit, which compiles the PMI with the Chartered Institue of Procurement & Supply (CIPS). Factory and services activity both declined in May, but manufacturing proved a bit more resilient, with the index at 35.0.

Duncan Brock, group director at CIPS, said:

May’s survey data painted a deeply concerning picture of a lockdown slowdown across the service sector as employment dropped at the second fastest rate on record, pipelines of new work were woefully empty and business confidence continued to suffer.

As the pandemic progressed any hoped-for bounceback in business output never really got going in May following the previous month’s awful results, though a modicum of recovery will offer small respite in some sectors. Pockets of trading began again as firms began adapting to social distancing measures, though only 15% of companies reported a rise in new orders this month.

In this aggressively unsympathetic marketplace, supply chain managers voiced their concerns that any significant improvement is unlikely to happen at least in the medium term. As supply chains began to awaken from their deep slumber, continuing logistics challenges increased costs for some firms though reduced wage bills helped to alleviate the pressure.

As restrictions are eased, there is still extreme uncertainty about how the pandemic will pan out. Continued anxiety about the coronavirus means consumer spending may not be the wind beneath the sails of any immediate return to pre-virus economic activity.

The German services PMI, at 32.6, is also better than the flash estimate and up from April’s record low of 16.2. But the unemployment rate in Europe’s biggest economy has gone up to 6.3%, more than the expected 6.2%.

And here is France. Its services PMI for May comes in at 31.1, up from 10.2 in April and higher than the flash estimate of 30.5.

The composite index, capturing the private sector, is at 32.1, also up from the flash estimate and April’s 11.1.

Eliot Kerr, economist at IHS Markit said:

Following April’s record decline, the latest PMI data pointed to a further contraction in French private sector business activity during May. Given the low likelihood of businesses being open in April but closed in May, the latest reduction in output reflects the deteriorating demand conditions that firms now face.

That said, rates of activity decline at both manufacturers and service providers did ease in May, and we should expect this trend to continue as more and more firms reopen for business. Although we might see further contractions while demand remains subdued, PMI figures should continue to climb in the months ahead barring a second outbreak.

The Italian services PMI has risen to 28.9 from April’s record low of 10.8 in the final reading, slightly better than expected, but still pointing to a sharp decline in activity in the eurozone’s third-largest economy.

The composite output index posted 33.9 in May, to signal a further substantial contraction in Italian private sector output, albeit up from April’s nadir of 10.9. Services saw the sharpest decline, with manufacturers registering only a modest drop in output.

Lewis Cooper, economist at IHS Markit said:

The Covid-19 pandemic and associated lockdowns continued to weigh heavily on the performance of the Italian service sector during May, with further substantial reductions in both business activity and new orders. With the economy beginning to reopen and restrictions loosening, however, the falls softened from April’s records.

Meanwhile, job cuts continued, with staff numbers falling at the second-quickest rate on record. Firms registered renewed optimism with regards to activity over the year ahead, but sentiment remained among the lowest in the series history.

A similar trend was seen in the manufacturing sector, where the downturn continued, albeit at a softer pace. Nonetheless, the Italian economy remains in an extremely challenging period. Preliminary GDP estimates for the first quarter of 2020 recorded a decline approaching 5% on a quarterly basis, and PMI data for the second quarter so far point to another considerable contraction.

On the markets, the FTSE 100 index has extended its gains and is trading more than 1% higher at 6,286, up 65 points.

Germany’s Dax is 1.1% ahead at 12,153, France’s CAC 40 has added 1.2% to 4,917 and Italy’s FTSE MiB has posted an even stronger gain of 1.5%,to 19,254.

Spain’s Ibex rose more than 1% in early trading but is now only 0.68% ahead at 7,458 after the latest services and private sector surveys, which confirmed the economy recovered from April’s trough, but remained very weak.

Paul Smith, economics director at IHS Markit said:

Despite the easing of lockdown measures, economic activity in Spain remained severely curtailed during May. Whilst rising markedly from the extreme readings of April, latest PMI readings remain considerably low and confirm that the Spanish economy will likely experience a contraction in second quarter GDP pushing towards double digits.

Spain’s final PMI readings for May from IHS Markit for the country’s services industries and the private sector as a whole are out.

They are slightly better than the flash estimates, but still indicate sharp contractions, as they are far below the 50 mark that divides expansion from contraction.

Markit says the two weakest sectors within services remained hotels and restaurants and transport and storage.

As Brexit talks have resumed this week, Nissan is warning that its Sunderland manufacturing plant is still under threat if the UK leaves the European Union without a trade deal, my colleague Mark Sweney writes.

Last week, Nissan said that the UK’s largest car manufacturing plant would stay open as it announced plans to cut £2.3bn in costs worldwide. However, the carmaker has said it would need to “improve efficiency” at the factory in the north-East of England, which employs 6,700 staff.

Today, Ashwani Gupta, the Japanese company’s global chief operating officer, warned that with the European Union Sunderland factory’s biggest customer the tariffs that would come with a no-deal Brexit would mean manufacturing in Britain would not be viable.

“You know we are the number one carmaker in the UK and we want to continue,” he told the BBC. “We are committed. Having said that, if we are not getting the current tariffs, it’s not our intention but the business will not be sustainable. That’s what everybody has to understand.”

And we are off.

• UK’s FTSE 100 index up 0.9%
• Germany’s Dax up 1.1%
• France’s CAC 40 up 1.1%
• Spain’s Ibex up 1%