Stocks around the world jumped on Monday after some of the hardest-hit areas offered sparks of hope that the worst of the coronavirus outbreak may be on the horizon.

U.S. stocks climbed 4.5% in morning trading, following up on gains that were nearly as big in Europe and Asia. In another sign that investors are feeling more optimistic about the economy’s path, the yield on the 10-year Treasury rose toward its first gain in four days.

New coronavirus infections and deaths are showing signs of slowing in Italy, Spain and France. The center of the U.S. outbreak, New York, also reported a dip in the number of daily deaths, though authorities warned it’s too early to tell whether it’s just a blip or the start of a trend. The U.S. is still bracing for a surge of upcoming deaths due to COVID-19.

The S&P 500 was up 4.5%, as of 10:30 a.m. Eastern time. It’s already on pace to erase all its losses from the prior week, when the government reported a record number of layoffs sweeping the economy. The Dow Jones Industrial Average rose 964 points, or 4.6%, to 22,017, and the Nasdaq was up 4.5%.

Markets have been waiting anxiously for signs that the rate of new infections may stop accelerating at some point. The explosion of cases has caused businesses around the world to shut down, layoffs to soar and flights to cancel as authorities hope to slow the spread of the virus. The strict measures mean markets are bracing for a sudden, steep recession.

But a peak in new cases would give some clarity on how long the downturn may last and how deep it would be. Until then, markets are grasping at guesses.

“Hundreds of people are passing away each day from the pandemic, but less so than previous days, giving markets hope that the lockdown measures are finally starting to prove effective,” Jeffrey Halley of Oanda said in a commentary.

“Like the rest of the world, financial markets are searching for any slivers of hope,” he said.

The S&P 500 is still down more than 23% since its record set in February, but the losses have been slowing since Washington promised massive amounts of aid to prop up the economy.

“Since this is a public health crisis, the response has been extreme,” Morgan Stanley strategists wrote in a report. “There are literally no governors on the amount of monetary or fiscal stimulus that will be used in this fight.”

In Japan, the prime minister said Monday that he’s preparing to announce a 108 trillion yen ($1 trillion) package to bolster the world’s third-largest economy. It would be Japan’s largest-ever package for the economy and nearly twice as much as expected.

Japan’s economy was already shrinking late last year before the outbreak forced the global economy into a protective coma induced by health authorities.

The announcement pushed Japan’s Nikkei 225 index to surge 4.2%. Elsewhere in Asia, South Kora’s Kospi jumped 3.9%, and Hong Kong’s Hang Seng rose 2.2%.

In Europe, Germany’s DAX returned 5.8% and France’s CAC 40 jumped 4.3%. The FTSE 100 in London rose 2.9%.

The yield on the 10-year Treasury yield rose to 0.64% from 0.58% late Friday. Yields tend to rise when investors are raising their expectations for economic growth and inflation.

Crude oil fell, giving up some of its huge gains from the prior week when expectations rose that Saudi Arabia and Russia may cut back on some of their production.

Demand for oil has plummeted due to the weakening economy, and any cutback in production would help prop up its price. A meeting between OPEC, Russia and other producers initially planned for Monday, though, was reportedly pushed back to Thursday.

Benchmark U.S. crude fell $1.35 to $26.99 per barrel after surging nearly $7 last week. It started the year above $60 per barrel.

Brent crude, the international standard, lost 89 cents, or 2.6%, to $33.22 per barrel.