Global stocks are pushing higher again as investors exhibit growing optimism. Wall Street, for example, is surging again Tuesday morning.

S&P 500 futures were up 3.5% before the open after the index surged 7% on Monday. The FTSE 100 has jumped 2.8% in London even though UK Prime Minister Boris Johnson, who is battling a coronavirus infection, has been moved into intensive care.

The MSCI All Country World Index is up 5.5%. And the CNN Business Fear & Greed Index, which tracks market sentiment, has moved out of the “extreme fear” range, suggesting the mood is improving.

The rally, which was triggered by trillions of dollars in global stimulus and signs that outbreaks in Italy, Spain and New York may be losing steam, is providing some relief. The VIX, a measure of stock market volatility, is at its lowest level in a month.

But market strategists are warning that the trajectory of the crisis remains unpredictable. And they note that it remains difficult to price assets in certain markets.

“Behind the tentative stability in asset prices, economies and markets are nowhere near normal,” John Normand, head of cross-asset fundamental strategy at JPMorgan, told clients in a note on Friday.

It’s bear market territory now for Wall Street as stocks plunge

Normand observed that market depth, or the amount and breadth of open orders, “remains unusually poor, even for a recession.” While liquidity always drops during a recession, it dissipated during the current crisis even faster than in the 2008, he said.

JPMorgan has said that conditions are right to start slowly increasing exposure to some riskier assets, citing recession-like prices, lighter selling pressure and extraordinary fiscal stimulus.

But the bank still sees the coronavirus itself as a huge wildcard. Normand noted that even though the infection rate in Italy and the rest of Europe is slowing, it “remains too high to have much confidence on the duration of lockdowns [and] social distancing and therefore the duration and depth of the recession.”

His takeaway: “Risky markets will remain volatile as long as infection rates preserve growth and earnings uncertainty.”

Others are urging caution, too.

“We believe it is too early to definitively call for a turn in the pandemic, and investors should continue to expect heightened volatility,” Mark Haefele, chief investment officer at UBS Global Wealth Management, told clients Tuesday. “However, this week’s rebound offers a further reminder of the importance of staying invested.”

How do you restart an economy? Ideas take shape

Signs that the pandemic could be easing in Italy, Spain and New York are sparking a fierce discussion among health experts, economists and investors: How and when should lockdowns be lifted?

Pressure is building on governments to explain their exit plans because of the mounting economic costs of measures designed to contain the coronavirus, my CNN Business colleague Charles Riley reports. Austria on Monday said it would gradually begin to reopen shops after Easter, becoming the first country in Europe to do so.

Wall Street turmoil to continue – get used to it

But restarting economic activity without allowing a resurgence of the novel coronavirus is a huge challenge.

One proposal: In Germany, where 103,000 people have tested positive for coronavirus and more than 1,800 have died, a group of economists, lawyers and medical experts are recommending a revival that would allow specific industries and workers to gradually resume their activities.

We’re not there yet. The German government has said it’s too soon to provide a timetable for lifting restrictions. And countries are still enacting fresh protective measures, with Japanese Prime Minister Shinzo Abe declaring a state of emergency on Tuesday.