Stock markets in New York and Toronto jumped significantly higher Tuesday on hopes that trillions of dollars in stimulus spending by governments around the world will be enough to offset the economic damage wrought by the COVID-19 pandemic.

The S&P/TSX composite index closed up 1,342 points, or almost 12 per cent, at 12,571. That's the best day for the TSX's benchmark index in 43 years, dating back to the creation of its predecessor in 1977.

In New York, the Dow Jones industrial average had its best day in almost a century, rising 2,112.98 points, or 11.3 per cent, to 20,704. That's the best percentage increase since 1933.

The rebounds came after the TSX fell to its lowest level since 2012 on Monday, as more parts of Canada's economy slowed to a crawl, with more jurisdictions moving toward lockdowns and mass quarantines.

"You've got to put this in context. We've had some horrific days preceding today," said Natalie Taylor, a portfolio manager with CIBC.

German stocks jumped 11 per cent and British blue chips added nine per cent as both stock exchanges also had their best days since 2008. South Korea's ravaged market climbed 8.6 per cent after the government doubled a planned economic rescue package worth more than $80 billion US.

In China, mainland stocks posted their biggest gain in three weeks, almost three per cent, while Japan's Nikkei soared seven per cent — its biggest daily gain in four years.

Among the reasons for optimism is word out of China that Wuhan, the city where the coronavirus outbreak originated, is scheduled to come out of the lockdown it has been in since the end of January. In all, the city will have been locked down for more than 10 weeks, but the easing is a sign for investors that there may be a light at the end of the tunnel North America has just entered into.

Another reason for optimism is that U.S. lawmakers seem to be lumbering toward some sort of deal in Washington that could see the world's richest economy pour roughly $2 trillion US into offsetting the impact of the virus there, which has shut down large swathes of the economy.

And the G7 group of rich and powerful nations on Tuesday pledged to work together and do whatever it takes to beat the pandemic, including spending money to help poorer vulnerable nations.

Despite the optimism, the volatility that has waylaid markets is showing no signs of dissipating completely. Wall Street's so-called fear index, the VIX, which measures volatility, fell to 52 points on Tuesday. While that's down from a 12-year high it hit earlier this month, it's still more than twice has high as its historic average of 20, which implies that volatility is twice what it normally is.

Ultimately, markets are likely to keep getting hit with every bleak new story about its spread, since the number of cases is still climbing around the world.

"We don't know how long it's going to take to peak. We don't know how to treat it. We don't have a vaccine. So all of those uncertainties are causing a myriad of aftershocks," said Nancy Perez, senior portfolio manager at Boston Private Wealth in Miami.

Others were more hopeful that the market may be nearing a bottom.

"I think that there's some view that we've had the start of a capitulation in the market," Taylor said.