London's FTSE 100 share index rose more than 3% after having sunk 7.7% in the previous session.

Markets were battered on Monday in reaction to the threat of an oil price war between Russia and Saudi Arabia.

But after falling as much as 30% on Monday, oil prices also saw some recovery, with Brent crude rising 8%.

The main share indexes in France and Germany were also up by more than 3% on Tuesday morning.

The response has been a fairly standard one when it comes to stock market behaviour, said Kathleen Brooks, director at Minerva Analysis.

"Markets are so emotional, it's unbelievable," she said. "Act first, think later. This was the same in 2008, you have these massive declines and then the market is on pause."

She said she thought markets would recover eventually, as "if you look at long-term charts they always recover".

However, in the short term, "we could see another decline if we don't see the stimulus that's required. We need to hear more positive things because that's when stock markets go up."

On Monday, US President Donald Trump said he would be taking "major" steps to strengthen the US economy against the impact of the coronavirus outbreak, and analysts said this had helped to lift markets.

The rebound has also been helped by a slowdown in reported cases of coronavirus in China, according to Michael Hewson, chief market analyst at CMC Markets UK.

"This optimism, along with expectations around further central bank actions is, for now, offsetting the news that the whole of Italy has gone into lockdown and the Spanish government has taken the decision to close all schools and universities in Madrid," he said.

Some investors will think that yesterday's panic was an over-reaction, and that some shares now look cheap.

That would explain the rise this morning of Tui, the holiday company, and the small gains shown by Royal Dutch Shell and BP. The seesaw pattern of trading is nothing new.

One of the curious features of bear markets, where prices fall more than 20% from their peak, is that they normally contain several one-day rallies within the overall fall.

That has been a feature of US and UK bear markets since the crash of 1929, and has already been part of the pattern of trading since the coronavirus struck.

Today's rally could easily be followed by another fall.

In Asia, shares in Japan rose after Prime Minister Shinzo Abe said his government would work closely with the central bank to boost the economy.

Japan's benchmark index, the Nikkei 225, had started Tuesday more than 3% down but bounced back following Mr Abe's comments to stand 1% higher.

In Hong Kong, the main Hang Seng market rose 1.4% buoyed by Japan's moves to calm investors. The index had fallen more than 4% on Monday.

Why should I care if stock markets fall?

Many people's initial reaction to "the markets" is that they are not directly affected, because they do not invest money.

Yet there are millions of people with a pension - either private or through work - who will see their savings (in what is known as a defined contribution pension) invested by pension schemes. The value of their savings pot is influenced by the performance of these investments.

So big rises or falls can affect your pension, but the advice is to remember that pension savings, like any investments, are usually a long-term bet.

Monday's market meltdown was sparked by a fallout between major oil exporters Russia and Saudi Arabia over output levels.

On Friday, Russia had rejected a proposal by oil exporting group Opec to cut supply to cope with lower demand due to the coronavirus outbreak.

In response, Saudi Arabia said it would slash prices and pump more oil, sparking fears of a price war.

As a result, the price of international oil benchmark Brent fell by as much as a third on Monday in its biggest drop since the Gulf War in 1991. taking the price to about $31 a barrel.

The sharp drop in oil prices unsettled investors already reeling from a global economic slowdown caused by quarantine measures to fight the spread of the coronavirus.

On Tuesday, the price of Brent crude regained some ground, rising about 8% to around $37 a barrel.

Major central banks have pledged to pump cash into the financial system while governments are mulling stimulus measures to tackle the economic hit. These include cuts to interest rates to encourage companies to borrow money and expand.

However, former Bank of England governor Mervyn King told BBC 5 live's Wake Up to Money: "I don't think that a cut in interest rates now is actually going to do a great deal to help the situation, it maybe a sign of reassurance but it is not more than that.

"What is needed now are targeted measures to help business deal with a short-term crisis and collapse of their cash flow, and I think the Bank of England understands that very well."

Reflecting jittery markets, gold prices crossed $1,700 per ounce on Monday, the highest since December 2012. Gold is often seen as a safer asset in times of economic and political uncertainty, along with government bonds.