Share markets rise in volatile tradingContinue reading the main story
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US and European shares have both risen, but trading remains volatile as concerns continue over eurozone debt.
Wall Street's main Dow Jones index ended up 3.9%, helped by data showing a fall in the number of unemployment claimants.
In Europe, indexes closed higher after French President Nicolas Sarkozy and German Chancellor Angela Merkel said they would meet to discuss eurozone financial governance.
The UK's FTSE 100 ended up 3.1%.
Germany's Dax added 3.3% and France's Cac rose 2.5%.
A statement from President Sarkozy's office said he and Ms Merkel would also discuss "other international issues".
French banking shares had started Thursday among the biggest gainers, with Societe Generale shares up 8%. The bank's shares then plunged as far as 8% down on the day, before recovering to finish 3% higher.
It comes a day after Societe Generale denied negative speculation about its financial health.
The US unemployment data showed that the weekly number of people claiming benefits had fallen by 7,000 to 395,000, the first time it had dropped below 400,000 since April.
This also lifted the two other main US share indexes, with the Nasdaq up 4.7% and the S&P's 500 adding 4.6%.
However, analysts cautioned that US investor sentiment could easily worsen again in the days ahead.
"Had we seen a jump [in unemployment claims] it would have reinforced recession fears," said Bucky Hellwig, senior vice president at BB&T Wealth Management.
"What we've seen here is not anything to allay those fears, but just to set them aside temporarily."'Irrational fears'
Mr Sarkozy held emergency talks with senior ministers on Wednesday when France became the centre of market turbulence on rumours that the country was about to lose its AAA credit rating, and the concern about Societe Generale.
The rumours about French government debt were denied by both the French Treasury and the three main global credit rating agencies.
Societe Generale chief executive Frederic Oudea said the speculation about his bank was "absolutely rubbish".
Mr Oudea also spoke to France Info radio. "People are scared," he said, "so the tiniest information touches off irrational fears. To our clients, we have to tell them that these rumours are baseless and that they can have confidence in Societe Generale."
The bank has asked the French market authorities to investigate the source of the rumours, which left its shares 23% lower at one point on Wednesday.
Some analysts have been saying that many shares have been "oversold", meaning they are now cheap at the price.
Vincent Ganne, chartist at TradingSat, said the market was still too volatile and nervous for many investors: "Have we seen capitulation yet? Has the sell-off reached its paroxysm? It's not clear at this point."'Dangerous time'
As concerns continue about the high level of government debt in both the US and eurozone nations, Chancellor George Osborne said the UK government had been right to start to work hard to reduce its deficit.
Are lenders to government, creditors of banks and investors in shares behaving in the kind of way that would guarantee them the kind of losses that presumably they would wish to avoid?”
He told Parliament that the coalition's efforts to tackle the deficit had make the UK a "safe haven" for investors.
Yet Mr Osborne warned that the UK economy was not "immune" to the international economic storm.
"History teaches us that recovery from this sort of debt-driven balance sheet recession was always going to be choppy and difficult," he said.
"The whole world now realises that the huge overhang of debt means that the recovery will take longer and be harder than had been hoped.
"Markets are waking up to this fact and that is what makes this the most dangerous time for the global economy since 2008."
Shadow chancellor Ed Balls told Mr Osborne that the government was trying to cut the deficit too quickly, warning that this was weakening the UK economy at a time of increased global risks.
"We do need a tough, medium-term plan to get our deficit down," said Mr Balls.
"But it is your reckless policies, too far and too fast, that have ripped out the foundation of the house, and left our economy deeply exposed to this brewing global hurricane."Italy's options
In Italy, Finance Minister Giulio Tremonti addressed a special parliamentary session to outline his country's response to the eurozone debt crisis, which is expected to include deficit reduction measures to meet its target of balancing its budget by 2013.
Mr Tremonti said budget cuts next year would be "very strong", but he queried European Central Bank demands for cuts in public sector salaries and labour law reforms to make firing easier.
He said: "The numbers and details are under discussion. The political choice about how we focus ourselves, for 2012 and 2013, is still a political choice we have to make."
Mr Tremonti told parliament that Italy needed to reduce its deficit of about 3.9% of national income this year to closer to 1% next year.
Italy's debt is the second highest in the eurozone after Greece at 120% of gross domestic product, but its deficit is among the lowest, meaning its debt is rising at a slower rate.Weak economies
The market turmoil of the past week stems from fears that tackling the high levels of national debt on both sides of the Atlantic could hurt already weak economic growth.Continue reading the main story
Top winner and loser
This is particularly true in the US, the world's largest economy, where the unemployment rate remains above 9%, and the Federal Reserve, the US central bank, warned that the economy was considerably weaker than expected.
The biggest market falls were seen on Monday, in the first day of trading following the decision of credit rating agency Standard & Poor's to downgrade its assesement of US national debt from AAA to AA+.
Before that, markets were concerned at the inability of US politicians to agree to raise the US debt ceiling, something that was finally agreed at the 11th hour.
In Europe, the concern centres on whether Spain and Italy will have to follow Greece, Portugal and the Republic of Ireland and require bailouts.
The fear has since spread this week to whether other eurozone countries, and most notably France, can afford to put funds into an expanded European Financial Stability Facility that will pay towards any required future bailouts.