BRUSSELS (AP) — Stocks remained extremely volatile Thursday but solid gains on Wall Street following strong U.S. jobs data helped European markets close higher despite another rollercoaster ride for the continent’s banks.

Wild swings on a daily basis and across time zones highlight how febrile markets are at the moment amid concerns over the global economy and the levels of debt in both the U.S. and Europe. Unconfirmed speculation that European markets were considering a ban on short-selling is clear indication of that volatility.

French banks have been particularly volatile as investors fret about their exposure to the debt of countries like Greece and Italy.

Having traded sharply lower for much of the day, most of the banks, including France’s second largest Societe Generale, closed higher, helping European markets to post one of their best days in recent weeks, which have been marked by massive declines all round the world.

“Investors made tentative attempts to pick up some of the more badly beaten stocks, taking confidence from a positive opening to U.S. markets,” said Joshua Raymond, chief market strategist at City Index. “This in turn sparked a revival of fortunes for European indices, whose early gains had been progressively sold into as the session continued.”

The FTSE 100 index of leading British shares closed up 3.1 percent to 5,162.83 points, while Germany’s DAX increased 3.3 percent to 5,797.66. France’s CAC-40 ended up 2.9 percent at 3,089.66.

On Wall Street, the Dow Jones industrial average was up 2.3 percent at 10,962 while the broader Standard & Poor’s 500 index rose an equivalent rate to 1,147.

Shares rose after new data showed that the number of people filing for unemployment benefits in the U.S. fell below 400,000 last week for the first time in four months. That was seen as a sign that the job market may slowly be improving.

Thursday’s share gains came after Wednesday’s hammering of stocks in Europe and the U.S. Any investor cheer to the news that the U.S. Federal Reserve was keeping its super-low interest rates until the middle of 2013 dissipated as they interpreted that stance to mean that the U.S. economy will not improve substantially by 2013.

Though stock markets have been swinging wildly, there’s been a measure of calm in the bond markets of Spain and Italy in the wake of the European Central Bank’s purchase of their bonds.

The yield, or interest rate, on Spanish and Italian 10-year bonds remained relatively stable at around 5 percent. That rate is considered manageable for now and is over a percentage point lower than where they were trading a week ago.

However, analysts think that they will have to get even lower to really dampen worries that Europe’s debt crisis will ensnare the eurozone’s third and fourth largest economies.

“The reality is they will need to buy an awful lot more to get them down to sustainable levels well below 5 percent,” warned Michael Hewson, market analyst at CMC Markets.

In currency markets, the Swiss franc dropped sharply after a senior Swiss National Bank official said the bank is examining further measures to soften the currency’s “massive overvaluation” against the U.S. dollar and the euro. The franc fell 5.3 percent to 92 euro cents and dropped 4.9 percent to $1.31. The increased uncertainty in financial markets had pushed the franc to record highs in recent days as investors were fleeing to safe assets.

Earlier, Asian markets were under pressure following Wednesday’s big reverse on Wall Street.

Hong Kong’s Hang Seng index fell 1 percent to 19,595.10, but China’s main index in Shanghai rose 1.3 percent to 2,703.90.

Japan’s Nikkei 225 index slipped 0.6 percent to close at 8,981.94 as a strengthening yen clobbered Japan’s crucial export sector. Honda Motor Corp. and Nissan Motor Corp. each lost 3.5 percent.

By late afternoon London time, the dollar was stable at 76.8 yen, while the euro rose 0.8 percent to $1.4246, thanks to a somewhat higher risk appetite.

In the oil markets, prices recovered alongside equities. The crude rose 61 cents to $83.50 a barrel.