* FTSEurofirst 300 up 7.56 points at 1,198.71
* BHP Billiton, Fresnillo updates lift miners
* Strong U.S. banking results boost European peers
* Smith falls on profit warning
By David Brett
LONDON, July 17 (Reuters) - A tumultuous session saw European shares close higher on Wednesday, bolstered by reassurances from the U.S. Federal Reserve that it will be flexible in its stimulus-trimming plans.
The FTSEurofirst 300 closed up 7.56 points, or 0.6 percent at 1,198.71 as comments from Fed Chairman Ben Bernanke helped the market recover from the blow of Bank of England committee voting 9-0 against extending the bank's bond-buying programme, known as "quantitative easing" (QE).
The Fed retained its view that stimulus would be dependent on economic data and investors took a more dovish view after weak U.S. housing data.
European shares, however, are still down 4.6 percent from levels hit on May 22, when volatility - a gauge of investor fear - increased on worries over the Fed scaling back stimulus.
"Volatility will rise from the levels we saw before May 22 and stay higher until investors become more comfortable with what the change of policy will mean. Until then you can expect more noise and higher risk," Gurvinder Brar, head of global quantitative research, at Macquarie Securities, said.
Among the top gainers in Europe on Wednesday were the banks , up 0.9 percent, boosted by strong results from U.S. peers Banks of America and BNY Mellon, traders said.
The "U.S. earnings season continues to impress, particularly the banks. Surely this is a tell-tale sign that we are over the worst and that lending and borrowing, a necessity for growth, are beginning to oil up again," William Nicholls, Dealer, Capital Spreads, said.
Miners rallied hardest, albeit from a low base, up 2.3 percent after BHP Billiton and Fresnillo backed-up Rio Tinto's reassuring update in the previous session.
Expectations remain low for European-listed miners which are expected to undershoot quarterly earnings forecasts by more than 7 percent, according to Thomson Reuters Starmine data.
There was earnings disappointment elsewhere, with engineering firm Smiths Group down 1 percent after issuing a profit warning.
The world's biggest cosmetics group L'Oreal fell 0.6 percent as second-quarter sales contracted.
On the whole, European companies are expected to beat second quarter earnings forecasts by 0.5 percent, albeit with year-on-year growth down 2.7 percent, according to Starmine data.