* Libor seen falling further after ECB, Bernanke
* Some U.S. appetite for longer-dated French bank debt
* U.S. interest rate volatility hovers at low levels
* Options suggest longer-term concerns about higher rates (New throughout, changes dateline, previous LONDON)
NEW YORK, March 2 (Reuters) - Short-term borrowing costs for dollars will likely fall further in the coming days as European banks are flush with cash after they aggressively bid for cheap funds from the European Central Bank this week.
Federal Reserve Chairman Ben Bernanke's assurance the U.S. central bank will likely cling to its near-zero interest rate policy at least until late 2014 leaves more room for interbank lending rates to fall, analysts said on Friday.
Another encouraging development for the dollar funding market was the emergence of investor appetite for unsecured, longer-dated French bank debt, they said.
At the end of 2011, most investors shunned French bank debt with the exception of overnight secured loans. French banks have the highest combined exposure to Greece and Italy, two heavily indebted euro zone countries.
"There is a lot of money coming from Europe," said Mike Lin, director of U.S. dollar funding at TD Securities in New York. "It's hard to fight the trend right now."
And the trend suggests the London interbank offered rate for three-month dollars could decline 0.5 basis point in the coming days, Lin said.
On Friday, three-month dollar Libor was fixed at 0.47575 percent, the lowest since mid-November.
Nearby Eurodollar futures, which gauge expectations on three-month Libor, rose for a fifth straight day. The December 2012 Eurodollar contract touched its highest in about a month on Friday at 99.430.
Most stress measures in the dollar funding market will likely ease further since ECB awarded 530 billion euros in three-year loans to 800 banks on Wednesday.
The spread between three-month Libor and the three-month Overnight Indexed Swap rate that measures expectations on the Fed's policy rate hovered at 36 basis points, the tightest since early November.
The gap between two-year dollar interest rate swaps and two-year Treasury note yields shrank to 25 basis points late Friday, the narrowest since mid-August, according to Tradeweb.
Since December, ECB's two three-year Long Term Refinancing Operations (LTROs) injected more than a trillion euros into the banking system.
While these ECB loans are denominated in euros, this hefty cash infusion lessens the urgency for banks to raise money in the open market, where investors remain wary about bank exposure from the region's sovereign debt problem.
"The LTROs have added a lot of cash there. It means their overall demand for cash is a lot lower," Lin said.
In light of the market's protracted low-rate outlook, measures of interest rate volatility hovered near their recent lows. For example, Bank of America Merrill Lynch's MOVE index on dollar interest rate swaption volatility was about 77 basis points on Friday, above its recent low of 70 basis points but far below the 118 basis points set in early August 2011.
A low-rate, low-volatility climate enables traders to take more risks and to engage in costly hedging strategies.
"They don't have to hedge as much," said Jim Vogel, interest rate strategist at FTN Financial in Memphis, Tennessee.
Even if a trader needs to exit from a position, he can easily find either a buyer or seller, Vogel said. "There is no shortage of cash around."
While the ECB and the Fed are committed to keeping rates low and ample cash in the bank system, some traders scaled back their longer-term expectations that U.S. rates would stay low once the central banks begin to withdraw monetary stimulus.
In the options market, the ratio on 10-year Treasury puts to 10-year Treasury calls rose above its 10-day moving average on Friday. This suggested more traders are bracing for higher longer-term Treasury yields on perception of a successful LTRO this week, less likelihood of more bond purchases from the Fed and encouraging U.S. economic data, according to Gennadiy Goldberg, fixed income strategist at 4Cast Ltd in New York. (Reporting by Richard Leong; Editing by James Dalgleish)