* Fed statement lifts dollar
* Euro hit by Fed, Greece
* World stocks slips led by banks
By Jeremy Gaunt, European Investment Correspondent
LONDON, Dec 17 (Reuters) - The dollar hit a three-month high against major currencies on Thursday following a slightly more optimistic assessment about the U.S. economy from the Federal Reserve.
World stocks fell more than 1 percent, with banks taking a hit at the prospect of less liquidity pumping from the U.S. central bank and others.
The Fed's policy-making committee left rates unchanged as expected on Wednesday but reminded markets it will let most of the special liquidity facilities, which have helped bolster the U.S. banking system after last year's credit crisis, expire by early next year.
Prospects that this will bring tighter monetary policy earlier than expected triggered an unwinding of short dollar positions ahead of the new year.
The euro was also hurt by Standard & Poor's cutting Greece's rating by one notch, to BBB-plus from A-minus, late on Wednesday. It said austerity steps announced by Prime Minister George Papandreou this week were unlikely to produce a "sustainable" reduction in the public debt burden.
"The problem for the euro is the mix of the (Fed) statement and the very strong concerns over Greece.... All the euro crosses have suffered," said Roberto Mialich, FX strategist at Unicredit in Milan.
The euro was down 1.3 percent against the dollar at $1.4348, touching September lows.
The dollar rose more than 1 percent on the day. Sterling lost 1.4 percent to $1.6102.
STOCKS WOBBLE
World stocks fell with MSCI's all-country index down 1.1 percent and its emerging market component off 1.5 percent.
In Europe, the FTSEurofirst 300 index was down 0.7 percent, having hit a one-month closing high on Wednesday.
The heavyweight banking sector took most points off the index. BNP Paribas, Banco Santander, Barclays and HSBC were among the big losers.
U.S. stock futures fell around 0.8 percent, pointing to a weaker open on Wall Street later.
Equities have had a robust year, especially since March, but are now becoming more volatile ahead of year-end and with large questions pending about 2010.
"Markets are still trying to find a trend and establish whether the improvement in the economy is due to stimulus packages," said Justin Urquhart Stewart, investment director at Seven Investment Management.
Earlier, Japan's Nikkei average ended down 0.1 percent, slipping from seven-week highs as investors pocketed profits on a rally in big banks such as Mitsubishi UFJ Financial Group.
German government bonds rallied as the downgrade of Greece's rating undermined already shaky sentiment for riskier peripheral euro zone debt.
The two-year Schatz yield fell 7 basis points to 1.158 percent, while the 10-year Bund yield slipped to 3.144 percent. (Additional reporting by Brian Gorman and Jessica Mortimer)