* FTSEurofirst 300 flat, trading volumes light
* Euro zone 'fear gauge' hits near 7-year low
* Whitbread touches record high on JPMorgan upgrade
LONDON, Nov 22 (Reuters) - European shares held steady on Friday while a closely watched measure of stock market volatility sank to a near seven-year low in a further sign of mounting investor confidence about the state of the global economy.
The Euro STOXX 50 Volatility Index which reflects options pricing and demand to protect against falls in the underlying cash market index, fell 2.7 percent to 14.68 points, having hit levels not seen since early 2007 earlier in the day.
The VSTOXX has been falling in a fairly steady fashion since hitting 59.8 points in 2011, helped by intervention by the European Central Bank and other central banks across the world to shore up the debt and funding markets.
"It's (the move on the VSTOXX) the effect of both the improved visibility on the macro front and strong liquidity from the central banks. Very few people feel the need to hedge their positions at the moment, very few people are buying volatility," said Vincent Cassot, head of equity derivatives strategy at Societe Generale.
"That's the short-term picture, however. Investors are feeling relaxed for the rest of 2013, but a little less relaxed for the start of 2014. The curve is quite steep between the spot V2X, and the January contract, which currently trades at 18.65."
The FTSEurofirst 300 was down 0.37 of a point at 1,295.24 points by 1134 GMT, within a whisker of a 5-1/2-year closing high of 1,304.25 seen on Monday. Trading volumes were light, at just a quarter of the 90-day daily average.
Dow Jones industrial average futures edged higher. The Dow closed above the psychologically key 16,000 level for the first time on Thursday when U.S. economic data showed its labour market was improving and inflation remained subdued.
Topping the gainers' list, Whitbread rose 3 percent and touched a record high as JPMorgan lifted its rating on the hotel and coffee shop operator to "overweight", citing robust newsflow on the British economy.
The investment bank said that recent strong macroeconomic trends should drive RevPAR (revenue per available room) upgrades into next year. "We expect Premier Inn to outperform on the back of its dynamic pricing and benefit from its asset heavy structure in an upswing," it said.
In the broader market, shares have been trading in a narrow band on concern the United States will soon start to scale back its monetary stimulus, but some strategists say investors are starting to take a more relaxed view.
"Investors are realising that when policy support starts to be wound down, it will be because the underlying economy is looking that much better, so it's not quite as scary a prospect that it maybe seemed to be even a month or so ago," Peel Hunt equity strategist Ian Williams said.
Central bank stimulus has been a major driver of European equities. The STOXX Europe 600 has rallied around 17 percent since a late June trough, as investors have moved out of safer bonds and into higher-yielding assets, such as stocks.
This has propelled valuations above their long-term averages, with the STOXX Europe 600 on a 12-month forward price/earnings ratio of 13.4 times against its 10-year average of 12 times, Thomson Reuters Datastream shows.
Yet investors are still putting their money into equities. European shares enjoyed a 21st straight week of inflows from U.S. investors in the seven days to Nov 20, according to Thomson Reuters' Lipper service. That was the longest streak of weekly inflows since Lipper started to monitor flows in 1992.
"Just when you see the valuations are starting to cap the upside, you've got the ... argument, 'actually, we've still got cash, where do we put it?" Peel Hunt's Williams said.
"Even at these valuations equities relatively still look like the most sensible place'."