* Dollar/yen dips, Nikkei rallies but hands back most gains
* Dollar index inches higher
* Fall in U.S. stock futures points to lower open on Wall St
* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh
LONDON, Feb 7 (Reuters) - The dollar lost half a percent against the yen on Wednesday, handing back earlier gains, as investors remained cautious after a heavy selloff in stock markets, and with many viewing the Japanese currency as undervalued.
A sharp decline in global share markets in recent days has had only a muted effect on the currency market, with traditional safe havens such as the yen and Swiss franc seeing only modest gains this week.
While most analysts believe this week's heavy selloff across stock markets has run its course for the moment, allowing volatility to abate a little, the prospect of monetary tightening across the globe remains a challenge for the long term, and pushed up the yen against the U.S. currency.
The dollar traded as low as 108.92 yen, erasing all of the previous day's gains.
The greenback had reached a high of 109.720 yen earlier in the day as regional equities such as Japan's Nikkei soared, taking their cue from a late rebound on Wall Street.
But it drifted lower as the Nikkei, which rose as much as 3.4 percent, gave back most of its gains on anxiety over more weakness in U.S. share markets. U.S. stock futures fell during Asian trade, stoking such fears.
"Everybody in the world can see dollar/yen is going to break lower at some point again and that the yen is going to make a move (higher) like the euro did and head back towards fair value, 30 seconds after the Bank of Japan even hints about tapering," said Societe Generale macro strategist Kit Juckes, in London.
"My sense is its going to take more and more of an effort by the Japanese authorities, and its going to take more and more of a combination of rising equity markets and higher U.S. yields to keep dollar/yen in a 105-115 range."
The focus remains on U.S. stocks, which looked set to open a little lower again, and which have been the source of the latest turbulence in global markets and currencies.
The surge in long-term U.S. bond yields to four-year highs helped trigger the slide in the equity market, and while yields have pulled back from those peaks, they still remain elevated.
"The 10-year Treasury yield has nudged back ahead of today's auction. Depending on how the auction goes, U.S. equities could face renewed pressure," said Makoto Noji, senior strategist at SMBC Nikko Securities.
"Global stocks are expected to remain on a nervous footing going forward," Noji said.
The dollar was flat against a basket of six major currencies at 89.61, after reaching a two-week peak of 90.034 overnight.
The Australian dollar, which tends to suffer during risk aversion, was 0.3 percent lower at $0.7879.
The Swiss franc, a perceived safe haven along with the yen, was flat at 0.9357 francs per dollar, and up only a third of a percent for the week.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s
(Reporting by Jemima Kelly; Additional reporting by Shinichi Saoshiro in Tokyo; Editing by Alison Williams)