* Greek debt swap deal could be done in days * U.S. jobless claims, housing starts beat expectations * Dollar hits highest vs yen since October By Luciana Lopez NEW YORK, Feb 16 (Reuters) - The euro reversed losses to rise against the U.S. dollar on Thursday, as hopes that a Greek bond swap deal could be within reach boosted global investor sentiment as well as the appeal of higher-risk assets. The single currency traded as high as $1.3120 against the dollar, after having spent almost all of Thursday's session in the red. That was well past the psychological support level at $1.30, also a reported options barrier. The euro last traded up 0.28 percent at $1.3107. "We're getting reports that the ECB (European Central Bank) is moving forward with its (Greek) bond swap, so the possibility of some concrete progress is reinvigorating risk appetite and pushing up the euro," said Kathy Lien, director of research at GFT Forex in Jersey City. "We're finally walking in the right direction." If a deal for a Greek debt swap is completed by Monday and followed by details about a second bailout, she said, the euro could push back above $1.33, but buying in the interim will be "cautious." "Investors have been short-changed too many times not to be careful," Lien added. The national central banks within the euro zone are set to exchange their holdings of Greek bonds into new bonds in the run up to a private sector debt deal to avoid taking any forced losses, euro zone sources said on Thursday, with the swap to happen over the weekend. The euro advanced against the yen, as well, trading as high as 103.35 yen. "The market is reacting to rumor that a Greek bond swap is in the works and a higher likelihood that a deal will be reached in the near term," said BNY Mellon currency strategist Michael Woolfolk. "This is not a euro move, it is a risk-on move." Meanwhile, stronger-than-expected U.S. economic data had already improved sentiment in the early hours of the New York session, helping the dollar hit a three-and-a-half-month high against the yen. Data suggested the U.S. labor and housing markets were gaining momentum, with new jobless claims falling to a near four-year low last week and January housing starts beating expectations. The dollar traded as high as 78.94 yen, its strongest against the yen since Oct. 31, when Japan unilaterally stepped into foreign exchange markets to weaken the currency. The greenback last traded up 0.7 percent at 78.88 yen. The dollar broke above reported stop-loss orders above 78.80 yen, although traders said option-related offers ahead of 79 yen may cap gains. The dollar's prospects against the yen were boosted after it broke above the 200-day moving average this week. But some analysts said that until U.S two-year yields move higher, the greenback was likely to stay under 80 yen. News of the possible euro zone bond swap relieved pressure on the euro after euro zone finance ministers failed on Wednesday to agree on a new bailout package for Athens, delaying a decision until Monday. Markets are still expecting Greece to avoid a disorderly default, said Ronald Simpson, managing director of global currency analysis at Action Economics in Tampa, Florida. "The market is being pretty sanguine in its belief that everything is going to be fine with Greece and Portugal and Spain," he said. The options market showed investors were increasingly looking to buy protection against further euro losses. "The market is probably pricing in a better-than-even probability that a near-term deal will be reached on Greece and avoid a messy default, which suggests there are more risks to the downside for the euro if there is no deal on Monday," said Adam Cole, global head of currency strategy at RBC. Greece is scrambling to clinch the 130 billion euro ($170 billion) bailout at the Monday meeting of euro zone finance ministers to avert a chaotic default when 14.5 billion euros in debt repayments fall due on March 20.