* Euro jumps to near 4-week high vs dollar, breaks $1.37 barrier * Markets believe Slovaks will eventually back EFSF expansion * Hopes grow that euro zone leaders will tackle debt crisis * Dollar index slides 1 percent, Aussie shines By Jessica Mortimer LONDON, Oct 12 (Reuters) - The euro jumped to a near four-week high versus the dollar on Wednesday on tentative optimism that European leaders would reach agreement on a way to resolve the euro zone debt crisis and as investors took profit on previous short positions. The euro recovered from earlier falls, made after Slovakia's parliament on Tuesday rejected a plan to strengthen the euro zone rescue fund, as investors took the view the government would eventually gather a majority to endorse the scheme. Traders said the euro shot higher following the break of an options barrier at $1.3700 which took it through a series of stop loss entry orders placed above that level. It gained more than 1 percent on the day to $1.3816, its strongest since Sep. 16. Its next target was $1.3848, the 50 percent retracement of the move down from the late August high of $1.4549 to the low around $1.3146 hit early last week. However, traders said the euro's rise could be limited as the gains looked overdone, with concerns lingering about political hurdles to containing the euro zone crisis. "This is all a short squeeze. Once the euro went above $1.37 everyone had stops above there and there may be a bit more scope for more upside," said Richard Wiltshire, chief FX broker at ETX Capital. "The euro is really resilient at the moment. There's no new bad news, but there is still plenty of bad news out there," ETX's Wiltshire said. Investors took comfort from German Chancellor Angela Merkel saying she was certain there would be full ratification of the European Financial Stability Facility (EFSF) by the time of the Oct. 23 European Union summit. There was also some relief that inspectors from the 'troika' of the European Union, IMF and European Central Bank said on Tuesday an 8 billion euro loan tranche to Greece should be paid in early November. The euro was well above a trough of $1.3582 hit in Asian trade in a knee-jerk response to the Slovak vote against the EFSF expansion. It also rose more than 1 percent versus the yen to hit 105.82 yen, its strongest since Sept. 16. "No one really believes Slovakia is able to stop the ratification of the EFSF and that's why euro/dollar is not lower," said Niels Christensen, currency strategist at Nordea in Copenhagen. WEAKER DOLLAR The dollar also turned weaker while perceived riskier currencies like the Australian dollar jumped higher, helped by higher stocks and commodity prices. Better-than-expected euro zone industrial output data also eased concerns the region's economy could be set to slow significantly. The dollar index hit a three-week low of 76.796, some distance away from an 8-1/2 month peak of 79.838 set on Oct. 4, while the Australian dollar jumped close to 2 percent to a three-week high around $1.0140 . Analysts said investors were wary about bickering between the United States and China over a bill aimed at pressing Beijing to lift the value of the yuan, as China urged the Obama administration to block such a move. Against the Japanese currency, the dollar was down 0.3 percent at 76.59 yen , staying away from a record low around 75.94 yen set in August. The perceived danger of yen-weakening intervention by Japanese authorities has seen the dollar/yen pair trapped in a narrow band recently.

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