* Dollar falls to 7-month low versus yen * Euro stays near 4-month high against dollar * Dollar could extend falls if Fed opts for more stimulus * SNB keeps Swiss franc cap at 1.20 per euro By Jessica Mortimer LONDON, Sept 13 (Reuters) - The dollar fell on Thursday, hitting a seven-month low against the yen and holding near a four-month low versus the euro on signs the Federal Reserve will announce a third bout of monetary stimulus. Many in the market expect the Fed to unveil a new 'QE3' asset purchase programme when it gives its policy decision later in the session. This would likely cause the dollar to extend losses. The dollar fell to 77.58 yen on trading platform EBS, its lowest since mid-February when the Bank of Japan unexpectedly eased monetary policy. Further falls would put markets on alert for possible intervention in Tokyo to stem the rise in the Japanese currency, traders said. The euro was up 0.1 percent at $1.2906, near a four-month high of $1.2937 reached on Wednesday. It remained firm after Germany's Constitutional Court on Wednesday cleared ratification of the euro zone's permanent rescue fund, paving the way for the European Central Bank to buy bonds of struggling countries in the region. "Although the market broadly expects more easing from the Fed, the euro should pop up (if the Fed announces more easing). It might get almost to $1.30 and next week should consolidate around that level," said Gavin Friend, currency strategist at National Australia Bank. "We are talking about a significant reduction in the tail risks surrounding the euro zone," Friend said, adding he expected the euro to trade in a higher range of between $1.26 and $1.31 in coming months. If the Fed fails to deliver the stimulus anticipated, he predicted the euro's falls would be limited to around $1.2850. Traders cited chart resistance for the euro at the 233-day moving average at $1.2938 while a reportedly large options expiry at $1.2900 later in the day could influence price action and keep the euro trading close to that level. The currency has risen more than 7 percent from July's two-year low of $1.2042, buoyed after an ECB pledge to do whatever it takes to preserve the currency. The euro rose 0.2 percent against the Swiss franc to 1.2109 francs, having earlier dipped after the Swiss National Bank said it would maintain its 1.20 franc floor in euro/Swiss. The move disappointed some investors who had speculated the SNB might raise the floor, but analysts said the fact the euro did not sell off heavily was a sign of growing confidence in the ECB's plan to tackle high peripheral borrowing costs. "We have had some fundamental decisions during the last week, people might think we have found something like a solution for the euro zone debt crisis," said Lutz Karpowitz, FX strategist at Commerzbank. "As long as we have got this optimism it seems this is the reason behind this rise in euro/Swiss." ALL EYES ON FED Mounting expectations the Fed might print more dollars, thereby cheapening their value, pushed the dollar index down 0.1 percent to 79.655, keeping it near a four-month low of 79.522 on Wednesday. Many Fed watchers believe any new asset purchase programme would be open-ended, unlike the past two cycles of quantitative easing. That would allow the central bank to review the size of its purchases on a frequent basis and adjust the programme as economic circumstances warranted. "The market has not 100 percent priced in QE3 yet," said Masafumi Yamamoto, chief FX strategist at Barclays, noting that whether the monthly purchase size was larger than the previous QE round's $75 billion would be important, regardless of whether the new programme was open-ended. Also helping the euro was the result of elections in the Netherlands, where pro-European parties crushed radical fringe groupings, dispelling concerns that eurosceptics could gain a power base in one of the euro zone's core states. The euro dipped against the yen, trading at 100.31 yen but staying not far from Wednesday's high of 100.64 yen.