* European shares fall, caution dominates ahead of U.S. vote * Dollar index touches 2-month highs on safety bids * Wall Street futures point to lower open * Gold steadies post plunge, holds above key technicals By Marc Jones LONDON, Nov 5 (Reuters) - World stocks fell and the dollar firmed on Monday as low-risk assets gained at the start of a week in which the United States elects a new president, China starts a leadership transition and Greece faces a fraught vote to secure fresh rescue funds. Opinion polls show the race between President Barack Obama and Republican challenger Mitt Romney remains neck-and-neck at the start of the last day of campaigning, and the uncertainty over the outcome left financial markets jittery. Safe-haven bids pushed the U.S. dollar to two-month highs against a basket of major currencies and German two-year government bond yields dropped below zero for the first time in two months. "You don't want to have too much risk ahead of the U.S. election tomorrow, so I think everyone is going to be very cautious until we see the first indications of who will win," said Tobias Blattner, an economist at Daiwa Securities. U.S. stock futures pointed to a lower open on Wall Street after a late sell off on Friday. European shares were down 0.7 percent at 1230 GMT having ended the previous week at a two-week high. World shares were 0.4 percent lower as falls in Asian equity markets followed on from Friday's U.S. sell off. The euro fell to a new two-month low against the dollar of $1.27710, extending recent losses ahead of a vote in Greece on Wednesday on unpopular spending cuts and tax hikes the EU, IMF and ECB "Troika" want passed before they offer more aid. "With the euro there is concern about what's going on in Greece, that they might not might not get the austerity vote through," said Arne Lohmann Rasmussen, head of currency research at Danske Bank in Copenhagen. FISCAL CLIFF Whatever the outcome of Tuesday's presidential race, financial markets are expected to remain fixated on U.S. politics in the coming months. After the election, Congress must deal with a "fiscal cliff", up to $600 billion in expiring tax cuts and spending reductions that are set to kick in next year, which threatens the country's economy. "With the dollar, the fiscal cliff is really getting some attention before the elections," Rasmussen said, adding that better-than-expected U.S. job data on Friday had boosted demand. Leaders at a G20 meeting in Mexico pressed the United States on Sunday to act decisively. A key concern of investors is that a narrow Obama victory combined with a convincing Republican win in Congress could blunt policymaking. That "would make negotiations over fixing the fiscal cliff (difficult)," said CMC markets analyst Ric Spooner. As well as the U.S. and Greek uncertainty, the European Central Bank and Bank of England also meet on Thursday, although neither are expected to move rates. China's once-a-decade leadership transition is also due to start that day. German government bonds, a favourite of risk-shy investors, rallied amid the caution, with two-year yields below zero for the first time since early September and Bund futures at a two-month high. "The situation is supportive for core markets. Not yet sufficient to trigger a massive rally but the economic situation is offering some support and also the risk element (in Greece) is favouring a bid for safe havens," said BNP Paribas strategist Patrick Jacq. OIL SLIPS, GOLD FIRMS Uncertainty over the Greek vote hit appetite for lower-rated debt across the bloc and bonds issued by Spain, seen as the next country to need a bailout, struggled, with 10-year yields rising 10 basis points on the day to 5.77 percent. Underscoring the damage the three-year long crisis is doing, Spanish unemployment rose another 2.7 percent in October new figures showed. In commodity markets, Brent crude oil slipped to $105 per barrel weighed down by a strong dollar and demand destruction after Superstorm Sandy. In line with the broader market caution, gold steadied at $1,677 after Friday's 2 percent plunge while economic growth-attuned copper hit two-month lows. Analysts believe an election victory for Barack Obama could be supportive for gold as Federal Reserve chairman Ben Bernanke, the architect of the central bank's stimulus strategy, could stay in his post. "Obama is supporting Bernanke, and is supporting monetary stimulus," Saxo Bank vice president Ole Hansen said. "With a Romney win - he has been criticising the approach of the Fed - Bernanke will not be renewing his contract."