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 .DXY 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. .L .EU .NEuropean shares .FTEU3 were down 0.7 percent at 1230 GMT having ended the previous week at a two-week high. World shares .MIWD00000PUS 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 CLIFFWhatever 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.