* Oversupply fears pressure crude prices after overnight rally
* European bourses open lower
* Dollar struggles across the board
* China's yuan hits four-year low in offshore trade

Global stock markets fell on Wednesday as oil prices slumped back towards 11-year lows, sapping investors' appetite for risky assets and hurting the shares of mining and energy companies.

Stock markets rallied the previous day as oil prices rebounded on prospects for lower temperatures on both sides of the Atlantic. But on Wednesday benchmark Brent crude slid back below $37 a barrel, with investors worried about slowing demand and high supplies.

The fall in oil prices has been a major driver of financial markets this year, hammering energy companies, lowering inflation expectations and reinforcing bets on loose monetary policy in Europe and a slow tightening in the United States.

The pan-European FTSEurofirst 300 index fell 0.5 percent, while the euro zone's blue-chip Euro STOXX 50 index  declined by 0.6 percent, having both gained in the previous session.

Asian shares unwound earlier gains, with continued weakness in Chinese stocks. MSCI's broadest index of Asia-Pacific shares outside Japan edged down 0.1 percent, on track for a flat monthly performance and down 12 percent for the year.

‘The ongoing weakness in the oil price is dragging down the markets,’ said John Plassard, senior equity sales executive at Mirabaud Securities in Geneva.

Crude prices have plunged by two-thirds since mid-2014 as soaring output from the Organization of the Petroleum Exporting Countries (OPEC), Russia and the United States led to a global surplus of between half a million and 2 million barrels per day.

Spreadex analyst Connor Campbell added that a warning by the head of the International Monetary Fund in a newspaper column that global economic growth would be disappointing next year was further pressuring markets.

The yen, which is traditionally sought at times of market uncertainty, inched up to 120.425 yen per dollar. That left it close to a two-month high of 120.05 yen hit last week.

DOLLAR LAGGING

The dollar was 0.1 percent lower against a basket of major currencies, adding to a weak end to the year that has seen it fall more than 2 percent in just under a month.

BNP Paribas currency strategist Michael Sneyd said there had been a disconnect between the dollar and US Treasury yields since the Federal Reserve raised interest rates for the first time in almost a decade earlier this month.

‘Since the Fed's liftoff, the dollar has lagged behind markedly. We would put that down to most market participants being out of the market at the moment,’ he said.

China's yuan fell to its weakest in over four years in offshore trading, after the People's Bank of China set a lower midpoint. Sources told Reuters the PBOC was temporarily suspending some foreign banks' foreign exchange, in an effort to curb the yuan's depreciation.

China's blue-chip CSI300 index was down 0.2 percent, while the Shanghai Composite Index was flat, ahead of December manufacturing activity surveys in the coming days which are expected to show the economy remains sluggish.

Japan's Nikkei ended the country's final trading day of the year up 0.3 percent, off session highs but still gaining 9.1 percent for 2015. But it shed 3.6 percent in December.

On the last trading day of 2015 for European bond markets, 10-year German Bund yields were flat at 0.63 percent and up nearly 10 basis points on the year.

Gold ticked higher, with gains capped by weaker oil, although the metal remained on track for a third successive yearly fall.