* Euro falls against dollar and yen
* Higher rate premium for dollars hurting euro
* Large option expiries weigh on trade
* Dip in yuan against dollar also seen as factor (Updates with fresh prices, quotes)
LONDON, June 10 (Reuters) - The euro fell against the dollar and yen on Tuesday, feeling the pressure of a rise in the premium for holding the U.S. currency since the European Central Bank cut all of its main rates last week.
The jury remains out on whether a series of policy moves by the ECB and an improvement in the U.S. economy are enough to weaken the single currency more durably and end a period of low volatility brought on by universally low interest rates.
Large volumes of expiring euro-dollar options at and on either side of $1.3600 were keeping the market around that level and traders said there were also expectations that Asian central banks would support the euro above $1.3520.
The single currency stopped just short of those levels after falling a third of a percent in morning trade in Europe.
"There is a lot against the euro at the moment," said one London-based currency spot dealer. "We only have U.S. data to go on this week, which should be strong, and the U.S. bond market gives you every reason to back the dollar a bit higher."
Many short-term bets on further euro weakness were squeezed out after the ECB's decision last week as many players chose to take profit on an almost five-cent fall since early May.
But the premium bond and money markets give investors for holding the dollar has steadily climbed in the meantime, drawing in a new round of bets against the euro.
Hans Redeker, head of global foreign exchange strategy at U.S. bank Morgan Stanley in London, argued that U.S. retail sales numbers on Thursday would add to the more positive picture of U.S. growth and to both a stronger dollar and stronger yen.
"The next big thing is going to be higher volatility. That is going to lead to a stronger dollar, but also the yen outpacing the dollar," he said.
The euro traded at $1.3545 and was more than half a percent weaker against the yen at 138.55 yen.
The dollar index rose to 80.81 , pulling further away from a near two-week trough of 80.240 touched last Friday. The yen was up 0.2 percent against the dollar at 102.33 yen.
The fall in euro zone peripheral bond yields, conversely, has been one of the big pieces of evidence explaining the euro's broader strength so far this year.
Investors seeking higher returns than the almost zero rates offered by benchmark U.S. and German instruments have poured money into Greece, Spain, Italy and Ireland.
But after another surge last Friday, there were signs that the rally in some of those bond markets is starting to ease.
Italian two-year bond yields, which rise as prices fall, are up 12 basis points since Friday.
The benchmark yield spread of two-year U.S. Treasuries over two-year German debt, however, widened to almost 37 basis points on Tuesday, , the highest since 2007. Euro zone overnight interbank interest rates were at their lowest levels on record.
"Rate differentials are partially to blame (for the euro's fall), with U.S. yields rising all morning and the U.S. 10-year breaking yesterday's high," said Stephen Gallo, European head of FX strategy with Canadian bank BMO in London.
"However, we also believe the shift towards a stronger yuan by the Chinese central bank is a very important culprit for EUR weakness, as expectations for USD-to-EUR reserve recycling have fallen." (Editing by Nigel Stephenson and Alison Williams)