* Positive U.S. data boosts risk sentiment, euro
* U.S. stocks still driving FX market
* Fed official says U.S. banks still at risk
* Markets await Australian central bank decision (Updates prices, adds quotes)
By Gertrude Chavez-Dreyfuss
NEW YORK, Nov 2 (Reuters) - The dollar and yen fell on Monday in volatile trading as steady stocks and data showing further evidence of an economic recovery around the world dampened safe-haven demand for the U.S. and Japanese currencies.
U.S. reports showed sharp improvements in manufacturing, construction and housing, encouraging investors to buy riskier assets with higher yields.
As a result, U.S. stock indexes rose, though stocks later trimmed gains on concerns about banks' soured loans and worries about whether the seven-month rally has run out of steam.
Commodity prices also rose, lifting commodity-linked currencies such as the Australian and Canadian dollars.
"The pattern in which stocks and the euro are correlated is intact. As stocks rise, so does the euro," said Marc Chandler, global head of FX strategy at Brown Brothers Harriman in New York.
"But I don't think we're out of this consolidation and correction in stocks and even in the euro. I'm not convinced that the downside correction in the euro is over," he said.
For much of the past year, the euro has had a positive correlation with moves in the stock market, gaining when good economic data and rising share prices boost risk appetite. The 25-day correlation between the euro and the S&P 500 was at a robust 0.83 on Monday, according to Reuters data.
In late afternoon trading, the euro rose 0.3 percent to $1.4765 after climbing as high as $1.4845, according to Reuters data. U.S. stocks were down from the session's highs, somewhat pressuring the euro.
Analysts said the slide in stocks and the euro began after a Federal Reserve official said U.S. banks remained at risk over soured property loans. That pushed the euro to as low as $1.4728.
"It was a day that seemed poised to rekindle the demand for risky assets. Instead, it showed that the current outbreak of caution continued to infect market sentiment," said David Watt, senior currency strategist at RBC Capital Markets in Toronto.
Against the yen, the dollar gained 0.2 percent to 90.29 yen after falling as low as 89.18 yen per dollar on electronic trading platform EBS. The euro rallied 0.5 percent to 133.35 yen.
The ICE Futures U.S. dollar index, a measure of the greenback's value against a basket of six major currencies, slipped 0.1 on the day to 76.223.
Losses in the dollar and the yen accelerated earlier in the session after news that U.S. manufacturing activity rose to its highest level in 3-1/2 years last month, offering hope the budding economic recovery would be sustained.
Other reports showed pending home sales, for homes under contract to be sold, unexpectedly surged in September and construction spending posted its largest gain in a year in September.
Markets then began looking ahead to the Reserve Bank of Australia's interest rate decision later in the global session. The RBA is widely expected to hike rates by 25 basis points to 3.50 percent.
The Australian dollar was up 0.5 percent at US$0.9035. (Additional reporting by Wanfeng Zhou; Editing by Leslie Adler) (gertrude.chavez@thomsonreuters.com; +1 646 223 6322; Reuters Messaging: gertrude.chavez.reuters.com@reuters.net))