FOREX-U.S. dollar, yen weaken as risky assets edge higher

* 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.