* Asian stock markets: https://tmsnrt.rs/2zpUAr4
* Financial markets trying to shake off virus woes
* Equities draw investors on hopes for more China stimulus
* Oil markets worried about demand disruptions
By Stanley White
TOKYO, Feb 5 (Reuters) - Asian stocks steadied on Wednesday as Chinese stocks nudged higher on hopes of additional stimulus to lessen the economic impact of a coronavirus outbreak, but risks remain as the illness continues to spread and the death toll neared 500.
MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.36%.
Shares in China rose 0.5% while stocks in Hong Kong climbed 0.42% in early trading.
The onshore yuan was little changed versus the dollar, highlighting the cautious mood as investors monitor the impact of the virus.
The safe-haven yen and Swiss franc nursed losses versus the dollar. Oil prices bounced in Asia on hopes for more output cuts from OPEC and its allies but sentiment remained weak on worries about a long-term dent in demand for energy and other commodities.
China and other countries have imposed travel restrictions to try to contain a new virus that emerged in the central Chinese city of Wuhan late last year, slamming the breaks on manufacturing and tourism in the world's second-largest economy.
Many investors argue that any slowdown will be temporary and that Chinese policy steps are reason to remain optimistic about the growth outlook, but so far public health officials have not found a way to stop the spread of the virus both inside and outside of China.
"We're going to have a strong day in Asia, but whether this is the reversal of a downtrend remains to be seen," said Michael McCarthy, chief market strategist at CMC Markets in Sydney.
"Oil investors remain pessimistic about demand disruptions, but equity investors, especially overseas, are discounting the impact of the virus."
Australian shares were up 0.37%, buoyed by gains in the mining sector. Japan's Nikkei stock index rose 0.99%, supported by shares of industrial equipment makers.
U.S. stock futures fell 0.23% in Asia on Wednesday. The S&P 500 rose 1.5% on Tuesday and the tech-heavy Nasdaq rose to a record high.
The People's Bank of China (PBOC) is likely to lower its key lending rate - the loan prime rate - on Feb. 20, and cut banks' reserve requirement ratios in the coming weeks, policy sources told Reuters.
The PBOC has already pumped hundreds of billions of dollars into the financial system this week. This helped Chinese stocks stabilise on Tuesday following a rout that wiped out around $700 billion in market capitalisation on Monday when Chinese markets opened after an extended holiday.