* Asian stock markets: https://tmsnrt.rs/2zpUAr4
* Trump's contraction of coronavirus stuns investors
* U.S. stock futures rise on expectations Trump will leave hospital
* Dollar falls against Swiss franc but rises versus the yen
By Stanley White
TOKYO, Oct 5 (Reuters) - Stocks rose on Monday as signs that President Donald Trump's health was improving eased some of the political uncertainty caused by his coronavirus infection, which sent investors rushing for safety last week.
Trump, 74, was flown to hospital for treatment for the coronavirus on Friday, but his doctors say he has responded well and could return to the White House on Monday.
That helped U.S. S&P 500 e-mini futures rise 0.62%, while Nasdaq futures gained 0.89%.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 1.08%. Euro Stoxx 50 futures were up 0.82%, German DAX futures rose 0.72%, and FTSE futures gained by 0.91%.
Overhanging the relief rally, however, are continued uncertainty about his condition and some concerns that Trump's case could be more severe than public disclosures suggest.
"Equities and other risk-on traders should be well-supported by easing concerns about Trump's health," said Junichi Ishikawa, senior currency strategist at IG Securities in Tokyo.
"For the dollar, the impact is not quite as clear cut. It should fall against most currencies due to an increase in risk appetite, but the yen is also weak, and that's the one currency the dollar can rise against."
Australian stocks jumped 2.48% for the biggest daily gain since July 21. Japan's Nikkei rose 1.19%. China's financial markets are closed for a public holiday.
The dollar edged higher against the yen but fell slightly against the Swiss franc as traders jockeyed for position ahead of what could be a volatile day in global markets.
Treasury yields rose slightly on reduced demand for the safety of holding government debt.
Doctors treating Trump say they are pleased with his progress. Relief about his health has fuelled a rally in equities and other risky assets as investors prepare for the run-up to next month's U.S. presidential election.
Investors around the world were stunned late Thursday after Trump announced that he and the first lady had tested positive for coronavirus.
With less than a month until the presidential election on Nov. 3, Trump's contraction of the coronavirus is another source of market volatility that makes the outcome of the vote even more difficult to predict.
Democrat Joe Biden opened his widest lead in a month in the U.S. presidential race, according to a Reuters/Ipsos poll released on Sunday.