(For a Reuters live blog on U.S., UK and European stock markets, click LIVE/ or type LIVE/ in a news window) Dec 16 (Reuters) - European shares extended gains to a third straight session on Wednesday on rising hopes of a Brexit trade deal and the possible roll-out of a COVID-19 vaccine in the continent before the new year. The pan-European STOXX 600 index rose 0.5%, with eyes on flash PMIs for December due in the morning session. Expectations are for a slight improvement in business activity over the previous month. The optimism in Europe follows an upbeat session in Asia after a strong close on Wall Street overnight with the Nasdaq hitting yet another record on growing prospect of more U.S. fiscal stimulus. Investors will also be watching for the outcome of the U.S. Federal Reserve’s two-day meeting. The decision is due after European markets hours, at 2 p.m. ET (1900 GMT). (Reporting by Susan Mathew in Bengaluru; Editing by Arun Koyyur)