The stock market showed some life following hopeful signs of progress in the US budget talks. The S&P enjoyed its biggest gain this month. Delta led gainers after the airline said it will buy almost half of Richard Branson’s Virgin Atlantic for $360 million as it goes after a bigger slice of the lucrative New York-London travel market. And AIG jumped after the Treasury sold the rest of its stake in the insurer. Investors were also encouraged by a report that showed an index of German investor optimism rose more than expected in December, suggesting market professionals think Europe’s largest economy will avoid a recession.