"Global economic recovery from the depths of the COVID-19 plunge this past winter and spring has proceeded significantly faster than we envisioned," Peter Hooper, Deutsche global head of economic research wrote in a note to clients.

"As Q3 draws toward a close, we estimate that the level of global GDP is about half way back to its pre-virus level, and we now see that journey being completed by the middle of next year, a couple quarters sooner than in our previous forecast."

Deutsche raised its forecast for global GDP, expecting it to shrink 3.9% this year after predicting in May a contraction of 5.9% for 2020. For 2021, Deutsche raised its growth forecast to 5.6% from 5.3%.

Yet there was also a lot of uncertainty and potential trouble ahead, Hooper added.

Fears over second infection waves gathering momentum in the United States and Europe had increased uncertainty over the economic outlook, with the U.S. election that was "too close to call" adding to the mix. Meanwhile, in Europe a hard Brexit shock was a risk, Deutsche said.

And a shift in monetary policy - though some years away - could spell further trouble.

"The expansion of debt and potential overvaluation of assets that has been fed by necessarily super easy monetary policy poses the serious risk of a looming global financial crisis as central banks begin to shift away from easy policy," Hooper wrote. "Any upward surprises to inflation would heighten this risk."

(Reporting by Karin Strohecker; Editing by Rachel Armstrong and Tomasz Janowski)