The S&P 500 index reached yet another record high Thursday, and it's got more room to rise, says Tom Lee, managing partner of Fundstrat research.

The S&P 500 slumped 10 percent from Sept. 19 to Oct. 15, and such a move historically presages a bigger rebound, he told CNBC.

"Whenever the market has a deep decline like we saw, typically the bounce that follows is around 20 percent over the next six months. From the low of 1,850 or 1,900, that's close to 400 points, which would take us to 2,200 or 2,300 by April."

The latter level would represent a 13 percent advance from Thursday's close of 2,031.21.

It's been said that bull markets need to climb a wall of worry, and that wall is there, Lee said. "There's been a lot of skepticism about the bounce. . . . [There are] the global issues. So I think there's enough of a wall of worry that the market can still surprise to the upside."

Strong third-quarter earnings reports have buttressed the market.

'What’s really important about this earnings season is that CEOs are no longer saying, 'We can survive.’ They’re saying, ‘We’re expanding our business,'" J. J. Kinahan, TD Ameritrade’s chief strategist, told The Associated Press. "There’s a note of optimism we haven’t heard in a long time."

Whole Foods reported a stronger-than-expected 5.8 percent profit increase for the latest quarter late Wednesday. 

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