Paramount and Skydance merged last week to form a new company officially called Paramount, a Skydance Corporation. Paramount Skydance announced a seven-year agreement for media rights to the Ultimate Fighting Championship on Monday, and analysts think more deals could be coming.

The newly formed Paramount Skydance's stock just earned its meme stock fame and surged. Should investors dive in or approach cautiously?

The new owners of the venerable studio, now trading as PSKY, have seen a volatile stock rally of 30 percent over two days.