B737 flight crew reported moderate to severe turbulence during departure climb.

Narrative

On departure leaving ZZZ; we encountered moderate to severe turbulence and airspeed deviations +/- 20 climbing through 7500'. The airspeed settled mostly above 9;000'; while the moderate turbulence continued through 15;000'. Passing through approximately 8000'; the airspeed dropped while the aircraft was experiencing the turbulence; and the low speed amber band and barber pole were jumping all over the place. We leveled momentarily to gain airspeed above the programmed VREF40+70 because the airspeed was so violently back and forth that for an instant the stick shaker even rattled; although the next instant we were well above the amber low speed band. The airplane was mostly controllable and responsive; and there was no buffet. All passengers and crew were seated for the duration. There were no injuries nor suspected damage.We notified ATC of the turbulence and dispatch of the turbulence and airspeed variability. The flight continued without further incident. Initially we reported the turbulence as moderate but updated the report to severe per FOM. I also updated ATC that we had experienced severe turbulence without damages nor injuries.