We used a series of CO5BOLD hydrodynamical model atmospheres covering stellar objects from white dwarfs to red giants to derive theoretical estimates of the photometric and photocentric stellar variability in wavelength-integrated light across the Hertzsprung-Russell diagram. We validated our models against solar measurements from the SoHO/VIRGO instrument. Within our set of models we find a systematic increase of the photometric as well as photocentric variability - which turn out to be closely connected - with decreasing surface gravity. The estimated absolute levels of the photocentric variability do not affect astrometric observations on a precision level expected to be achieved by the GAIA mission - with the exception of close-by giant...