  [Abbreviated] We search for scaling relations between the fundamental AGN
parameters and rest-frame UV/optical variability properties for a sample of
$\sim$90 X-ray selected AGNs covering a wide redshift range from the XMM-COSMOS
survey, with optical light curves in four bands provided by the Pan-STARRS1
(PS1) Medium Deep Field 04 survey. To estimate the variability amplitude we
utilize the normalized excess variance ($\sigma_{\mathrm{rms}}^{2}$) and probe
variability on rest-frame timescales of several months and years by calculating
$\sigma_{\mathrm{rms}}^{2}$ from different parts of our light curves. In
addition, we derive the rest-frame optical PSD for our sources using
continuous-time autoregressive moving average (CARMA) models. We observe that
the excess variance and the PSD amplitude are strongly anti-correlated with
wavelength, bolometric luminosity and Eddington ratio. There is no evidence for
a dependency of the variability amplitude on black hole mass and redshift.
These results suggest that the accretion rate is the fundamental physical
quantity determining the rest-frame UV/optical variability amplitude of quasars
on timescales of months and years. The optical PSD of all of our sources is
consistent with a broken power law showing a characteristic bend at rest-frame
timescales ranging between $\sim$100 and $\sim$300 days. The break timescale
exhibits no significant correlation with any of the fundamental AGN parameters.
The low frequency slope of the PSD is consistent with a value of $-1$ for most
of our objects, whereas the high frequency slope is characterized by a broad
distribution of values between $\sim-2$ and $\sim-4$. These findings unveil
significant deviations from the simple "damped random walk" model, frequently
used in previous optical variability studies. We find a weak tendency for AGNs
with higher black hole mass having steeper high frequency PSD slopes.
