  We analyze 168 Swift monitoring observations of the nearest broad absorption
line quasar Mrk 231 in the UV and X-ray bands, where we detect significant
variability in the UV ($\sim$2246\AA) light curve with a null probability of
$4.3\times10^{-10}$ for a constant model. Separately, from an archival sample
of Swift observed active galactic nuclei (AGN), we measure the relation between
UV excess variance and luminosity, finding that the normalized UV excess
variance decreases with luminosity. Comparing to this mean relation, the
normalized UV excess variance of Mrk 231 is smaller, however within the scatter
characterising the full population. The upper limit of the X-ray excess
variance is consistent with other AGN. The power spectrum density of the UV
light curve can be well fit by a power law model with a slope of $1.82\pm0.14$
between $10^{-7.5}$ and $10^{-6}$ Hz, consistent with those for typical AGN,
with no obvious quasi-periodical oscillation peaks. The UV variability and its
power spectrum suggest that a significant amount of the UV emission of Mrk 231
is from the accretion disk. The consistencies in the normalized UV variability
and the shape of the power spectrum density between Mrk 231 and other normal
AGN suggest that the origin of UV variability of broad absorption line quasars
is similar to other AGN, and dust scattering at large scales such as the torus
is not a dominating process for the UV emission of Mrk 231. Significant
scattering, if present, is constrained to smaller than $\sim$10 light days. We
perform lagged correlation analysis between the UV and X-ray light curves and
find the correlation insignificant within the present data.
