  Recent observations of accreting black holes reveal the presence of
quasi-periodic oscillations (QPO) in the optical power density spectra. The
corresponding oscillation periods match those found in the X-rays, implying a
common origin. Among the numerous suggested X-ray QPO mechanisms, some may also
work in the optical. However, their relevance to the broadband -- optical
through X-ray -- spectral properties have not been investigated. For the first
time, we discuss the QPO mechanism in the context of the self-consistent
spectral model. We propose that the QPOs are produced by Lense-Thirring
precession of the hot accretion flow, whose outer parts radiate in the optical
wavelengths. At the same time, its innermost parts are emitting the X-rays,
explaining the observed connection of QPO periods. We predict that the X-ray
and optical QPOs should be either in phase or shifted by half a period,
depending on the observer position. We investigate the QPO harmonic content and
find that the variability amplitudes at the fundamental frequency are larger in
the optical, while the X-rays are expected to have strong harmonics. We then
discuss the QPO spectral dependence and compare the expectations to the
existing data.
