We present simultaneous X-ray and optical B and V band light curves of the Seyfert Galaxy NGC 3783 spanning 2 years. The flux in all bands is highly variable and the fluctuations are significantly correlated. As shown before by Stirpe et al. the optical bands vary simultaneously, with a delay of less than 1.5 days but both B and V bands lag the X-ray fluctuations by 3–9 days. This delay points at optical variability produced by X-ray reprocessing and the value of the lag places the reprocessor close to the broad line region. A power spectrum analysis of the light curve, however, shows that the X-ray variability has a power law shape bending to a steeper slope at a timescale ∼ 2.9 days while the variability amplitude in the optical bands continues to grow towards the longest time-scale covered, ∼ 300 days. We show that the power spectra together with the small value of the time delay is inconsistent with a picture where all the optical variability is produced by X-ray reprocessing, though the small amplitude, rapid optical fluctuations might be produced in this way. We detect larger variability amplitudes on long time-scales in the optical bands than in the X-rays. This behaviour adds to similar results recently obtained for at least three other AGN and indicates a separate source of long term optical variability, possibly accretion rate or thermal fluctuations in the optically emitting accretion disc.