The arm cavities of real gravitational wave detectors can show small deviations like a tilt or a spatial shift between the cavity mirrors. These deviations lead to a separation of the optical mode centres with respect to the mirrorʼs centre. In this Letter we perform the computation of parametric instable modes considering the described displacement. We further analyse the possibility of parametric oscillatory instability in the Advanced LIGO interferometer for the case of a displaced arm cavity. Our results reveal an additional number of optical and elastic mode combinations due to a displacement that can give rise to the undesirable effect of parametric oscillatory instability. ► We analyse the possibility of parametric oscillatory instability in the Advanced LIGO interferometer. ► We perform the computation of parametric instable modes considering the mirror displacement. ► Our results reveal an additional number of optical and elastic mode unstable combinations.