The temperature, hydrostatic pressure, and external electric field effects on the confined exciton in cylindrical quantum dots by considering a parabolic confining potential are investigated. The effects of these external perturbations on the binding energy and interband emission energy are calculated numerically by adopting the variational method within the effective mass approximation. Our findings indicate that the exciton binding energy and interband emission energy depend significantly on decreasing electric field, diminishing temperature, and enhancing the hydrostatic pressure. The contribution of the electric field on the binding energy becomes more important for wide axial parabolic quantum well. We have also shown that the Stark effect of exciton diminishes almost linearly with increasing hydrostatic pressure. Furthermore, the electric field and the quantum dot height lead to enhancing the Stark shift. The behaviour of the excitonic Stark shift as a function of the applied electric field proves the existence of a dipole moment. This physical parameter becomes important for the weak confinement regime.