  Physics of high-$T_c$ superconducting cuprates is obscured by the effect of
strong electronic correlations. One way to overcome the problem is to seek for
an exact solution at least within the small cluster and expand it to the whole
crystal. Such an approach is in the heart of the cluster perturbation theory
(CPT). Here we develop CPT for the dynamic spin and charge susceptibilities
(spin-CPT and charge-CPT), within which the correlation effects are explicitly
taken into account by the exact diagonalization. We apply spin-CPT and
charge-CPT to the effective two-band Hubbard model for the cuprates obtained
from the three-band Emery model and calculate one- and two-particle correlation
functions, namely, spectral function and spin and charge susceptibilities.
Doping dependence of the spin susceptibility was studied within spin-CPT and
CPT-RPA that is the CPT generalization of the random phase approximation (RPA).
Both methods produce the low energy response at four incommensurate wave
vectors in qualitative agreement to the results of the inelastic neutron
scattering on overdoped cuprates.
