  We study the three-band Hubbard model for the copper oxide plane of the
high-temperature superconducting cuprates using determinant quantum Monte Carlo
and the dynamical cluster approximation (DCA) and provide a comprehensive view
of the pairing correlations in this model using these methods. Specifically, we
compute the pair-field susceptibility and study its dependence on temperature,
doping, interaction strength, and charge-transfer energy. Using the DCA, we
also solve the Bethe-Salpeter equation for the two-particle Green's function in
the particle-particle channel to determine the transition temperature to the
superconducting phase on smaller clusters. Our calculations reproduce many
aspects of the cuprate phase diagram and indicate that there is an "optimal"
value of the charge-transfer energy for the model where $T_c$ is largest. These
results have implications for our understanding of superconductivity in both
the cuprates and other doped charge-transfer insulators.
