[en] We present a variational estimate for the binding energy of a Frenkel exciton in the insulating cuprate superconductors. Starting from the three-band Hubbard model we perform a canonical transformation to O(t²), where t is the bare nearest-neighbour copper-oxygen hopping integral. An effective Hamiltonian is then derived to describe the hopping of the exciton through the copper oxide plane. The critical parameter in the model is the nearest-neighbour copper-oxygen Coulomb repulsion, V. It is found that a critical value of V is needed to observe bound Frenkel excitons, and that these excitons have the same symmetry as the parent copper orbital, d(x²-y²). We determine the critical value of V using a variational approach, and attempt to fit the parameters of the model to known experimental results. (author)