  In this paper, we employ a fully microscopic approach to the study of
interlayer excitons in hetero-bilayers. We use Fowler's and Karplus' method to
access the dynamical polarizability of non--interacting interlayer excitons in
a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$--based van der Waals heterostructure.
Following from the calculation of the linear polarizability, we consider
Svendsen's variational method to the calculation of the dynamic third--order
polarizability. With this variational method, we study both two--photon
absorption and third--harmonic generation processes for interlayer excitons in
a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$ hetero--bilayer, discussing the various
selection rules of intra--excitonic energy level transitions.
