We develop a quantum mechanical theory to describe the optical response of semiconductor nanostructures with a particular emphasis on higher-order harmonic generation. Based on a tight-binding approach we take all two-particle correlations into account thus describing the creation, evolution, and annihilation of electrons and holes. In the limiting case of bulk materials, we obtain the same precision as that achieved by solving the well-established semiconductor Bloch equations. For semiconducting structures of finite extent, we also incorporate the surrounding space thus enabling a description of electron emission. In addition, we incorporate different relaxation mechanisms such as dephasing and damping of intraband currents. Starting from precise material data as, e.g., from tight-binding parameters obtained from density-functional-theory calculations, we obtain a numerical description being by far less computationally challenging and resource-demanding as comparable ab initio approaches, e.g., those based on time-dependent density functional theory.