  Using finite temperature diagonalization techniques it is shown that the
quarter-filled t-J-V model on a trellis lattice structure provides a
quantitative explanation of the highly anisotropic optical conductivity of the
$\alpha'-NaV_{2}O_{5}$ compound. The combined effects of the short-range
Coulomb interaction and valence fluctuations of V-ions determine the main
absorption and the fundamental gap. Inter-ladder hopping is necessary for the
explanation of the anomalous in-gap absorption and generation of spectral
weight at high energy. The role of valence fluctuations is explained in terms
of the domain wall excitations of an anisotropic 2D Ising model in a transverse
field close to criticality.
