Eumelanin is a naturally occurring skin pigment which is responsible for developing a suntan. The complex structure of eumelanin consists of pi-stacked oligomers of various indole derivatives, such as the monomeric building block 5,6-dihydroxyindole (DHI) In this work, we present an ab initio wave-function study of the absorption behavior of DHI oligomers and of doubly and triply pi-stacked species of these oligomers. We have simulated the onset of the electronic absorption spectra by employing the MP2 and the linear-response CC2 methods. Our results demonstrate the effect of an increasing degree of oligomerization of DHI and of an increasing degree of pi-stacking of DHI oligomers on the onset of the absorption spectra and on the degree of red-shift toward the visible region of the spectrum. We find that pi-stacking of DHI and its oligomers substantially red-shifts the onset of the absorption spectra. Our results also suggest that the optical properties of biological eumelanin cannot be simulated by considering the DHI building blocks alone, but instead the building blocks indole-semiquinone and indole-quinone have to be considered as well. This study contributes to advancing the understanding of the complex photophysics of the eumelanin biopolymer.