A viral quasispecies, the ensemble of viral strains populating an infected person, can be highly diverse. For optimal assessment of virulence, pathogenesis and therapy selection, determining the haplotypes of the individual strains can play a key role. As many viruses are subject to high mutation and recombination rates, high-quality reference genomes are often not available at the time of a new disease outbreak. We present SAVAGE, a computational tool for reconstructing individual haplotypes of intra-host virus strains without the need for a high-quality reference genome. SAVAGE makes use of either FM-index based data structures or ad-hoc consensus reference sequence for constructing overlap graphs from patient sample data. In this overlap graph, nodes represent reads and/or contigs, while edges reflect that two reads/contigs, based on sound statistical considerations, represent identical haplotypic sequence. Following an iterative scheme, a new overlap assembly algorithm that is based on the enumeration of statistically well-calibrated groups of reads/contigs then efficiently reconstructs the individual haplotypes from this overlap graph. In benchmark experiments on simulated and on real deep coverage data, SAVAGE drastically outperforms the only de novo viral quasispecies assembler available so far. When run on ad-hoc consensus reference sequence, SAVAGE performs very favorably in comparison with state-of-the-art reference genome guided tools. We also apply SAVAGE on a deep coverage (30000x) sample of a patient infected by the Zika virus, which sheds light on the genetic structure of the respective viral quasispecies.