The optical constants of methylammonium lead halide single crystals CH3NH3PbX3 (X = I, Br, Cl) are interpreted with high level ab initio calculations using the relativistic quasiparticle self-consistent GW approximation (QSGW). Good agreement between the optical constants derived from QSGW and those obtained from spectroscopic ellipsometry enables the assignment of the spectral features to their respective inter-band transitions. We show that the transition from the highest valence band (VB) to the lowest conduction band (CB) is responsible for almost all the optical response of MAPbI3 between 1.2 and 5.5 eV (with minor contributions from the second highest VB and the second lowest CB). The calculations indicate that the orientation of [CH3NH3]+ cations has a significant influence on the position of the bandgap suggesting that collective orientation of the organic moieties could result in significant local variations of the optical properties. The optical constants and energy band diagram of CH3NH3PbI3 are then used to simulate the contributions from different optical transitions to a typical transient absorption spectrum (TAS).