  The development of high efficiency perovskite solar cells has sparked a
multitude of measurements on the optical properties of these materials. For the
most studied methylammonium(MA)PbI$_3$ perovskite, a large range (6-55 meV) of
exciton binding energies has been reported by various experiments. The
existence of excitons at room temperature is unclear. For the MAPb$X_3$
perovskites we report on relativistic $GW$-BSE calculations. This method is
capable to directly calculate excitonic properties from first-principles. At
low temperatures it predicts exciton binding energies in agreement with the
reported 'large' values. For MAPbI$_3$, phonon modes present in this frequency
range have a negligible contribution to the ionic screening. By calculating the
polarisation in time from finite temperature molecular dynamics, we show that
at room temperature this does not change. We therefore exclude ionic screening
as an explanation for the experimentally observed reduction of the exciton
binding energy at room temperature.
