this question has beatiful answer from theory of quantum electrodynamics
feyneman the father of this theory has convincingly explained that there is no neccessity of a particle-wave picture.
he explained with his theory how even paricles of light can be used explain patterns of interference.. hence no need attribute this nature of light to be as a wave.
his theory is based on something called sum over histories..
a probablistic approach.
for more info on quantum electrodynamics(qed) u can see this webpage