A microscopic theory is presented for the giant amplification from microcavities in the strong exciton-photon coupling regime, providing excellent agreement with recent angle-resolved pump-probe experiments. The analytical and numerical solutions give insight into the physics of the polariton parametric amplifier. The coherent gain, due to polariton four-wave-mixing, has a threshold dependence on the pump power and is spectrally blueshifted from the lower polariton energy. The gain shift does not depend on the power, but on the unperturbed polariton linewidth.