We propose a concept of a quantum cascade laser based on transitions of bosonic quasiparticles (excitons) in a parabolic potential trap in a semiconductor microcavity. This laser would emit terahertz radiation due to bosonic stimulation of excitonic transitions. The dynamics of a bosonic cascade is strongly different from the dynamics of a conventional fermionic cascade laser. We show that populations of excitonic ladders are parity dependent and quantized if the laser operates without an external terahertz cavity.