A investigation of the linear and nonlinear optical properties for intersubband electronic transitions associated with a biexciton in a quantum dot has been performed by using the method of few-body physics. The optical absorption coefficients and the refractive index changes have been examined based on the computed energies and wave functions. It is over two orders of magnitude higher than that obtained in an exciton quantum dot. The results show that the optical absorption saturation intensity can be controlled by the confinement potential frequency and the relaxation time.