In the context of second generation stability criteria assessments, the present paper introduces a fast time domain algorithm for parametric roll assessment in irregular seas. Two features can be distinguished in the present proposal: a) it involves the essential heave-roll-pitch nonlinear coupling and b) it is a pre-calculated derivative model, convenient for the required systematic Monte Carlo simulations. The main features of the model are described. The proposed methodology is based on a 3D panel method in which hydrostatic and wave-induced forces are computed on the actual body surface considering a set of systematic pre-defined hull positions. This set of data is preprocessed through polynomial fitting and the coefficients of the derivative model, corresponding to a Taylor series expansion defined up to the third order, are obtained. The methodology is applied to a container ship in head seas. The model is capable of reflecting the non-ergodicity of the head seas parametric rolling. At the same time, heave and pitch motions display "weakly ergodic" responses.