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Abstract: We study the effect of quantum fluctuations on the parametric instability of a degenerate parametric oscillator at threshold. Relying on a weak nonlinearity, we identify an (effective) universal Liouvillian consistent with the symmetries of the system that captures the slow (long-time) dynamics. We find that all cumulants exhibit universal power-law scaling with the nonlinearity, with the Fano factor showing a maximum near the threshold. For a voltage biased Josephson junction, the method of third quantization method is used to identify the slow modes and to derive the effective dynamics by adiabatic elimination of the fast modes. In this way, the parameters entering the effective model can be linked to the microscopic parameters of the experimental platform. Our findings offer insights into the oscillator’s behavior and provide a foundation for understanding and predicting the parametric instability at threshold.