Unlike the traditional displacement vessels, the modern roll-on roll-off (Ro–Ro), container and cruise vessels designed over the past two decades are seen to be prone to dynamic instabilities, which in some cases may lead to capsizing. Although the vulnerability of a design to dynamic instabilities can be assessed through simulations, this approach is time consuming and unsuitable for analyzing several interim designs during the design spiral iterations. Recent global efforts by the International Maritime Organization (IMO) towards a second generation level 2 criterion attempt to adopt a first principles approach without resorting to time consuming numerical simulations or expensive physical model tests. This work provides such a tool for one of the identified capsizing mechanisms known as parametric rolling in a realistic random seaway. The technique of stochastic averaging is applied to a previously developed realistic model for parametric excitation in random waves. A semi-analytic design criterion for the comparative assessment of different hull forms to parametric roll in random seas is formulated in terms first passage statistics of the system. A sensitivity analysis is performed on the C11 container ship hull form to quantify and gain a deeper understanding of the relative importance of both physical parameters (restoring arm and damping) and environmental parameters (wave spectra intensity and characteristic frequency) on the instability. © 2019 Elsevier Ltd