<p>How will extreme events due to human activities and climate change affect the oceanic thermohaline circulation is a key concern in climate predictions. The stability of the thermohaline circulation with respect to extreme events, such as fresh-water oscillations, greenhouse gas accumulations and collapse of the Atlantic meridional overturning circulation, is examined using a conceptual stochastic Stommel two-compartment model. The extreme fluctuations are modeled by symmetric α-stable Lévy motions whose pathways are cádlág functions with at most a countable number of jumps. The mean first passage time, escape probability and stochastic basin of attraction are used to perform the stability analysis of <i>on</i> (<i>off</i>) equilibrium states. Our results argue that for model with weak fresh-water forcing strength, the greatest threat to the stability of the <i>on</i>-state represents noise with low jumps and higher frequency that can be seen as civilization-induced greenhouse gas accumulation. On the other hand, the <i>off</i>-state stability is more vulnerable to the agitations with moderate jumps and frequencies which can be interpreted as wind- driven circulations towards higher latitudes. Under the repercussion of stochastic noise, <i>on</i> to <i>off</i> transitions are more expected in the model if the fresh-water influx is strong. Moreover, transitions from one metastable state to another are equiprobable when the fresh-water input induces a symmetric potential well.</p>