In this paper we extend the model of Kato and Nishiyama (2005) by introducing fat-tailed shocks in a simple new Keynesian framework where the central bank explicitly considers the zero lower-bound constraint on interest rates. We find that shocks with `excess kurtosis' make monetary policy relatively more aggressive far away from the zero lower bound region though, this difference reverts as the economy gets closer to the constrained region. From a quantitative point of view, our findings suggest that variance-preserving shifts in kurtosis, in the shape of Laplace distributed shocks, do not produce significant effects on the optimal reaction of the central bank.