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This article studies the implication of extreme shocks for monetary policy. The analysis is based on a small‐scale New Keynesian model with sticky prices and wages where shocks are drawn from asymmetric generalized extreme value distributions. A nonlinear perturbation solution of the model is estimated by the simulated method of moments. Under the Ramsey policy, the central bank responds nonlinearly and asymmetrically to shocks. The trade‐off between targeting a gross inflation rate above 1 as insurance against extreme shocks and targeting an average gross inflation at unity to avoid adjustment costs is unambiguously decided in favor of strict price stability.