We evaluate and compare alternative monetary policy rules, namely average inflation targeting, price level targeting, and traditional inflation targeting rules, in a standard New Keynesian model that features recurring, transient zero lower bound regimes. We use determinacy and expectational stability (E-stability) of equilibrium as the criteria for stabilization policy. We find that price level targeting policy, including nominal income targeting as a special case, most effectively promotes determinacy and E-stability among the policy frameworks, whereas standard inflation targeting rules are prone to indeterminacy. Average inflation targeting can induce determinacy and E-stability effectively, provided the averaging window is sufficiently long.