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We provide a quantitative assessment of policy options to inform the 2021 review of the EU Emissions Trading System (ETS) and raise climate ambition. We use a permit trading model in which firms utilize rolling finite planning horizons, which replicates historical price and banking developments well compared to an infinite horizon. When firms have bounded foresight, indirectly raising ambition through the Market Stability Reserve (MSR) is not equivalent to directly raising ambition through the emissions cap trajectory. Leveraging the MSR turns out to be efficiency improving as it compensates for firms’ bounded foresight by frontloading abatement efforts. We analyze the MSR interaction with the cap trajectory to exploit synergies and minimize the cost of raising ambition. We also provide a comparative assessment of a complete suite of changes in the MSR parameters. Whatever its parameters, MSR-induced resilience to demand shocks remains limited by design: the MSR acts more as an unconditional price support provider than as a responsive price stabilizer.