In the aftermath of the Great Financial Crisis (GFC), central banks from several advanced, small, open economies have used FX interventions (FXI) in order to stimulate inflation, given that their policy rates were very low. We present a quantitative DSGE model that allows us to study the effectiveness of this unconventional monetary policy tool. We apply the model to Switzerland, a country that has seen frequent and sizable central bank interventions. The model implies that FXI are effective and long-lasting: FXI of approximately CHF 27 billion (5% of annual GDP) are necessary to prevent the Swiss franc from appreciating by 1.1%. The effect is stronger the longer the central bank can commit to keep its policy rate constant in response to the inflationary effect of the interventions. We also find that FXI create significant additional leeway for monetary policy in small, open economies. This effect can be shown by the "shadow rate", the policy rate required to keep CPI inflation on its realised path without FXI. This "shadow rate" was up to 1 pp below the realised policy rate and close to -1.5% from 2015 to mid-2022 in Switzerland. Our framework also allows us to study the sensitivity of the shadow rate in an environment in which the policy rate is at (or close to) its lower bound. If the persistence of the policy rate increases at the lower bound, the shadow rate rises in absolute terms.