We propose a two-stage stochastic model for optimizing the operation of energy storage. The model captures two important features: uncertain real-time prices when day-ahead operational commitments are made; and the price impact of charging and discharging energy storage. We demonstrate that if energy storage has full flexibility to make real-time adjustments to its day-ahead commitment and market prices do not respond to charging and discharging decisions, there is no value in using a stochastic modeling framework, i.e., the value of stochastic solution is always zero. This is because in such a case the energy storage behaves purely as a financial arbitrageur day ahead, which can be captured using a deterministic model. We show also that prices responding to its operation can make it profitable for energy storage to “waste” energy, for instance by charging and discharging simultaneously, which is normally sub-optimal. We demonstrate our model and how to calibrate the price-response functions from historical data with a practical case study.