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This paper introduces a novel modelling of the economics of energy storages providing frequency containment reserves. The focus lies both on the practical operation of day-ahead markets and the stochastic and autocorrelation characteristics of the grid frequency as they are practical concerns for any energy storage operator. Based on yearly series of grid-frequency measurements we put in light seasonal trends in the grid frequency. After having removed these trends we build an ARMA-GARCH model with fat-tail feature to explain the remaining autocorrelation. The overall model can be used to generate scenarios of 15-minute time-step frequency deviations and we explain how these scenarios can be used along with stochastic programming to dispatch and compute the revenues of a storage providing frequency containment reserves. By considering two different cases, battery storage and variable-speed pumped-storage, the paper emphasizes the importance of the technical characteristics of energy ... Abstract-This paper introduces a novel modelling of the economics of energy storages providing frequency containment reserves. The focus lies both on the practical operation of dayahead markets and the stochastic and autocorrelation characteristics of the grid frequency as they are practical concerns for any energy storage operator. Based on yearly series of gridfrequency measurements we put in light seasonal trends in the grid frequency. After having removed these trends we build an ARMA-GARCH model with fat-tail feature to explain the remaining autocorrelation. The overall model can be used to generate scenarios of 15-minute time-step frequency deviations and we explain how these scenarios can be used along with stochastic programming to dispatch and compute the revenues of a storage providing frequency containment reserves. By considering two different cases, battery storage and variable-speed pumped-storage, the paper emphasizes the importance of the technical characteristics of energy storages providing frequency containment reserves.