In this paper, we consider a scenario where a group of investor-owned independently-operated storage units seek to offer energy and reserve in the day-ahead market and energy in the hour-ahead market. We are particularly interested in the case where a significant portion of the power generated in the grid is from wind and other intermittent renewable energy resources. In this regard, we formulate a stochastic programming framework to choose optimal energy and reserve bids for the storage units that takes into account the fluctuating nature of the market prices due to the randomness in the renewable power generation availability. We show that the formulated stochastic program can be converted to a convex optimization problem to be solved efficiently. Our simulation results also show that our design can assure profitability of the private investment on storage units. We also investigate the impact of various design parameters, such as the size and location of the storage unit on increasing the profit.