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This paper presents two mathematical formulations to represent uncertainties in self-scheduling models of a price-taker Compressed Air Energy Storage (CAES) facility. The proposed model is from the point of view of the plant owner participating in the energy, spinning, and idle reserve markets. The first described formulation is based on Robust Optimization (RO) and the second one is based on Affine Arithmetic (AA) techniques, which are both range arithmetic methodologies, and consider the thermodynamic characteristics of the CAES facility for a more realistic representation. The implementation of both methods are tested, validated and compared with each other and with Monte Carlo Simulations (MCS) using prices from the Ontario market. From the simulation results, it can be observed that both methods have some similarities, presenting lower computational burden compared with MCS, and demonstrate the advantage of applying the proposed models for CAES plant owners to hedge against price uncertainties. [ABSTRACT FROM AUTHOR]