In this paper, a novel approach for providing incentives for caching in small cell networks (SCNs) is proposed based on the economics framework of contract theory. In this model, a mobile network operator (MNO) designs contracts that will be offered to a number of content providers (CPs) to motivate them to cache their content at the MNO's small base stations (SBSs). A practical model in which information about the traffic generated by the CPs' users is not known to the MNO is considered. Under such asymmetric information, the incentive contract between the MNO and each CP is properly designed so as to determine the amount of allocated storage to the CP and the charged price by the MNO. The contracts are derived by the MNO in a way to maximize the global benefit of the CPs and prevent them from using their private information to manipulate the outcome of the caching process. For this interdependent contract model, the closed-form expressions of the price and the allocated storage space to each CP are derived. This proposed mechanism is shown to satisfy the sufficient and necessary conditions for the feasibility of a contract. Moreover, it is shown that the proposed pricing model is budget balanced, enabling the MNO to cover all the caching expenses via the prices charged to the CPs. Simulation results show that none of the CPs will have an incentive to choose a contract designed for CPs with different traffic loads.