In the electricity grid, networked sensors which record and transmit increasingly high-granularity data are being deployed. In such a setting, privacy concerns are a natural consideration. We present an attack model for privacy breaches, and, using results from estimation theory, derive theoretical results ensuring that an adversary will fail to infer private information with a certain probability, independent of the algorithm used. We show utility companies would benefit from less noisy, higher frequency data, as it would improve various smart grid operations such as load prediction. We provide a method to quantify how smart grid operations improve as a function of higher frequency data. In order to obtain the consumer's valuation of privacy, we design a screening mechanism consisting of a menu of contracts to the energy consumer with varying guarantees of privacy. The screening process is a means to segment customers. Finally, we design insurance contracts using the probability of a privacy breach to be offered by third-party insurance companies.