In this paper we analyze the statistical properties of realized variance esti-mators under the assumption that financial logarithmic prices follow a time-changed diffusion process. The time-change takes the form of a counting pro-cess implying that the logarithmic price is a pure jump process with stochastic and time-varying tick volatility. This framework is more appropriate to cap-ture the dynamics of observed logarithmic price processes than the standard diffusion model, and it is also more general than the compound Poisson pro-cess with constant tick volatility. We show that our approach is particularly suited to model the logarithmic transaction prices of stocks, as they exhibit time-varying tick volatility. Our analysis deals with three types of sampling schemes, namely clock-time sampling, business time sampling and transaction time sampling. We theoretically show that, under no market microstructure noise, realized variance is an unbiased estimator of integrated variance and that business time sampling is optimal in terms of mean squared error. To deal with market microstructure noise, we theoretically and empirically consider various bias-corrected realized variance estimators. Our simulation results show that transaction time sampling outperforms business time sampling for high sampling frequencies and large levels of market microstructure noise.