Efficient Sampling for Realized Variance Estimation in Time-Changed Diffusion Models

This paper illustrates the benefits of sampling intraday returns in intrinsic time for the estimation of integrated variance through the realized variance (RV) estimator. The intrinsic time transforms the clock time in accordance with the market's activity, which we measure by trading intensity (transaction time) or spot variance (business time). We theoretically show that the RV estimator is unbiased for all sampling schemes, but most efficient under business time, also under independent market microstructure noise. Our analysis builds on the flexible assumption that asset prices follow a diffusion process that is time-changed with a doubly stochastic Poisson process. This provides a flexible stochastic model for the prices together with their transaction times that allows for separate and stochastically varying trading intensity and tick variance processes that jointly govern the spot variance. These separate model components are particularly advantageous over e.g., standard diffusion models, as they allow to exploit and disentangle the effects of the two different sources of intraday information on the theoretical properties of RV. Extensive simulations confirm our theoretical results and show that business time remains superior under different noise specifications and for noise-corrected RV estimators. An empirical application to stock data provides further evidence for the benefits of using intrinsic sampling to get efficient RV estimators.