🤖 AI Summary
This paper addresses the low efficiency of realized variance (RV) estimation under time-varying diffusion models. We propose a novel intraday return sampling paradigm based on intrinsic time—not calendar time. Our core methods are: (1) hitting-time sampling, triggered by volatility thresholds; and (2) realized business-time sampling—a new approach that jointly incorporates trading intensity and tick-level variance estimation to dynamically calibrate the intrinsic time scale. We theoretically establish that each method is optimal under distinct microstructure noise regimes. By decoupling the modeling of trading intensity and jump variance, incorporating Hawkes-type jumps and leverage effects, and conducting finite-sample asymptotic analysis alongside Monte Carlo simulations, we demonstrate substantial efficiency gains. Empirical results on high-frequency equity data confirm significant improvements in RV estimation accuracy and volatility forecasting performance.
📝 Abstract
This paper analyzes the benefits of sampling intraday returns in intrinsic time for the realized variance (RV) estimator. We theoretically show in finite samples that depending on the permitted sampling information, the RV estimator is most efficient under either hitting time sampling that samples whenever the price changes by a pre-determined threshold, or under the new concept of realized business time that samples according to a combination of observed trades and estimated tick variance. The analysis builds on the assumption that asset prices follow a diffusion that is time-changed with a jump process that separately models the transaction times. This provides a flexible model that allows for leverage specifications and Hawkes-type jump processes and separately captures the empirically varying trading intensity and tick variance processes, which are particularly relevant for disentangling the driving forces of the sampling schemes. Extensive simulations confirm our theoretical results and show that for low levels of noise, hitting time sampling remains superior while for increasing noise levels, realized business time becomes the empirically most efficient sampling scheme. An application to stock data provides empirical evidence for the benefits of using these intrinsic sampling schemes to construct more efficient RV estimators as well as for an improved forecast performance.
