Recently, two types of innovative estimators of the quadratic variation (QV), namely, RVB and RVQ estimators, are established in Yu (2020, doi.org/10.1002/mma.6863) for an asset's log‐price process permitting time‐varying spot volatility. Both estimators utilize either higher order or cross‐terms of log‐return and they hence have been demonstrated having better convergence property than existing ones (e.g., the widely known realized volatility). However, the proof of the convergence property of RVB/RVQ is rather cumbersome and algebraically complicated. Besides, imposing the spot volatility to be deterministic function of time in the log‐price process seems to have deviated from reality. This article devotes attention to (1) relaxing the volatility restriction on the semimartingale process of asset's price and (2) substantially shortening the original proofs by alternatively employing two useful lemmas (called high‐order Itô isometry and adjoint Itô identity) developed in this study.
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