Asymptotic theory of range-based multipower variation

TL;DR

This paper develops a new asymptotic theory for range-based multipower variation estimators, improving jump-robustness and efficiency in high-frequency financial data analysis.

Contribution

It introduces a hybrid range-based estimator that removes bias from jumps and demonstrates efficiency gains under sparse sampling conditions.

Findings

The new estimator effectively removes jump bias in volatility estimation.

Range-based multipower variations outperform return-based estimators in sparse data scenarios.

Simulation and real data applications validate the theoretical advantages.

Abstract

In this paper, we present a realized range-based multipower variation theory, which can be used to estimate return variation and draw jump-robust inference about the diffusive volatility component, when a high-frequency record of asset prices is available. The standard range-statistic -- routinely used in financial economics to estimate the variance of securities prices -- is shown to be biased when the price process contains jumps. We outline how the new theory can be applied to remove this bias by constructing a hybrid range-based estimator. Our asymptotic theory also reveals that when high-frequency data are sparsely sampled, as is often done in practice due to the presence of microstructure noise, the range-based multipower variations can produce significant efficiency gains over comparable subsampled return-based estimators. The analysis is supported by a simulation study and we illustrate the practical use of our framework on some recent TAQ equity data.