Asymptotic theory of range-based multipower variation

2026-02-22

AI Summary

This study addresses the bias in volatility estimation caused by price jumps when using conventional range-based statistics, as well as the low estimation efficiency under market microstructure noise with sparsely sampled high-frequency data. To overcome these limitations, the authors develop a multi-power variation theory based on price ranges and propose the first hybrid estimator that integrates range-based statistics with multi-power variation. This approach robustly disentangles the continuous diffusive volatility component from jump-induced discontinuities, effectively eliminating jump-related estimation bias. Theoretical analysis demonstrates its superior estimation efficiency under both sparse sampling and microstructure noise. Extensive Monte Carlo simulations and empirical analyses using TAQ equity data confirm the estimator’s enhanced performance relative to existing methods.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• range-based estimation
• jump-robust inference
• volatility estimation
• high-frequency data
• microstructure noise

Innovation

• range-based multipower variation
• jump-robust inference
• diffusive volatility
• microstructure noise
• hybrid estimator