Inference on the intraday spot volatility from high-frequency order prices with irregular microstructure noise

We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an Itô semimartingale with jumps and general stochastic volatility, we present a simple and explicit estima...

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Bibliographic Details
Published inJournal of applied probability Vol. 61; no. 3; pp. 858 - 885
Main Author Bibinger, Markus
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2024
Subjects
Algorithms
Approximation
Asymptotic properties
Asymptotic series
Brownian motion
Central limit theorem
Martingales
Microstructure
Monte Carlo simulation
Numerical analysis
Original Article
Prices
Random variables
Statistics
Time series
Volatility
60J65
market microstructure
volatility estimation
Arcsine law
nonparametric boundary model
62M09
60F05
limit order book
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Summary:We consider estimation of the spot volatility in a stochastic boundary model with one-sided microstructure noise for high-frequency limit order prices. Based on discrete, noisy observations of an Itô semimartingale with jumps and general stochastic volatility, we present a simple and explicit estimator using local order statistics. We establish consistency and stable central limit theorems as asymptotic properties. The asymptotic analysis builds upon an expansion of tail probabilities for the order statistics based on a generalized arcsine law. In order to use the involved distribution of local order statistics for a bias correction, an efficient numerical algorithm is developed. We demonstrate the finite-sample performance of the estimation in a Monte Carlo simulation.
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content type line 14
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2023.96