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

Part of: Markov processes Inference from stochastic processes Limit theorems

Published online by Cambridge University Press:  14 February 2024

Markus Bibinger
Markus Bibinger*
Affiliation:
Julius-Maximilians-Universität Würzburg
*
*Postal address: Chair of Applied Stochastics, Faculty of Mathematics and Computer Science, Institute of Mathematics, Julius-Maximilians-Universität Würzburg, Emil-Fischer-Straße 30, 97074 Würzburg, Germany. Email: markus.bibinger@uni-wuerzburg.de
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Abstract

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.

Keywords

Arcsine lawlimit order bookmarket microstructurenonparametric boundary modelvolatility estimation

MSC classification

Primary: 62M09: Non-Markovian processes
Secondary: 60J65: Brownian motion 60F05: Central limit and other weak theorems
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 28
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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