Open Access
October 2016 Volatility estimation under one-sided errors with applications to limit order books
Markus Bibinger, Moritz Jirak, Markus Reiß
Ann. Appl. Probab. 26(5): 2754-2790 (October 2016). DOI: 10.1214/15-AAP1161


For a semi-martingale $X_{t}$, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation $\langle X,X\rangle_{t}$ is constructed based on observations in the vicinity of $X_{t}$. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive $n^{-1/3}$ as optimal convergence rate in a high-frequency framework with $n$ observations (in mean). We discuss a potential application for the estimation of the integrated squared volatility of an efficient price process $X_{t}$ from intra-day order book quotes.


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Markus Bibinger. Moritz Jirak. Markus Reiß. "Volatility estimation under one-sided errors with applications to limit order books." Ann. Appl. Probab. 26 (5) 2754 - 2790, October 2016.


Received: 1 June 2015; Revised: 1 November 2015; Published: October 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1353.60044
MathSciNet: MR3563193
Digital Object Identifier: 10.1214/15-AAP1161

Primary: 60H30
Secondary: 60G55

Keywords: Brownian excursion area , Feynman–Kac , high-frequency data , integrated volatility , limit order book , nonparametric minimax rate , Poisson point process

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.26 • No. 5 • October 2016
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