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Volatility estimation under one-sided errors with applications to limit order books

16 August 2014
M. Bibinger
M. Jirak
M. Reiß
ArXiv (abs)PDFHTML
Abstract

For a semi-martingale XtX_tXt​, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation ⟨X,X⟩t\langle X, X \rangle_t⟨X,X⟩t​ is constructed based on observations in the vicinity of XtX_tXt​. 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−1/3n^{-1/3}n−1/3 as optimal convergence rate in a high-frequency framework with nnn observations (in mean). We discuss a potential application for the estimation of the integrated squared volatility of an efficient price process XtX_tXt​ from intra-day order book quotes.

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