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

2014/08/16 by Markus Bibinger, Bibinger, Markus, Moritz Jirak +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1408.3768

Extended version including empirical example

arxiv created 2015/11/23 · arxiv updated 2015/11/24

Abstract

For a semi-martingale X_t, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation ⟨ X, X ⟩_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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