Improved volatility estimation based on limit order books

Markus Bibinger, Moritz Jirak and Markus Reiss

No 2014-053, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: For a semi-martingale Xt, 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 Xt. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. A major application is the estimation of the integrated squared volatility of an effcient price process Xt from intra-day order book quotes. We derive n -1/3 as optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with n observations (in mean). This considerably improves upon the classical n -1/4-rate obtained from transaction prices under microstructure noise.

Keywords: Brownian excursion area; limit order book; integrated volatility; Feynman-Kac; high-frequency data; Poisson point process (search for similar items in EconPapers)
JEL-codes: C22 C58 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb649:sfb649dp2014-053

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