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

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