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. A major application is the estimation of the integrated squared volatility of an efficient price process from intra-day order book quotes. We derive as optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with observations (in mean). This considerably improves upon the classical -rate obtained from transaction prices under microstructure noise. %An estimator based on local order statistics attaining the rate is presented.
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