Improved volatility estimation based on limit order books

Markus Bibinger, Moritz Jirak & Markus Reiss
For a semi-martingale Xt, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation hX;Xit is con- structed 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 ar- eas. A major application is the estimation of the integrated squared volatility of an efficient price process Xt from intra-day order book quotes. We derive...
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