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arxiv: 1408.3768 · v4 · pith:OS4TXSSCnew · submitted 2014-08-16 · 🧮 math.PR · math.ST· stat.TH

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

classification 🧮 math.PR math.STstat.TH
keywords estimationframeworkobservationsorderprocessvolatilityapplicationapplications
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For a semi-martingale $X_t$, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation $\langle X, X \rangle_t$ 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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