Volatility estimation under one-sided errors with applications to limit order books
Probability
2015-11-24 v4 Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1408.3768,
title = {Volatility estimation under one-sided errors with applications to limit order books},
author = {Markus Bibinger and Moritz Jirak and Markus Reiß},
journal= {arXiv preprint arXiv:1408.3768},
year = {2015}
}
Comments
Extended version including empirical example