English

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 XtX_t, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation X,Xt\langle X, X \rangle_t is constructed based on observations in the vicinity of XtX_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 n1/3n^{-1/3} as optimal convergence rate in a high-frequency framework with nn observations (in mean). We discuss a potential application for the estimation of the integrated squared volatility of an efficient price process XtX_t 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

R2 v1 2026-06-22T05:31:02.053Z