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

Markus Bibinger (Universität Mannheim)
Thursday, December 17, 2015 - 4:15pm
HU Berlin, Rudower Chaussee 25, Room 1.115

We consider a semi-martingale which forms a stochastic boundary, where we have discrete observations with one-sided errors. A rate-optimal estimator of the quadratic variation is constructed. 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 (minimax) convergence rate in a high-frequency framework with n observations (in mean). This reveals an intriguing improved rate in comparison to the prominent model with regular noise which is standard to describe volatility estimation under market microstructure. We discuss an application for the estimation of the integrated squared volatility of an efficient price process from intra-day limit order book quotes.

(joint work with Moritz Jirak and Markus Reiß)