VOLATILITY ESTIMATION UNDER ONE-SIDED ERRORS WITH APPLICATIONS TO LIMIT ORDER BOOKS

• 成果类型: Article
• 署名作者: Bibinger, Markus; Jirak, Moritz; Reiss, Markus
• 署名单位: University of Mannheim; Humboldt University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1161
• 发表日期: 2016
• 页码: 2754-2790
• 关键词: asymptotic equivalence; MODEL; THEOREMS; MARKET

摘要

For a semi-martingale X-t, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation (X, X)(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 infra-day order book quotes.