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Title: Parametric and semi-parametric renewal based high-frequency volatility estimator Authors:  Yifan Li - The University of Manchester (United Kingdom) [presenting]
Abstract: High-frequency volatility is proposed to be estimated parametrically based on a renewal process in business time. We show that based on this estimator, an instantaneous volatility estimator can be constructed without involving infill asymptotics. We study the property of the integrated variance process under the assumption that the calendar time point process constructed based on the observed price process follows some parametric autoregressive processes, such as variants of the autoregressive conditional duration model or autoregressive conditional intensity model. We derive asymptotic results for our parametric volatility estimator, proving its consistency and providing a formula to estimate its asymptotic variance. Moreover, we show that a semi-parametric volatility estimator can be constructed, which is more robust to model misspecifications than a full parametric structure at the cost of some estimation efficiency. We provide simulation and empirical evidence for the validity of the estimator.