We provide a structural approach to disentangle Granger versus instantaneous causality effects from transaction durations to price volatility. So far, in the literature, instantaneous causality effects have either been excluded or cannot be identified separately from Granger type causality...

We derive nonparametric bounds for inference about functionals of high-frequency volatility, in particular, integrated power variance. In the absence of microstructure noise, we find that standard Realized Variance attains the nonparametric efficiency bound, also in case of unequally spaced...

We develop an Arbitrage Pricing Theory framework extension to study the pricing of squared returns/volatilities. We analyze the interplay between factors at the return level and those in idiosyncratic variances. We confirm the presence of a common idiosyncratic variance factor, but do not find...

An exact discretization of continuous time stochastic volatility processes observed at irregularly spaced times is used to give insights on how a coherent GARCH model can be specified for such data. The relation of our approach with those in the existing literature is studied