Stochastic Volatility Models with Transaction Time Risk

Abstract

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 effects. By giving explicit moment conditions for observed returns over (random) transaction duration intervals, we are able to identify the instantaneous causality effect, where news events drive simultaneously surprises in durations and surprises in volatilities. Based on ten large stocks traded at the NYSE, we conclude that instantaneous variance forecasts must be decreased by as much as one-third when not having seen the next transaction before its conditional median time. Also, taking into account the causality effects that we document, instantaneous variances are found to be much higher than indicated by standard volatility assessment procedures.

Keywords: Causality, continuous time models, transaction prices, transaction times, ultra-high frequency data