Information loss in volatility measurement with flat price trading

A model of financial asset price determination is proposed that incorporates flat trading features into an efficient price process. The model involves the superposition of a Brownian semimartingale process for the efficient price and a Bernoulli process that determines the extent of flat price trading. The approach is related to sticky price modeling and the Calvo pricing mechanism in macroeconomic dynamics. A limit theory for the conventional realized volatility (RV) measure of integrated volatility is developed. The results show that RV is still consistent but has an inflated asymptotic variance that depends on the probability of flat trading. Estimated quarticity is similarly affected, so that both the feasible central limit theorem and the inferential framework suggested in Barndorff-Nielsen and Shephard (J Royal Stat Soc Ser B (Stat Methodol) 64:253–280, 2002) remain valid under flat price trading even though there is information loss due to flat trading effects. The results are related to work by Jacod (J Financ Econom 16:526–569, 2018) and Mykland and Zhang (Ann Stat 34:1931–1963, 2006) on realized volatility measures with random and intermittent sampling, and to ACD models for irregularly spaced transactions data. Extensions are given to include models with microstructure noise. Some simulation results are reported. Empirical evaluations with tick-by-tick data indicate that the effect of flat trading on the limit theory under microstructure noise is likely to be minor in most cases, thereby affirming the relevance of existing approaches.