A model of 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. 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-Nielson and Shephard (2002) remain valid under flat price trading.
Phillips, Peter C.B. and Yu, Jun, "Information Loss in Volatility Measurement with Flat Price Trading" (2007). Cowles Foundation Discussion Papers. 1891.