Time-bridge estimators of integrated variance

We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within n subsequent time-step intervals. The main purpose of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the highs and lows of the bridge associated with the original process makes these estimators significantly more efficient than the standard realized variance estimators and their generalizations. Adding the information on the occurrence times of the high and low values further improves the efficiency of the estimators, far exceeding that of the well-known realized variance estimator and those derived from the sum of the Garman and Klass spot variance estimators. The exact analytical results are derived for a case in which the underlying log-price process is an Ito stochastic process. Our results suggest more efficient ways to record financial prices at intermediate frequencies.