Time-Bridge Estimators of Integrated Variance

TL;DR

This paper introduces new log-price integrated variance estimators that leverage high, low, and occurrence time information to significantly improve efficiency over standard methods, especially for Itô processes.

Contribution

The paper develops a novel class of estimators combining open-high-low-close data and occurrence times, enhancing the accuracy of integrated variance estimation.

Findings

Estimators outperform standard realized variance in efficiency.

Inclusion of occurrence times further improves estimator performance.

Analytical results are derived for Itô stochastic processes.

Abstract

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 characteristics 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 high's and low's of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the well-known realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying log-price process is an It\^o stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies.