Estimating correlation from high, low, opening and closing prices

TL;DR

This paper develops an unbiased estimator for the correlation between two stocks using daily high, low, opening, and closing prices, achieving significantly lower variance than previous methods.

Contribution

It introduces a novel unbiased estimator for stock correlation based on high, low, open, and close prices, reducing variance compared to existing estimators.

Findings

Estimator halves the variance of correlation estimates.

Unbiasedness of the estimator is theoretically proven.

Method improves accuracy of correlation estimation in financial data.

Abstract

In earlier studies, the estimation of the volatility of a stock using information on the daily opening, closing, high and low prices has been developed; the additional information in the high and low prices can be incorporated to produce unbiased (or near-unbiased) estimators with substantially lower variance than the simple open--close estimator. This paper tackles the more difficult task of estimating the correlation of two stocks based on the daily opening, closing, high and low prices of each. If we had access to the high and low values of some linear combination of the two log prices, then we could use the univariate results via polarization, but this is not data that is available. The actual problem is more challenging; we present an unbiased estimator which halves the variance.