2008/03/25 by L. C. G. Rogers, Fanyin Zhou
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #math.PR #msc:60J65 #msc:62P20 #q-fin.ST
paper · pdf · doi:10.1214/07-aap460
published as Annals of Applied Probability 2008, Vol. 18, No. 2, 813-823 · Published in at http://dx.doi.org/10.1214/07-AAP460 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/03/25 · arxiv created 2008/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.