Estimating correlation from high, low, opening and closing prices

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.Comment: 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

Stochastic volatility models including open, close, high and low prices

“…In that regard, we can start by writing a model for the multivariate log-asset prices y t as a multivariate GBM, with time variance covariance matrix, and deriving the joint density for closing, high and low prices conditional on the opening prices, in a manner similar to what we did in this paper. This joint likelihood contains all relevant information in the extremes and avoid the calculation of cross ranges (Rogers & Zhou, 2008), which scale badly to higher dimensions.…”

Correlation estimation using components of Japanese candlesticks

“…The BERs were (implicitly) used for correlation estimation in Rogers and Zhou (2008) for the first time. Under the assumption of a standard bivariate BM, the authors derive the following correlation estimator as a solution to an optimization problem based on the nine cross-functionals of highs, lows and close returns: The estimator has a minimum variance (1/2) for ρ = 0 and is unbiased for ρ = −1, 0 and 1.…”

“…In this way the simulation study differs from the one in Rogers and Zhou (2008), where the inefficient ρ 0;C -see (10) -is used as a benchmark.…”

“…A promising new strand of research on correlation estimation using OHLC price data has been initiated by an important result of Rogers and Shepp (2006), which gives the product moment of the extreme values of two correlated Brownian motions with correlation ρ as a function of the latter. Based on this result, Rogers and Zhou (2008) derive a correlation (covariance) estimator from OHLC data under the assumption of two correlated standard Brownian motions. In a first step, an estimator is constructed as a linear combination of the nine product moments between the open-high, open-low and open-close returns of two Brownian motions, which is unbiased if the two processes are either uncorrelated or perfectly correlated, and has minimum variance, when the processes are uncorrelated.…”

Value-at-risk modeling and forecasting with range-based volatility models: empirical evidence

“…The literature has claimed that range-based volatility estimators are more effective than historical volatility estimators (e.g. Garman & Klass, 1980;Parkinson, 1980;Rogers & Satchell, 1991;Yang & Zhang, 2000). This approach is easy to implement; it only requires readily available high, low, opening, and closing prices.…”