Articlebronze2008

Estimating correlation from high, low, opening and closing prices

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41 citations0/0 files storedThe Annals of Applied Probability

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Financial Risk and Volatility Modeling Financial Markets and Investment Strategies Stochastic processes and financial applications

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.

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References

1980The Extreme Value Method for Estimating the Variance of the Rate of Return 1980On the Estimation of Security Price Volatilities from Historical Data 2005A Tale of Two Time Scales 2008Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise 2002Range‐Based Estimation of Stochastic Volatility Models 19965 Stochastic volatility 2004Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics 1991Estimating Variance From High, Low and Closing Prices

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2014Range Volatility: A Review of Models and Empirical Studies 2018An approximate long-memory range-based approach for value at risk estimation 2010Stochastic volatility models including open, close, high and low prices 2014A reflection principle for a random walk with implications for volatility estimation using extreme values of asset prices 2022Modeling and forecasting dynamic conditional correlations with opening, high, low, and closing prices

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