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Estimating correlation from high, low, opening and closing prices

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Author Info
L. C. G. Rogers
Fanyin Zhou

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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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File URL: http://arxiv.org/abs/0804.0162
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Publisher Info
Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0804.0162.

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Date of creation: Apr 2008
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Publication status: Published in Annals of Applied Probability 2008, Vol. 18, No. 2, 813-823
Handle: RePEc:arx:papers:0804.0162

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Michael W. Brandt & Francis X. Diebold, 2006. "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," Journal of Business, University of Chicago Press, vol. 79(1), pages 61-74, January. [Downloadable!]
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  2. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January. [Downloadable!] (restricted)
  3. Ball, Clifford A & Torous, Walter N, 1984. "The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing," Journal of Business, University of Chicago Press, vol. 57(1), pages 97-112, January. [Downloadable!] (restricted)
  4. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December. [Downloadable!] (restricted)
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  5. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January. [Downloadable!] (restricted)
  6. Carmen Broto & Esther Ruiz, 2002. "Estimation Methods For Stochastic Volatility Models: A Survey," Statistics and Econometrics Working Papers ws025414, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
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  7. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," Journal of Business, University of Chicago Press, vol. 65(2), pages 295-302, April. [Downloadable!] (restricted)
  8. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  9. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, 05. [Downloadable!] (restricted)
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  1. Abel Rodriguez & Henryk Gzyl & German Molina & Enrique ter Horst, 2009. "Stochastic Volatility Models Including Open, Close, High and Low Prices," Quantitative Finance Papers 0901.1315, arXiv.org. [Downloadable!]
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