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Estimating correlation from high, low, opening and closing prices

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  • L. C. G. Rogers
  • Fanyin Zhou

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/pdf/0804.0162
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Bibliographic Info

Paper provided by arXiv.org in its series 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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  1. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 53(1), pages 61-65, January.
  2. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers, CIRANO 95s-49, CIRANO.
  3. Michael W. Brandt & Francis X. Diebold & April, . "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 03-15, Wharton School Center for Financial Institutions, University of Pennsylvania.
  4. Carmen Broto & Esther Ruiz, 2002. "Estimation Methods For Stochastic Volatility Models: A Survey," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws025414, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 53(1), pages 67-78, January.
  6. 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, Econometric Society, vol. 72(3), pages 885-925, 05.
  7. 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, American Statistical Association, vol. 100, pages 1394-1411, December.
  8. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, American Finance Association, vol. 57(3), pages 1047-1091, 06.
  9. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 65(2), pages 295-302, April.
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  11. repec:oxf:wpaper:264 is not listed on IDEAS
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Cited by:
  1. Kumar, Dilip & Maheswaran, S., 2014. "A reflection principle for a random walk with implications for volatility estimation using extreme values of asset prices," Economic Modelling, Elsevier, Elsevier, vol. 38(C), pages 33-44.
  2. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series, Oxford Financial Research Centre 2005fe08, Oxford Financial Research Centre.
  3. Abel Rodriguez & Henryk Gzyl & German Molina & Enrique ter Horst, 2009. "Stochastic Volatility Models Including Open, Close, High and Low Prices," Papers 0901.1315, arXiv.org.
  4. Maheswaran, S. & Kumar, Dilip, 2013. "An automatic bias correction procedure for volatility estimation using extreme values of asset prices," Economic Modelling, Elsevier, Elsevier, vol. 33(C), pages 701-712.

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