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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.

Suggested Citation

  • L. C. G. Rogers & Fanyin Zhou, 2008. "Estimating correlation from high, low, opening and closing prices," Papers 0804.0162, arXiv.org.
  • Handle: RePEc:arx:papers:0804.0162
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    References listed on IDEAS

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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, vol. 53(1), pages 61-65, January.
    2. Ball, Clifford A & Torous, Walter N, 1984. "The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing," The Journal of Business, University of Chicago Press, vol. 57(1), pages 97-112, January.
    3. Michael W. Brandt & Francis X. Diebold, 2006. "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," The Journal of Business, University of Chicago Press, vol. 79(1), pages 61-74, January.
    4. 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, vol. 53(1), pages 67-78, January.
    5. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
    6. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    7. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
    8. 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, May.
    9. repec:oxf:wpaper:264 is not listed on IDEAS
    10. 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.
    11. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    12. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 295-302, April.
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    Citations

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    Cited by:

    1. Enrique Ter Horst & Abel Rodriguez & Henryk Gzyl & German Molina, 2012. "Stochastic volatility models including open, close, high and low prices," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 199-212, May.
    2. 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, vol. 38(C), pages 33-44.
    3. Dilip Kumar, 2016. "Estimating and forecasting value-at-risk using the unbiased extreme value volatility estimator," Proceedings of Economics and Finance Conferences 3205528, International Institute of Social and Economic Sciences.
    4. repec:eee:quaeco:v:65:y:2017:i:c:p:355-362 is not listed on IDEAS
    5. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Papers 2005-W16, Economics Group, Nuffield College, University of Oxford.
    6. Kazemilari, Mansooreh & Djauhari, Maman Abdurachman, 2015. "Correlation network analysis for multi-dimensional data in stocks market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 62-75.
    7. Cook, Steve & Watson, Duncan, 2017. "Revisiting the returns–volume relationship: Time variation, alternative measures and the financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 228-235.
    8. Lakshmi Padmakumari & S Maheswaran, 2016. "A Regression Based Approach to Capturing the Level Dependence in the Volatility of Stock Returns," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 6(12), pages 706-718, December.
    9. Maheswaran, S. & Kumar, Dilip, 2013. "An automatic bias correction procedure for volatility estimation using extreme values of asset prices," Economic Modelling, Elsevier, vol. 33(C), pages 701-712.
    10. Kumar, Dilip & Maheswaran, S., 2014. "Modeling and forecasting the additive bias corrected extreme value volatility estimator," International Review of Financial Analysis, Elsevier, vol. 34(C), pages 166-176.

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