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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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    Cited by:

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    3. 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.
    4. Muneer Shaik & S. Maheswaran, 2019. "Robust Volatility Estimation with and Without the Drift Parameter," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(1), pages 57-91, March.
    5. Neil Shephard & Ole E. Barndorff-Nielsen & Department of Mathematical Sciences & University of Aarhus & Denmark, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," Economics Series Working Papers 240, University of Oxford, Department of Economics.
    6. Meng, Xiaochun & Taylor, James W., 2018. "An approximate long-memory range-based approach for value at risk estimation," International Journal of Forecasting, Elsevier, vol. 34(3), pages 377-388.
    7. Lakshmi Padmakumari & S. Maheswaran, 2018. "Covariance estimation using random permutations," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-21, March.
    8. V. Popov, 2016. "Correlation estimation using components of Japanese candlesticks," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1615-1630, October.
    9. Liao, Yin & Anderson, Heather M., 2019. "Testing for cojumps in high-frequency financial data: An approach based on first-high-low-last prices," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 252-274.
    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.
    11. 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.
    12. Dilip Kumar, 2020. "Value-at-Risk in the Presence of Structural Breaks Using Unbiased Extreme Value Volatility Estimator," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(3), pages 587-610, September.
    13. Muneer Shaik & S. Maheswaran, 2020. "A new unbiased additive robust volatility estimation using extreme values of asset prices," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 313-347, September.
    14. Fiszeder, Piotr & Fałdziński, Marcin & Molnár, Peter, 2023. "Modeling and forecasting dynamic conditional correlations with opening, high, low, and closing prices," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 308-321.
    15. Padmakumari, Lakshmi & S., Maheswaran, 2017. "A new statistic to capture the level dependence in stock price volatility," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 355-362.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

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