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A new look at variance estimation based on low, high and closing prices taking into account the drift

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  • Piotr Fiszeder
  • Grzegorz Perczak

Abstract

The joint distribution of low, high and closing prices of the arithmetic Brownian motion is used to evaluate the properties of the most popular estimators of the variance constructed on the basis of high, low and closing prices. The expected values and mean square errors of the Parkinson, Garman–Klass and Rogers–Satchell estimators for the process with a zero drift and a non‐zero drift are derived. Moreover, new volatility estimators, more efficient in the majority of financial applications than the Rogers–Satchell estimator, are proposed. The considered estimators are applied to the estimation of the volatility of the Polish stock index WIG20.

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  • Piotr Fiszeder & Grzegorz Perczak, 2013. "A new look at variance estimation based on low, high and closing prices taking into account the drift," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 456-481, November.
    • Handle: RePEc:bla:stanee:v:67:y:2013:i:4:p:456-481
    DOI: 10.1111/stan.12017
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    Cited by:

    1. Aneta Wlodarczyk & Iwona Otola, 2016. "Analysis of the Relationship between Market Volatility and Firms Volatility on the Polish Capital Market," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 16, pages 87-116.
    2. Fiszeder, Piotr & Fałdziński, Marcin & Molnár, Peter, 2019. "Range-based DCC models for covariance and value-at-risk forecasting," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 58-76.
    3. Fiszeder, Piotr & Perczak, Grzegorz, 2016. "Low and high prices can improve volatility forecasts during periods of turmoil," International Journal of Forecasting, Elsevier, vol. 32(2), pages 398-410.
    4. Milton Abdul Thorlie & Lixin Song & Muhammad Amin & Xiaoguang Wang, 2015. "Modeling and forecasting of stock index volatility with APARCH models under ordered restriction," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 329-356, August.
    5. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    6. Lyócsa, Štefan & Todorova, Neda & Výrost, Tomáš, 2021. "Predicting risk in energy markets: Low-frequency data still matter," Applied Energy, Elsevier, vol. 282(PA).
    7. Piotr Fiszeder, 2018. "Low and high prices can improve covariance forecasts: The evidence based on currency rates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(6), pages 641-649, September.
    8. Będowska-Sójka, Barbara & Kliber, Agata, 2021. "Information content of liquidity and volatility measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    9. Fiszeder, Piotr & Fałdziński, Marcin, 2019. "Improving forecasts with the co-range dynamic conditional correlation model," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).

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