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Rounding Errors and Volatility Estimation

Author

Listed:
  • Yingying Li
  • Per A. Mykland

Abstract

Financial prices are often discretized—with smallest tick size of one cent, for example. Thus prices involve rounding errors. Rounding errors affect the estimation of volatility, and understanding them is critical, particularly when using high frequency data. We study the asymptotic behavior of realized volatility (RV), which is commonly used as an estimator of integrated volatility. We prove the convergence of the RV and scaled RV under varous conditions on the rounding level and the number of observations. A bias-corrected volatility estimator is proposed and an associated central limit theorem is shown. The simulation and empirical results demonstrate that the proposed method can yield substantial statistical improvement.

Suggested Citation

  • Yingying Li & Per A. Mykland, 2015. "Rounding Errors and Volatility Estimation," Journal of Financial Econometrics, Oxford University Press, vol. 13(2), pages 478-504.
    • Handle: RePEc:oup:jfinec:v:13:y:2015:i:2:p:478-504.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbu005
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    Citations

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    Cited by:

    1. Z. Merrick Li & Oliver Linton, 2022. "A ReMeDI for Microstructure Noise," Econometrica, Econometric Society, vol. 90(1), pages 367-389, January.
    2. Li, Yingying & Zhang, Zhiyuan & Li, Yichu, 2018. "A unified approach to volatility estimation in the presence of both rounding and random market microstructure noise," Journal of Econometrics, Elsevier, vol. 203(2), pages 187-222.
    3. Naoto Kunitomo & Hiroumi Misaki & Seisho Sato, 2015. "The SIML Estimation of Integrated Covariance and Hedging Coefficient Under Round-off Errors, Micro-market Price Adjustments and Random Sampling," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 333-368, September.
    4. Naoto Kunitomo & Daisuke Kurisu, 2017. "Effects of Jumps and Small Noise in High-Frequency Financial Econometrics," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(1), pages 39-73, March.
    5. Li, Yingying & Xie, Shangyu & Zheng, Xinghua, 2016. "Efficient estimation of integrated volatility incorporating trading information," Journal of Econometrics, Elsevier, vol. 195(1), pages 33-50.

    More about this item

    Keywords

    rounding errors; bias-correction; diffusion process; market microstructure; realized volatility (RV);
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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