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Estimating the Volatility of Discrete Stock Prices

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  • Cho, David Chinhyung
  • Frees, Edward W

Abstract

This paper introduces an estimator of stock price volatility which eliminates, at least asymptotically , the biases that are caused by the discreteness of observed stock pr ices. Assuming that the observed stock prices are continuously monito red, an estimator is constructed using the notion of how quickly the price changes rather than how much the price changes. It is shown tha t this estimator has desirable asymptotic properties, including consi stency and normality. Also, through a simulation study, the authors s how that it outperforms natural estimators for low and middle priced stocks. Further, the simulation study demonstrates that the proposed estimator is robust to certain misspecifications in measuring the tim e between price changes. Copyright 1988 by American Finance Association.

Suggested Citation

  • Cho, David Chinhyung & Frees, Edward W, 1988. "Estimating the Volatility of Discrete Stock Prices," Journal of Finance, American Finance Association, vol. 43(2), pages 451-466, June.
    • Handle: RePEc:bla:jfinan:v:43:y:1988:i:2:p:451-66
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    Cited by:

    1. Parthajit Kayal & Sayanti Mondal, 2020. "Speed of Price Adjustment in Indian Stock Market: A Paradox," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(4), pages 453-476, December.
    2. Antonios Antoniou & Constantinos E. Vorlow, 2004. "Price Clustering and Discreteness: Is there Chaos behind the Noise?," Papers cond-mat/0407471, arXiv.org.
    3. Hausman, Jerry A. & Lo, Andrew W. & MacKinlay, A. Craig, 1992. "An ordered probit analysis of transaction stock prices," Journal of Financial Economics, Elsevier, vol. 31(3), pages 319-379, June.
    4. Vuorenmaa, Tommi A., 2008. "Decimalization, Realized Volatility, and Market Microstructure Noise," MPRA Paper 8692, University Library of Munich, Germany.
    5. Hellström, Jörgen & Simonsen, Ola, 2006. "Does the Open Limit Order Book Reveal Information About Short-run Stock Price Movements?," Umeå Economic Studies 687, Umeå University, Department of Economics.
    6. Lo, Andrew W. & MacKinlay, A. Craig & Zhang, June, 2002. "Econometric models of limit-order executions," Journal of Financial Economics, Elsevier, vol. 65(1), pages 31-71, July.
    7. Gerhard, Frank & Hess, Dieter & Pohlmeier, Winfried, 1998. "What a Difference a Day Makes: On the Common Market Microstructure of Trading Days," CoFE Discussion Papers 98/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    8. Frank Gerhard & Dieter Hess & Winfried Pohlmeier, 1999. "What a Difference a Day Makes: On the Common Market Microstructure of Trading Days," Finance 9904006, University Library of Munich, Germany.
    9. David Walsh & Glenn Yu-Gen Tsou, 1998. "Forecasting index volatility: sampling interval and non-trading effects," Applied Financial Economics, Taylor & Francis Journals, vol. 8(5), pages 477-485.
    10. Vladimir Petrov & Anton Golub & Richard Olsen, 2019. "Instantaneous Volatility Seasonality of High-Frequency Markets in Directional-Change Intrinsic Time," JRFM, MDPI, vol. 12(2), pages 1-31, April.
    11. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    12. Hautsch, Nikolaus & Pohlmeier, Winfried, 2001. "Econometric Analysis of Financial Transaction Data: Pitfalls and Opportunities," CoFE Discussion Papers 01/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    13. Song, Shijia & Li, Handong, 2023. "Is a co-jump in prices a sparse jump?," The North American Journal of Economics and Finance, Elsevier, vol. 67(C).
    14. Gerhard, Frank & Hautsch, Nikolaus, 2002. "Volatility estimation on the basis of price intensities," Journal of Empirical Finance, Elsevier, vol. 9(1), pages 57-89, January.
    15. Weaver, Robert D & Natcher, William C, 2000. "Commodity Price Volatility under New Market Orientations," MPRA Paper 9862, University Library of Munich, Germany.
    16. Zhicheng Li & Haipeng Xing, 2022. "High-Frequency Quote Volatility Measurement Using a Change-Point Intensity Model," Mathematics, MDPI, vol. 10(4), pages 1-24, February.
    17. Antoniou, Antonios & Vorlow, Constantinos E., 2005. "Price clustering and discreteness: is there chaos behind the noise?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 389-403.
    18. Yadav, Pradeep K., 1992. "Event studies based on volatility of returns and trading volume: A review," The British Accounting Review, Elsevier, vol. 24(2), pages 157-184.
    19. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    20. Roy A. Fletcher, 1995. "The Role Of Information And The Time Between Trades: An Empirical Investigation," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(2), pages 239-260, June.
    21. Pohlmeier, Winfried & Liesenfeld, Roman, 2003. "A Dynamic Integer Count Data Model for Financial Transaction Prices," CoFE Discussion Papers 03/03, University of Konstanz, Center of Finance and Econometrics (CoFE).
    22. Pandey, Ajay, 2003. "Modeling and Forecasting Volatility in Indian Capital Markets," IIMA Working Papers WP2003-08-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    23. Dubofsky, David, 1997. "Limit orders and ex-dividend day return distributions," Journal of Empirical Finance, Elsevier, vol. 4(1), pages 47-65, January.
    24. Lau, Sie Ting & McInish, Thomas H., 1995. "Reducing tick size on the Stock Exchange of Singapore," Pacific-Basin Finance Journal, Elsevier, vol. 3(4), pages 485-496, December.

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