IDEAS home Printed from
   My bibliography  Save this article

Estimation Bias Induced by Discrete Security Prices


  • Ball, Clifford A


Commonly, equilibrium security prices are modeled by continuous state stochastic processes while observed prices are rounded i nto discrete units. This paper models the rounding mechanism and exam ines the probabilistic structure of the resultant rounded process. Th e author provides accurate and simple estimates of the inflation in e stimated variance and kurtosis induced by ignoring rounding. In parti cular, the maximum likelihood estimate of security price volatility, using rounded prices, is developed and a simulation analysis is perfo rmed to examine the small sample properties of this estimator. For ma ny practical applications, a simple correction for rounding becomes a vailable. Copyright 1988 by American Finance Association.

Suggested Citation

  • Ball, Clifford A, 1988. " Estimation Bias Induced by Discrete Security Prices," Journal of Finance, American Finance Association, vol. 43(4), pages 841-865, September.
  • Handle: RePEc:bla:jfinan:v:43:y:1988:i:4:p:841-65

    Download full text from publisher

    File URL:
    File Function: full text
    Download Restriction: Access to full text is restricted to JSTOR subscribers. See for details.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Nelson, Charles R, 1976. "Inflation and Rates of Return on Common Stocks," Journal of Finance, American Finance Association, vol. 31(2), pages 471-483, May.
    2. Nelson, Charles R, 1979. "Recursive Structure in U.S. Income, Prices, and Output," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1307-1327, December.
    3. Pearce, Douglas K & Roley, V Vance, 1985. "Stock Prices and Economic News," The Journal of Business, University of Chicago Press, vol. 58(1), pages 49-67, January.
    4. Gallant, A. Ronald & Jorgenson, Dale W., 1979. "Statistical inference for a system of simultaneous, non-linear, implicit equations in the context of instrumental variable estimation," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 275-302.
    5. Laurence J. Kotlikoff & Daniel E. Smith, 1983. "Introduction to "Pensions in the American Economy"," NBER Chapters,in: Pensions in the American Economy, pages 1-19 National Bureau of Economic Research, Inc.
    6. Kotlikoff, Laurence J. & Smith, Daniel E., 1984. "Pensions in the American Economy," National Bureau of Economic Research Books, University of Chicago Press, edition 0, number 9780226451466.
    7. Schwert, G William, 1981. "The Adjustment of Stock Prices to Information about Inflation," Journal of Finance, American Finance Association, vol. 36(1), pages 15-29, March.
    8. Fama, Eugene F, 1981. "Stock Returns, Real Activity, Inflation, and Money," American Economic Review, American Economic Association, vol. 71(4), pages 545-565, September.
    9. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
    10. Bodie, Zvi, 1976. "Common Stocks as a Hedge against Inflation," Journal of Finance, American Finance Association, vol. 31(2), pages 459-470, May.
    11. Geske, Robert & Roll, Richard, 1983. " The Fiscal and Monetary Linkage between Stock Returns and Inflation," Journal of Finance, American Finance Association, vol. 38(1), pages 1-33, March.
    12. Zvi Bodie & Alan J. Marcus & Robert C. Merton, 1988. "Defined Benefit versus Defined Contribution Pension Plans: What are the Real Trade-offs?," NBER Chapters,in: Pensions in the U.S. Economy, pages 139-162 National Bureau of Economic Research, Inc.
    13. Bernard, Victor L., 1986. "Unanticipated inflation and the value of the firm," Journal of Financial Economics, Elsevier, vol. 15(3), pages 285-321, March.
    14. Hong, Hai, 1977. "Inflation and the Market Value of the Firm: Theory and Tests," Journal of Finance, American Finance Association, vol. 32(4), pages 1031-1048, September.
    15. French, Kenneth R & Ruback, Richard S & Schwert, G William, 1983. "Effects of Nominal Contracting on Stock Returns," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 70-96, February.
    16. Pesando, James E, 1987. "Discontinuities in Pension Benefit Formulas and the Spot Model of the Labor Market: Implications for Financial Economists," Economic Inquiry, Western Economic Association International, vol. 25(2), pages 215-238, April.
    17. Pearce, Douglas K, 1987. "Short-term Inflation Expectations: Evidence from a Monthly Survey: A Note," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 19(3), pages 388-395, August.
    18. Jeremy I. Bulow, 1982. "What are Corporate Pension Liabilities?," The Quarterly Journal of Economics, Oxford University Press, vol. 97(3), pages 435-452.
    19. Feldstein, Martin & Seligman, Stephanie, 1981. "Pension Funding, Share Prices, and National Savings," Journal of Finance, American Finance Association, vol. 36(4), pages 801-824, September.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Brown, Gregory W. & Hartzell, Jay C., 2001. "Market reaction to public information: The atypical case of the Boston Celtics," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 333-370, May.
    2. Fernández, C. & Steel, M.F.J., 1997. "On the Dangers of Modelling through Continuous Distributions : A Bayesian Perspective," Discussion Paper 1997-05, Tilburg University, Center for Economic Research.
    3. Jeremy Large, 2005. "Estimating quadratic variation when quoted prices jump by a constant increment," Economics Papers 2005-W05, Economics Group, Nuffield College, University of Oxford.
    4. 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.
    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. Bianchi, Carlo & Calzolari, Giorgio & Sterbenz, Frederic P., 1991. "Simulation of interest rate options using ARCH," MPRA Paper 24844, University Library of Munich, Germany.
    7. 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.
    8. Anand S. Desai & M. Nimalendran & S. Venkataraman, 1998. "Changes In Trading Activity Following Stock Splits And Their Effect On Volatility And The Adverse-Information Component Of The Bid-Ask Spread," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 21(2), pages 159-183, June.
    9. Frank Gerhard & Dieter Hess & Winfried Pohlmeier, 1999. "What a Difference a Day Makes: On the Common Market Microstructure of Trading Days," Finance 9904006, EconWPA.
    10. Bollerslev, Tim & Domowitz, Ian & Wang, Jianxin, 1997. "Order flow and the bid-ask spread: An empirical probability model of screen-based trading," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1471-1491, June.
    11. Field, Jonathan & Large, Jeremy, 2008. "Pro-rata matching and one-tick futures markets," CFS Working Paper Series 2008/40, Center for Financial Studies (CFS).
    12. Large, Jeremy, 2011. "Estimating quadratic variation when quoted prices change by a constant increment," Journal of Econometrics, Elsevier, vol. 160(1), pages 2-11, January.
    13. Chen, Chun-nan & Wu, Chunchi, 2009. "Small trades and volatility increases after stock splits," International Review of Economics & Finance, Elsevier, vol. 18(4), pages 592-610, October.
    14. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    15. Kalotychou, Elena & Staikouras, Sotiris K. & Zagonov, Maxim, 2009. "The UK equity market around the ex-split date," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(3), pages 534-549, July.
    16. 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.
    17. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    18. Dubofsky, David, 1997. "Limit orders and ex-dividend day return distributions," Journal of Empirical Finance, Elsevier, vol. 4(1), pages 47-65, January.
    19. 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.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jfinan:v:43:y:1988:i:4:p:841-65. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.