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Estimation Bias Induced by Discrete Security Prices

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  • Ball, Clifford A

Abstract

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
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    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. repec:gam:jrisks:v:6:y:2018:i:2:p:52-:d:144971 is not listed on IDEAS
    11. 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.
    12. Field, Jonathan & Large, Jeremy, 2008. "Pro-rata matching and one-tick futures markets," CFS Working Paper Series 2008/40, Center for Financial Studies (CFS).
    13. 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.
    14. 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.
    15. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    16. 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.
    17. 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.
    18. 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.
    19. Dubofsky, David, 1997. "Limit orders and ex-dividend day return distributions," Journal of Empirical Finance, Elsevier, vol. 4(1), pages 47-65, January.
    20. 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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