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On the Distribution of Stock Price Differences


  • Benoit Mandelbrot

    (International Business Machines, Yorktown Heights, New York)

  • Howard M. Taylor

    (Cornell University, Ithaca, New York)


Price changes over a fixed number of transactions may have a Gaussian distribution. Price changes over a fixed time period may follow a stable Paretian distribution, whose variance is infinite. Since the number of transactions in any time period is random, the above statements are not necessarily in disagreement. A possible explanation is proposed by Taylob, and then shown by Mandelbrot to be intimately related to an earlier discussion of the specialists' function of ensuring the continuity of the market.

Suggested Citation

  • Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
  • Handle: RePEc:inm:oropre:v:15:y:1967:i:6:p:1057-1062

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    Cited by:

    1. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
    2. Sandrine Jacob Leal & Mauro Napoletano & Andrea Roventini & Giorgio Fagiolo, 2016. "Rock around the clock: An agent-based model of low- and high-frequency trading," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 49-76, March.
    3. Sandrine Jacob Leal & Mauro Napoletano & Andrea Roventini & Giorgio Fagiolo, 2016. "Rock around the clock: An agent-based model of low- and high-frequency trading," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 49-76, March.
    4. Long, Hongwei & Ma, Chunhua & Shimizu, Yasutaka, 2017. "Least squares estimators for stochastic differential equations driven by small Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1475-1495.
    5. Roberto Mota Navarro & Hern'an Larralde Ridaura, 2016. "A detailed heterogeneous agent model for a single asset financial market with trading via an order book," Papers 1601.00229,, revised Jul 2016.
    6. repec:bla:acctfi:v:57:y:2017:i::p:277-298 is not listed on IDEAS
    7. Daniel Friedman & Stoddard Vandersteel, 1980. "Short-Run Fluctuations in Foreign Exchange Rates: An Exploration of the Data," UCLA Economics Working Papers 171, UCLA Department of Economics.
    8. Joel Hasbrouck, 1999. "Trading Fast and Slow: Security Market Events in Real Time," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-012, New York University, Leonard N. Stern School of Business-.
    9. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    10. repec:sbe:breart:v:20:y:2000:i:1:a:2773 is not listed on IDEAS
    11. Kyoung-hun Bae & Albert S. Kyle & Eun Jung Lee & Anna Obizhaeva, 2016. "Invariance of buy-sell switching points," Working Papers w0232, Center for Economic and Financial Research (CEFIR).
    12. Senarathne, Chamil W & Jayasinghe, Prabhath, 2017. "Information Flow Interpretation of Heteroskedasticity for Capital Asset Pricing: An Expectation-based View of Risk," MPRA Paper 78771, University Library of Munich, Germany, revised 04 Apr 2017.
    13. Rene Carmona & Kevin Webster, 2017. "The microstructure of high frequency markets," Papers 1709.02015,
    14. Missaka Warusawitharana, 2016. "Time-varying Volatility and the Power Law Distribution of Stock Returns," Finance and Economics Discussion Series 2016-022, Board of Governors of the Federal Reserve System (U.S.).
    15. Parker, Edgar, 2016. "Flash Crashes: The Role of Information Processing Based Subordination and the Cauchy Distribution in Market Instability," MPRA Paper 80039, University Library of Munich, Germany.
    16. Smith, Geoffrey Peter, 2012. "Google Internet search activity and volatility prediction in the market for foreign currency," Finance Research Letters, Elsevier, vol. 9(2), pages 103-110.
    17. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    18. Beirlant, J. & Schoutens, W. & Segers, J.J.J., 2004. "Mandelbrot's Extremism," Discussion Paper 2004-125, Tilburg University, Center for Economic Research.
    19. José Antonio Climent-Hernández, 2017. "Portafolios de dispersión mínima con rendimientos log-estables Minimum dispersion portfolios with log-stable returns," Remef - The Mexican Journal of Economics and Finance, Instituto Mexicano de Ejecutivos de Finanzas. Remef, March.
    20. repec:sbe:breart:v:21:y:2001:i:2:a:2752 is not listed on IDEAS
    21. Pradosh Simlai, 2012. "Endogenous Information, Risk Characterization, and the Predictability of Average Stock Returns," Brazilian Review of Finance, Brazilian Society of Finance, vol. 10(3), pages 291-315.

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