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Modeling record-breaking stock prices

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  • Wergen, Gregor
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    Abstract

    We study the statistics of record-breaking events in daily stock prices of 366 stocks from the Standard and Poor’s 500 stock index. Both the record events in the daily stock prices themselves and the records in the daily returns are discussed. In both cases we try to describe the record statistics of the stock data with simple theoretical models. The daily returns are compared to i.i.d. RVs and the stock prices are modeled using a biased random walk, for which the record statistics are known. These models agree partly with the behavior of the stock data, but we also identify several interesting deviations. Most importantly, the number of records in the stocks appears to be systematically decreased in comparison with the random walk model. Considering the autoregressive AR(1) process, we can predict the record statistics of the daily stock prices more accurately. We also compare the stock data with simulations of the record statistics of the more complicated GARCH(1, 1) model, which, in combination with the AR(1) model, gives the best agreement with the observational data. To better understand our findings, we discuss the survival and first-passage times of stock prices on certain intervals and analyze the correlations between the individual record events. After recapitulating some recent results for the record statistics of ensembles of N stocks, we also present some new observations for the weekly distributions of record events.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 396 (2014)
    Issue (Month): C ()
    Pages: 114-133

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    Handle: RePEc:eee:phsmap:v:396:y:2014:i:c:p:114-133

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Record statistics; Extreme value statistics; Extreme events in financial markets; Random walks; Autoregressive processes; GARCH-models;

    References

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    1. A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 1(2), pages 141-143, January.
    2. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
    3. Satya N. Majumdar & Gregory Schehr & Gregor Wergen, 2012. "Record statistics and persistence for a random walk with a drift," Papers 1206.6972, arXiv.org, revised Aug 2012.
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    6. Gregor Wergen & Satya N. Majumdar & Gregory Schehr, 2012. "Record Statistics for Multiple Random Walks," Papers 1204.5039, arXiv.org.
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    10. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    11. Baillie, R.T. & Degennaro, R.P., 1988. "Stock Returns And Volatility," Papers 8803, Michigan State - Econometrics and Economic Theory.
    12. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-66, December.
    13. P. Sibani, 2007. "Linear response in aging glassy systems, intermittency and the Poisson statistics of record fluctuations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 58(4), pages 483-491, 08.
    14. Brooks,Chris, 2008. "Introductory Econometrics for Finance," Cambridge Books, Cambridge University Press, number 9780521694681.
    15. Daniel Gembris & John G. Taylor & Dieter Suter, 2007. "Evolution of Athletic Records: Statistical Effects versus Real Improvements," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(5), pages 529-545.
    16. Ditlevsen, Susanne, 2007. "A result on the first-passage time of an Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1744-1749, December.
    17. Gregor Wergen & Miro Bogner & Joachim Krug, 2011. "Record statistics for biased random walks, with an application to financial data," Papers 1103.0893, arXiv.org.
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