Modeling record-breaking stock prices
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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Volume (Year): 396 (2014)
Issue (Month): C ()
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- 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.
- Gregor Wergen & Satya N. Majumdar & Gregory Schehr, 2012. "Record Statistics for Multiple Random Walks," Papers 1204.5039, arXiv.org.
- Baillie, R.T. & Degennaro, R.P., 1988.
"Stock Returns And Volatility,"
8803, Michigan State - Econometrics and Economic Theory.
- Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
- 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.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
- Lamoureux, Christopher G & Lastrapes, William D, 1990. " Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-229, March.
- 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;EDP Sciences, vol. 58(4), pages 483-491, 08.
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- 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.
- 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.
- 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.
- Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
- A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 1(2), pages 141-143, January.
- Gregor Wergen & Miro Bogner & Joachim Krug, 2011. "Record statistics for biased random walks, with an application to financial data," Papers 1103.0893, arXiv.org.
- Krug, Joachim & Jain, Kavita, 2005. "Breaking records in the evolutionary race," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 358(1), pages 1-9.
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