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Scaling in financial prices: I. Tails and dependence

Author

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  • B. B. Mandelbrot

Abstract

The scaling properties of financial prices raise many questions. To provide background - appropriately so in the first issue of a new journal! - this paper, part I (sections 1 to 3), is largely a survey of the present form of some material that is well known yet repeatedly rediscovered. It originated in the author's work during the 1960s. Part II follows as sections 4 to 6, but can to a large extent be read separately. It is more technical and includes important material on multifractals and the 'star equation'; part of it appeared in 1974 but is little known or appreciated - for reasons that will be mentioned. Part II ends by showing the direct relevance to finance of a very recent improvement on the author's original (1974) theory of multifractals.

Suggested Citation

  • B. B. Mandelbrot, 2001. "Scaling in financial prices: I. Tails and dependence," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 113-123.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:1:p:113-123
    DOI: 10.1080/713665539
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    Citations

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    Cited by:

    1. Arun Kumar & Palaniappan Vellaisamy, 2012. "Fractional Normal Inverse Gaussian Process," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 263-283, June.
    2. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    3. A. K. M. Azhar & Vincent B. Y. Gan & W. A. T. Wan Abdullah & H. Zainuddin, 2015. "On the Fractal Geometry of the Balance Sheet and the Fractal Index of Insolvency Risk," Papers 1512.09280, arXiv.org.
    4. Wilhelm Berghorn & Sascha Otto, 2017. "Mandelbrot Market-Model and Momentum," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 8(3), pages 1-26, July.
    5. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    6. Gu, Gao-Feng & Zhou, Wei-Xing, 2007. "Statistical properties of daily ensemble variables in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 497-506.
    7. Raj Aggarwal & Min Qi, 2009. "Distribution of extreme changes in Asian currencies: tail index estimates and value-at-risk calculations," Applied Financial Economics, Taylor & Francis Journals, vol. 19(13), pages 1083-1102.
    8. Heinrich, Torsten, 2016. "The Narrow and the Broad Approach to Evolutionary Modeling in Economics," MPRA Paper 75797, University Library of Munich, Germany.
    9. Kelvin J. L. Koa & Yunshan Ma & Ritchie Ng & Huanhuan Zheng & Tat-Seng Chua, 2024. "Temporal Relational Reasoning of Large Language Models for Detecting Stock Portfolio Crashes," Papers 2410.17266, arXiv.org.
    10. Benoit B. Mandelbrot, 2005. "Parallel cartoons of fractal models of finance," Annals of Finance, Springer, vol. 1(2), pages 179-192, October.
    11. Sutthisit Jamdee & Cornelis A. Los, 2005. "Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate," Finance 0502021, University Library of Munich, Germany.
    12. Dr. Brian J. Jacobsen, 2005. "The Use of Downside Risk Measures in Portfolio Construction and Evaluation," Computing in Economics and Finance 2005 5, Society for Computational Economics.
    13. M. A. H. Dempster, 2011. "Benoit B. Mandelbrot (1924-2010): a father of Quantitative Finance," Quantitative Finance, Taylor & Francis Journals, vol. 11(2), pages 155-156.
    14. Wilhelm Berghorn & Martin T. Schulz & Markus Vogl & Sascha Otto, 2021. "Trend Momentum II: Driving Forces of Low Volatility and Momentum," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 12(3), pages 300-319, May.
    15. Iacopo Giampaoli & Wing Lon Ng & Nick Constantinou, 2013. "Periodicities Of Foreign Exchange Markets And The Directional Change Power Law," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 20(3), pages 189-206, July.
    16. Jean de Carufel & Martin Brooks & Michael Stieber & Paul Britton, 2017. "A Topological Approach to Scaling in Financial Data," Papers 1710.08860, arXiv.org.
    17. Chris Heyde, 2009. "Scaling issues for risky asset modelling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 593-603, July.
    18. Dai, Zhifeng & Kang, Jie & Wen, Fenghua, 2021. "Predicting stock returns: A risk measurement perspective," International Review of Financial Analysis, Elsevier, vol. 74(C).

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