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Scaling in financial prices: II. Multifractals and the star equation

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  • B. B. Mandelbrot

Abstract

This is a direct continuation of the preceding paper, with which it shares the front material and the numbering of the sections. A little repetition makes it possible to read this paper, part II, by itself. It describes the progression of the formalism from the financial model the author introduced in 1963, with independence and [iopmath latex="$alphalt 2$"] <2 [/iopmath], to the financial model the author developed 1997, with multifractal dependence and [iopmath latex="$1lt alphalt infty$"] 1<< [/iopmath], and on to current developments. The long informal discussion in section 3 of the preceding paper is rephrased in formal fashion and extended. The presentation describes the original and the multifractal forms of a 'star equation' and then moves beyond it.

Suggested Citation

  • B. B. Mandelbrot, 2001. "Scaling in financial prices: II. Multifractals and the star equation," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 124-130.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:1:p:124-130
    DOI: 10.1080/713665540
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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. 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.
    5. Benoit B. Mandelbrot, 2005. "Parallel cartoons of fractal models of finance," Annals of Finance, Springer, vol. 1(2), pages 179-192, October.
    6. 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.
    7. 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.
    8. 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.
    9. Jean de Carufel & Martin Brooks & Michael Stieber & Paul Britton, 2017. "A Topological Approach to Scaling in Financial Data," Papers 1710.08860, arXiv.org.
    10. 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.

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