Parallel cartoons of fractal models of finance
Having been crafted to welcome a new scientific journal, this paper looks forward but requires no special prerequisite. The argument builds on a technical wrinkle (used earlier but explained here fully for the first time), namely, the author’s grid-bound variant of Brownian motion B(t). While B(t) itself is additive, this variant is a multiplicative recursive process the author calls a ‘‘cartoon.’’ Reliance on this and related cartoons allows a new perspicuous exposition of the various fractal/multifractal models for the variation of financial prices. These illustrations do not claim to represent reality in its full detail, but suffice to imitate and bring out its principal features, namely, long tailedness, long dependence, and clustering. The goal is to convince the reader that the fractals/multifractals are not an exotic technical nightmare that could be avoided. In fact, the author’s models arose successively as proper, ‘‘natural,’’ and even ‘‘unavoidable’’ generalization of the Brownian motion model of price variation. Considered within the context of those generalizations, the original Brownian comes out as very special and narrowly constricted, while the fractal/multifractal models come out as nearly as simple and parsimonious as the Brownian. The cartoons are stylized recursive variants of the author’s fractal/multifractal models, which are even more versatile and realistic. Copyright Springer-Verlag Berlin Heidelberg 2005
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
- T. Lux, 2001. "Power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 560-562.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- B. B. Mandelbrot, 2001. "Stochastic volatility, power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 558-559.
- Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation for Research in Economics, Yale University.
When requesting a correction, please mention this item's handle: RePEc:kap:annfin:v:1:y:2005:i:2:p:179-192. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Christopher F. Baum)
If references are entirely missing, you can add them using this form.