Large Deviations and the Distribution of Price Changes
AbstractThe Multifractal Model of Asset Returns ("MMAR," see Mandelbrot, Fisher, and Calvet, 1997) proposes a class of multifractal processes for the modelling of financial returns. In that paper, multifractal processes are defined by a scaling law for moments of the processes' increments over finite time intervals. In the present paper, we discuss the local behavior of multifractal processes. We employ local Holder exponents, a fundamental concept in real analysis that describes the local scaling properties of a realized path at any point in time. In contrast with the standard models of continuous time finance, multifractal processes contain a multiplicity of local Holder exponents within any finite time interval. We characterize the distribution of Holder exponents by the multifractal spectrum of the process. For a broad class of multifractal processes, this distribution can be obtained by an application of Cramer's Large Deviation Theory. In an alternative interpretation, the multifractal spectrum describes the fractal dimension of the set of points having a given local Holder exponent. Finally, we show how to obtain processes with varied spectra. This allows the applied researcher to relate an empirical estimate of the multifractal spectrum back to a particular construction of the Stochastic process.
Download InfoIf 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.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1165.
Length: 30 pages
Date of creation: Sep 1997
Date of revision:
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
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.:
- Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999.
"A Multifractal Model of Assets Returns,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
99-072, New York University, Leonard N. Stern School of Business-.
- Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation for Research in Economics, Yale University.
- Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997.
"A Multifractal Model of Asset Returns,"
Cowles Foundation Discussion Papers
1164, Cowles Foundation for Research in Economics, Yale University.
- Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999. "A Multifractal Model of Assets Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-072, New York University, Leonard N. Stern School of Business-.
- Calvet, Laurent & Fisher, Adlai, 2001.
"Forecasting multifractal volatility,"
Journal of Econometrics,
Elsevier, vol. 105(1), pages 27-58, November.
- Laurent Calvet & Adlai Fisher, 1999. "Forecasting Multifractal Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-017, New York University, Leonard N. Stern School of Business-.
- Laurent Calvet, 2000. "Forecasting Multifractal Volatility," Harvard Institute of Economic Research Working Papers 1902, Harvard - Institute of Economic Research.
- Lux, Thomas & Kaizoji, Taisei, 2007.
"Forecasting volatility and volume in the Tokyo Stock Market: Long memory, fractality and regime switching,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 31(6), pages 1808-1843, June.
- Taisei Kaizoji & Thomas Lux, 2006. "Forecasting Volatility and Volume in the Tokyo Stock Market: Long Memory, Fractality and Regime Switching," Working Papers wp06-20, Warwick Business School, Finance Group.
- Lux, Thomas & Kaizoji, Taisei, 2006. "Forecasting volatility and volume in the Tokyo stock market: Long memory, fractality and regime switching," Economics Working Papers 2006,13, Christian-Albrechts-University of Kiel, Department of Economics.
- Mulligan, Robert F. & Lombardo, Gary A., 2004. "Maritime businesses: volatile stock prices and market valuation inefficiencies," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 321-336, May.
- Céline Azizieh & Wolfgang Breymann, 2005. "Estimation of the Stylized Facts of a Stochastic Cascade Model," Working Papers CEB 05-009.RS, ULB -- Universite Libre de Bruxelles.
- Mulligan, Robert F., 2004. "Fractal analysis of highly volatile markets: an application to technology equities," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(1), pages 155-179, February.
- repec:ebl:ecbull:v:3:y:2003:i:31:p:1-12 is not listed on IDEAS
- Suárez-García, Pablo & Gómez-Ullate, David, 2014. "Multifractality and long memory of a financial index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 226-234.
- Cornelis A. Los, 2005. "The Degree of Stability of Price Diffusion," Finance 0508006, EconWPA.
- Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, School of Economics and Management, University of Aarhus.
- Benoit B. Mandelbrot, 2005. "Parallel cartoons of fractal models of finance," Annals of Finance, Springer, vol. 1(2), pages 179-192, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If references are entirely missing, you can add them using this form.