This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Forecasting Multifractal Volatility

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Laurent Calvet

Additional information is available for the following registered author(s):

Abstract

| Paper

This paper develops analytical methods to forecast the distribution of future returns for a new continuous-time process, the Poisson multi-fractal. The process captures the thick tails, volatility persistence and moment scaling exhibited by many financial time series. It can be interpreted as a stochastic volatility model with multiple frequencies and a Markov latent state. We assume for simplicity that the forecaster knows the true generating process with certainty but only observes past returns. The challenge in this environment is long memory and the corresponding infinite dimension of the state space. We introduce a discretized version of the model that has a finite state space and allows for an analytical solution to the conditioning problem. As the grid size goes to infinity, the discretized model weakly converges to the continuous-time process, implying the consistsency of the density forecasts.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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.

File URL: ftp://all.repec.org/RePEc/fth/harver/hier1902.pdf
Our checks indicate that this address may not be valid because: 404 File not found. If this is indeed the case, please notify (Thomas Krichel)
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 1902.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length:
Date of creation: 2000
Date of revision:
Handle: RePEc:fth:harver:1902

Contact details of provider:
Postal: 200 Littauer Center, Cambridge, MA 02138
Web page: http://www.economics.harvard.edu/journals/hier
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Thomas Krichel).

Related research
Keywords:

Other versions of this item:

This paper has been announced in the following NEP Reports: 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.:
  1. Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  3. Kurz, Mordecai, 1994. "On Rational Belief Equilibria," Economic Theory, Springer, vol. 4(6), pages 859-76, October.
  4. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July. [Downloadable!] (restricted)
  5. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  6. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July. [Downloadable!] (restricted)
  7. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation, Yale University. [Downloadable!]
  8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  9. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Lux, Thomas, 2003. "The multi-fractal model of asset returns : its estimation via GMM and its use for volatility forecasting," Economics Working Papers 2003,13, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
    Other versions:
  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2005. "Roughing it Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," NBER Working Papers 11775, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Marina Resta & Davide Sciutti, . "A characterization of self-affine processes in finance through the scaling function," Modeling, Computing, and Mastering Complexity 2003 13, Society for Computational Economics. [Downloadable!]
  4. Céline Azizieh & Wolfgang Breymann, 2005. "Estimation of the Stylized Facts of a Stochastic Cascade Model," Working Papers CEB 05-009.RS, Université Libre de Bruxelles, Solvay Brussels School of Economics and Management, Centre Emile Bernheim (CEB). [Downloadable!]
  5. Laurent E. Calvet & Adlai J. Fisher, 2006. "Multifrequency Jump-Diffusions: An Equilibrium Approach," NBER Working Papers 12797, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  6. Idier, J., 2008. "Long term vs. short term comovements in stock markets: the use of Markov-switching multifractal models," Documents de Travail 218, Banque de France. [Downloadable!]
  7. Benoit Pochard & Jean-Philippe Bouchaud, 2003. "Option pricing and hedging with minimum expected shortfall," Science & Finance (CFM) working paper archive 500029, Science & Finance, Capital Fund Management. [Downloadable!]
  8. Laurent E. Calvet & Adlai J. Fisher, 2005. "Multifrequency News and Stock Returns," NBER Working Papers 11441, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold,, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," CFS Working Paper Series 2003/35, Center for Financial Studies. [Downloadable!]
    Other versions:
  10. Lux, Thomas & Kaizoji, Taisei, 2004. "Forecasting volatility and volume in the Tokyo stock market : the advantage of long memory models," Economics Working Papers 2004,05, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  11. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  12. 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. [Downloadable!]
    Other versions:
  13. Oriol Pont & Antonio Turiel & Conrad Perez-Vicente, 2009. "Description, modelling and forecasting of data with optimal wavelets," Journal of Economic Interaction and Coordination, Springer, vol. 4(1), pages 39-54, June. [Downloadable!] (restricted)
  14. Laurent E. Calvet & Adlai J. Fisher & Samuel B. Thompson, 2004. "Volatility Comovement: A Multifrequency Approach," NBER Technical Working Papers 0300, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
Statistics
Access and download statistics

Did you know? RePEc stands for Research Papers in Economics.

This page was last updated on 2009-12-2.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.