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Estimation of the Stylized Facts of a Stochastic Cascade Model

  • Céline Azizieh
  • Wolfgang Breymann
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    We present a time series model that integrates properties from Levy-type and multifractal models. Formally, it is a stochastic volatility model with discrete time steps, t-distributed return innovations and a stochastic cascade for the volatility process. This model reproduces very well different stylized facts which cannot be reproduced together by other classes of models. We also present an estimation procedure based on the reproduction of stylized facts. This procedure is general and can easily be adapted and/or extended to other models. It may be considered as an extension of the generalized method of moments.

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    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/53907/1/RePEc_sol_wpaper_05-009.pdf
    File Function: RePEc_sol_wpaper_05-009
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    Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers CEB with number 05-009.RS.

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    Length: 22 p.
    Date of creation: 2005
    Date of revision:
    Publication status: Published by:
    Handle: RePEc:sol:wpaper:05-009
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    Web page: http://difusion.ulb.ac.be
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    1. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    2. 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.
    3. 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.
    4. 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-.
    5. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53.
    6. Olivier V. Pictet & Michel M. Dacorogna & Ulrich A. Muller, 1996. "Hill, Bootstrap and Jackknife Estimators for Heavy Tails," Working Papers 1996-12-10, Olsen and Associates.
    7. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
    8. Laurent-Emmanuel Calvet & Adlai J. Fisher, 2001. "Forecasting multifractal volatility," Post-Print hal-00477952, HAL.
    9. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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