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Estimation of the Stylized Facts of a Stochastic Cascade Model

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  • Céline Azizieh
  • Wolfgang Breymann

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:sol:wpaper:05-009
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    References listed on IDEAS

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    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    2. 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.
    3. 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.
    4. Wolfgang Breymann & Shoaleh Ghashghaie & Peter Talkner, 2000. "A Stochastic Cascade Model For Fx Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 357-360.
    5. Wolfgang Breymann & Shoaleh Ghashghaie & Peter Talkner, 2000. "A Stochastic Cascade Model for FX Dynamics," Papers cond-mat/0004179, arXiv.org.
    6. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    7. 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.
    8. 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.
    9. 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.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    11. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    12. 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.
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    Cited by:

    1. Crepaldi, Antonio F. & Neto, Camilo Rodrigues & Ferreira, Fernando F. & Francisco, Gerson, 2009. "Multifractal regime transition in a modified minority game model," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1364-1371.

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    More about this item

    Keywords

    stochastic cascade; multifractal models; stochastic volatility;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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