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Estimation of the Stylized Facts of a Stochastic Cascade Model

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Author Info
Céline Azizieh () (Centre Emile Bernheim, Solvay Business School, Université Libre de Bruxelles, Brussels)
Wolfgang Breymann () (Department of Mathematics, ETHZ, Zürich Switzerland)
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.

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File URL: http://www.solvay.edu/EN/Research/Bernheim/documents/wp05009.pdf
File Format: application/pdf
File Function: First version, 2005
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Publisher Info
Paper provided by Université Libre de Bruxelles, Solvay Brussels School of Economics and Management, Centre Emile Bernheim (CEB) in its series Working Papers CEB with number 05-009.RS.

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Length: 22 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:sol:wpaper:05-009

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Related research
Keywords: stochastic cascade; multifractal models; stochastic volatility;

Find related papers by 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: General - - - Estimation

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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. [Downloadable!] (restricted)
  2. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November. [Downloadable!] (restricted)
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  3. 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. [Downloadable!]
  4. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation, Yale University. [Downloadable!]
  5. Adlai Fisher & Laurent Calvet & Benoit Mandelbrot, 1997. "Multifractality of Deutschemark/US Dollar Exchange Rates," Cowles Foundation Discussion Papers 1166, Cowles Foundation, Yale University. [Downloadable!]
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