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Continuous cascade models for asset returns

Author

Listed:
  • Emmanuel Bacry

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Alexey Kozhemyak

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • J.-F. Muzy

    () (SPE - Sciences pour l'environnement - UPP - Université Pascal Paoli - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we make a short overview of continuous cascade models recently introduced to model asset return fluctuations. We show that these models account in a very parcimonious manner for most of 'stylized facts' of financial time-series. We review in more details the simplest continuous cascade namely the log-normal multifractal random walk (MRW). It can simply be considered as a stochastic volatility model where the (log-) volatility memory has a peculiar 'logarithmic' shape. This model possesses some appealing stability properties with respect to time aggregation. We describe how one can estimate it using a GMM method and we present some applications to volatility and (VaR) Value at Risk forecasting.

Suggested Citation

  • Emmanuel Bacry & Alexey Kozhemyak & J.-F. Muzy, 2008. "Continuous cascade models for asset returns," Post-Print hal-00604449, HAL.
  • Handle: RePEc:hal:journl:hal-00604449
    DOI: 10.1016/j.jedc.2007.01.024
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00604449
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    Cited by:

    1. van den Berg, Gerard J. & Lundborg, Petter & Nystedt, Paul & Rooth, Dan-Olof, 2009. "Critical Periods During Childhood and Adolescence: A Study of Adult Height Among Immigrant Siblings," IZA Discussion Papers 4140, Institute of Labor Economics (IZA).
    2. M. Rypdal & O. L{o}vsletten, 2011. "Multifractal modeling of short-term interest rates," Papers 1111.5265, arXiv.org.
    3. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Papers 1803.06917, arXiv.org.
    4. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    5. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters,in: Handbook of Research on Complexity, chapter 9 Edward Elgar Publishing.
    6. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW).
    7. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW).
    8. Cristina Sattarhoff & Marc Gronwald, 2018. "How to Measure Financial Market Efficiency? A Multifractality-Based Quantitative Approach with an Application to the European Carbon Market," CESifo Working Paper Series 7102, CESifo Group Munich.
    9. Josselin Garnier & Knut Solna, 2018. "Emergence of Turbulent Epochs in Oil Prices," Papers 1808.09382, arXiv.org, revised Apr 2019.
    10. Malo, Pekka, 2009. "Modeling electricity spot and futures price dependence: A multifrequency approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4763-4779.
    11. Morales, Raffaello & Di Matteo, T. & Aste, Tomaso, 2013. "Non-stationary multifractality in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6470-6483.
    12. Rypdal, Martin & Løvsletten, Ola, 2013. "Modeling electricity spot prices using mean-reverting multifractal processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 194-207.
    13. Annabel Vanroose, 2014. "Factors that explain the regional expansion of microfinance institutions in Peru," Working Papers CEB 14-030, ULB -- Universite Libre de Bruxelles.
    14. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Working Papers hal-01754054, HAL.
    15. Caraiani, Petre & Haven, Emmanuel, 2015. "Evidence of multifractality from CEE exchange rates against Euro," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 395-407.
    16. repec:eee:ecomod:v:241:y:2012:i:c:p:15-29 is not listed on IDEAS
    17. Martin Rypdal & Ola L{o}vsletten, 2012. "Modeling electricity spot prices using mean-reverting multifractal processes," Papers 1201.6137, arXiv.org.
    18. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    19. Francesco Sergi, 2015. "L'histoire (faussement) naïve des modèles DSGE," Documents de travail du Centre d'Economie de la Sorbonne 15066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    20. Lee, Hojin & Song, Jae Wook & Chang, Woojin, 2016. "Multifractal Value at Risk model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 113-122.
    21. Jochen Heberle & Cristina Sattarhoff, 2017. "A Fast Algorithm for the Computation of HAC Covariance Matrix Estimators," Econometrics, MDPI, Open Access Journal, vol. 5(1), pages 1-16, January.

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