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Multiple time scales in volatility and leverage correlation: A stochastic volatility model

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  • Josep Perello
  • Jaume Masoliver
  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

Abstract

Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.

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Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 50001.

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Date of creation: Feb 2003
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Handle: RePEc:sfi:sfiwpa:50001

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Cited by:
  1. Yang, Honglin & Wan, Hong & Zha, Yong, 2013. "Autocorrelation type, timescale and statistical property in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1681-1693.
  2. Griffin, Jim & Steel, Mark F.J., 2008. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," MPRA Paper 11071, University Library of Munich, Germany.
  3. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Publishing House "SINERGIA PRESS", Publishing House "SINERGIA PRESS", vol. 15(3), pages 94-138.
  4. Lisa Borland & Jean-Philippe Bouchaud, 2005. "On a multi-timescale statistical feedback model for volatility fluctuations," Science & Finance (CFM) working paper archive 500059, Science & Finance, Capital Fund Management.
  5. Danilo Delpini & Giacomo Bormetti, 2012. "Stochastic Volatility with Heterogeneous Time Scales," Papers 1206.0026, arXiv.org, revised Apr 2013.
  6. Pierre-Alain Reigneron & Romain Allez & Jean-Philippe Bouchaud, 2010. "Principal Regression Analysis and the index leverage effect," Papers 1011.5810, arXiv.org, revised Feb 2011.
  7. Matthew Lorig, 2010. "Time-Changed Fast Mean-Reverting Stochastic Volatility Models," Papers 1010.5203, arXiv.org, revised Apr 2012.
  8. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models : from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
  9. Buchbinder, G.L. & Chistilin, K.M., 2007. "Multiple time scales and the empirical models for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 168-178.
  10. 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.

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