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Multiple time scales in volatility and leverage correlations: a stochastic volatility model

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  • Josep Perello
  • Jaume Masoliver
  • Jean-Philippe Bouchaud

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. This paper extends the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. It is found that the resulting three-dimensional diffusion process can account for different correlation time scales. It is shown 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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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 11 (2004)
Issue (Month): 1 ()
Pages: 27-50

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Handle: RePEc:taf:apmtfi:v:11:y:2004:i:1:p:27-50

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Cited by:
  1. 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.
  2. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 15(3), pages 94-138.
  3. Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
  4. Matthew Lorig, 2010. "Time-Changed Fast Mean-Reverting Stochastic Volatility Models," Papers 1010.5203, arXiv.org, revised Apr 2012.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Danilo Delpini & Giacomo Bormetti, 2012. "Stochastic Volatility with Heterogeneous Time Scales," Papers 1206.0026, arXiv.org, revised Apr 2013.

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