Multiple time scales in volatility and leverage correlation: A stochastic volatility model
AbstractFinancial 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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Bibliographic InfoPaper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 50001.
Date of creation: Feb 2003
Date of revision:
Other versions of this item:
- Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2004. "Multiple time scales in volatility and leverage correlations: a stochastic volatility model," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 11(1), pages 27-50.
- Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2003. "Multiple time scales in volatility and leverage correlations: An stochastic volatility model," Papers cond-mat/0302095, arXiv.org.
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-02-13 (All new papers)
- NEP-ETS-2005-02-13 (Econometric Time Series)
- NEP-FIN-2005-02-13 (Finance)
- NEP-FMK-2005-02-13 (Financial Markets)
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