Multiple time scales in volatility and leverage correlations: 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. 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 InfoArticle provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 11 (2004)
Issue (Month): 1 ()
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Other versions of this item:
- Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2003. "Multiple time scales in volatility and leverage correlation: A stochastic volatility model," Science & Finance (CFM) working paper archive 50001, Science & Finance, Capital Fund Management.
- 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)
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