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

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dc.creatorPerello, Josep
dc.creatorMasoliver, Jaume
dc.creatorBouchaud, Jean-Philippe
dc.date2003-02-05
dc.date.accessioned2026-07-07T12:06:45Z
dc.date.available2026-07-07T12:06:45Z
dc.descriptionFinancial 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.
dc.description19 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0302095
dc.identifierhttp://arxiv.org/abs/cond-mat/0302095
dc.identifierApplied Mathematical Finance 11 (2004) 27-50
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208745
dc.subjectStatistical Mechanics
dc.subjectPhysics and Society
dc.subjectStatistical Finance
dc.titleMultiple time scales in volatility and leverage correlations: An stochastic volatility model
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