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

Josep Perelló (), Jaume Masoliver () and Jean-Philippe Bouchaud
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Jean-Philippe Bouchaud: Science & Finance, Capital Fund Management

No 50001, Science & Finance (CFM) working paper archive from Science & Finance, Capital Fund Management

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.

JEL-codes: G10 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets, nep-fin and nep-fmk
Date: 2003-02

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Journal Article: Multiple time scales in volatility and leverage correlations: a stochastic volatility model (2004)
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Persistent link: http://EconPapers.repec.org/RePEc:sfi:sfiwpa:50001

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