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

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

2003-02-05

arxiv.org/abs/cond-mat/0302095v1

Applied Mathematical Finance 11 (2004) 27-50

Physics

Condensed Matter

Statistical Mechanics

19 pages, 5 figures

Scientific paper

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.

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