Multiple Time Scales in Volatility and Leverage Correlations: An Stochastic Volatility Model

19 Pages Posted: 14 Oct 2003 Last revised: 16 Nov 2013

See all articles by Josep Perelló

Josep Perelló

University of Barcelona - Department of Physics

Jaume Masoliver

University of Barcelona - Department of Physics

Jean-Philippe Bouchaud

Capital Fund Management

Date Written: February 5, 2003

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.

Keywords: financial markets, stochastic volatility model, leverage correlation, volatility autocorrelation

Suggested Citation

Perello, Josep and Masoliver, Jaume and Bouchaud, Jean-Philippe, Multiple Time Scales in Volatility and Leverage Correlations: An Stochastic Volatility Model (February 5, 2003). Applied Mathematical Finance, Vol. 11, 2004. Available at SSRN: https://ssrn.com/abstract=381780 or http://dx.doi.org/10.2139/ssrn.381780

Josep Perello (Contact Author)

University of Barcelona - Department of Physics ( email )

Diagonal, 647
Barcelona, E-08028
Spain
+34 9 34021150 (Phone)
+34 34021149 (Fax)

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

Jean-Philippe Bouchaud

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

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