Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
Centre de Recherche Paul Pascal, Avenue Schweitzer 33600 Pessac,
2 Centre de Mathématiques appliquées, École Polytechnique, 91128 Palaiseau Cedex, France
Published online: 15 October 2000
In this paper, we provide a simple, "generic"interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as recently observed in reference , naturally emerge. We then propose a simple solvable "stochastic volatility"model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.45.Df – Fractals / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000