Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
Abstract
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 observed recently by Bonanno et al., 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.
Keywords
Cite
@article{arxiv.cond-mat/0005400,
title = {Modelling fluctuations of financial time series: from cascade process to stochastic volatility model},
author = {J. F. Muzy and J. Delour and E. Bacry},
journal= {arXiv preprint arXiv:cond-mat/0005400},
year = {2009}
}
Comments
21 pages, 5 figures