4,658 research outputs found

    Modelling fluctuations of financial time series: from cascade process to stochastic volatility model

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    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.Comment: 21 pages, 5 figure

    Volatility fingerprints of large shocks: Endogeneous versus exogeneous

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    Finance is about how the continuous stream of news gets incorporated into prices. But not all news have the same impact. Can one distinguish the effects of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991 from financial crashes such as Oct. 1987 as well as smaller volatility bursts? Using a parsimonious autoregressive process with long-range memory defined on the logarithm of the volatility, we predict strikingly different response functions of the price volatility to great external shocks compared to what we term endogeneous shocks, i.e., which result from the cooperative accumulation of many small shocks. These predictions are remarkably well-confirmed empirically on a hierarchy of volatility shocks. Our theory allows us to classify two classes of events (endogeneous and exogeneous) with specific signatures and characteristic precursors for the endogeneous class. It also explains the origin of endogeneous shocks as the coherent accumulations of tiny bad news, and thus unify all previous explanations of large crashes including Oct. 1987.Comment: Latex document, 12 pages, 2 figure

    Self-Excited Multifractal Dynamics

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    We introduce the self-excited multifractal (SEMF) model, defined such that the amplitudes of the increments of the process are expressed as exponentials of a long memory of past increments. The principal novel feature of the model lies in the self-excitation mechanism combined with exponential nonlinearity, i.e. the explicit dependence of future values of the process on past ones. The self- excitation captures the microscopic origin of the emergent endogenous self-organization properties, such as the energy cascade in turbulent flows, the triggering of aftershocks by previous earthquakes and the "reflexive" interactions of financial markets. The SEMF process has all the standard stylized facts found in financial time series, which are robust to the specification of the parameters and the shape of the memory kernel: multifractality, heavy tails of the distribution of increments with intermediate asymptotics, zero correlation of the signed increments and long-range correlation of the squared increments, the asymmetry (called "leverage" effect) of the correlation between increments and absolute value of the increments and statistical asymmetry under time reversal
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