Modeling of Financial Data: Comparison of the Truncated Lévy Flight and the ARCH(1) and GARCH(1,1) processes

Details Modeling of Financial Data: Comparison of the Truncated Lévy Flight and the ARCH(1) and GARCH(1,1) processes Modeling of Financial Data: Comparison of the Truncated Lévy Flight and the ARCH(1) and GARCH(1,1) processes

1998-04-11

arxiv.org/abs/cond-mat/9804126v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, no figures, to appear in Physica A

Scientific paper

We compare our results on empirical analysis of financial data with simulations of two stochastic models of the dynamics of stock market prices. The two models are (i) the truncated L\'evy flight recently introduced by us and (ii) the ARCH(1) and GARCH(1,1) processes. We find that the TLF well describes the scaling and its breakdown observed in empirical data, while it is not able to properly describe the fluctuations of volatility empirically detected. The ARCH(1) and GARCH(1,1) models are able to describe the probability density function of price changes at a given time horizon, but both fail to describe the scaling properties of the PDFs for short time horizons.

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