Multifractal model of asset returns with leverage effect

Details Multifractal model of asset returns with leverage effect Multifractal model of asset returns with leverage effect

2004-03-31

arxiv.org/abs/cond-mat/0403767v2

Physica A 343, 603-622 (2004)

Physics

Condensed Matter

Other Condensed Matter

23 pages, 8 figures, updated some figures and references, fixed two typos, accepted to Physica A

Scientific paper

10.1016/j.physa.2004.05.061

Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the Lux model and refine the underlying phenomenological picture. We also give a procedure of fitting all parameters to empirical data. We present a new approach to account for the effective length of power-law memory in volatility. The second part of the paper deals with the consequences of asymmetry in returns. We incorporate two related stylized facts, skewness and leverage autocorrelations into the model. Then from Monte Carlo measurements we show, that this asymmetry significantly increases the mean squared error of volatility forecasts. Based on a filtering method we give evidence on similar behavior in empirical data.

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