2004/03/31 by Zoltan Eisler, Zoltán Eisler, János Kertész +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Asymmetry #Complex Systems and Time Series Analysis #Computer science #Econometrics #Economics #Financial Risk and Volatility Modeling #Fractal #Leverage (statistics) #Market Dynamics and Volatility #Mathematics #Monte Carlo method #Multifractal system #Realized variance #Skewness #Statistics #Stochastic volatility #Stock market #Stylized fact #Volatility (finance) #cond-mat.other #cond-mat.stat-mech #q-fin.ST
paper · pdf · doi:10.1016/j.physa.2004.05.061
published as Physica A 343, 603-622 (2004) · 23 pages, 8 figures, updated some figures and references, fixed two typos, accepted to Physica A
arxiv created 2004/05/11 · openalex publication_date 2004/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.