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Multifractal model of asset returns with leverage effect

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  • Zoltan Eisler
  • Janos Kertesz

Abstract

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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  • Zoltan Eisler & Janos Kertesz, 2004. "Multifractal model of asset returns with leverage effect," Papers cond-mat/0403767, arXiv.org, revised May 2004.
    • Handle: RePEc:arx:papers:cond-mat/0403767
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    References listed on IDEAS

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    1. Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
    2. Benoit Pochard & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Science & Finance (CFM) working paper archive 0204047, Science & Finance, Capital Fund Management.
    3. Ghysels, E. & Jasiak, J., 1994. "Stochastic Volatility and time Deformation: An Application of trading Volume and Leverage Effects," Cahiers de recherche 9403, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Perelló, Josep & Masoliver, Jaume & Anento, Napoleón, 2004. "A comparison between several correlated stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 134-137.
    5. Gopikrishnan, P. & Plerou, V. & Gabaix, X. & Amaral, L.A.N. & Stanley, H.E., 2001. "Price fluctuations and market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 137-143.
    6. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    7. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    8. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    9. Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N, 2000. "Dynamics of the number of trades of financial securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(1), pages 136-141.
    10. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    11. Marc Potters & Jean-Philippe Bouchaud, 2001. "More stylized facts of financial markets: leverage effect and downside correlations," Science & Finance (CFM) working paper archive 29960, Science & Finance, Capital Fund Management.
    12. V. Plerou & P. Gopikrishnan & X. Gabaix & L. A. N. Amaral & H. E. Stanley, 2001. "Price fluctuations, market activity and trading volume," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 262-269.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    14. Laurent Calvet & Adlai Fisher, 2003. "Regime-Switching and the Estimation of Multifractal Processes," NBER Working Papers 9839, National Bureau of Economic Research, Inc.
    15. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161, arXiv.org.
    16. Bouchaud, Jean-Philippe & Potters, Marc, 2001. "More stylized facts of financial markets: leverage effect and downside correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 60-70.
    17. Benoit Pochart & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 303-314.
    18. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    19. Jaume Masoliver & Josep Perelló, 2002. "A Correlated Stochastic Volatility Model Measuring Leverage And Other Stylized Facts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 541-562.
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    Cited by:

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    5. Suárez-García, Pablo & Gómez-Ullate, David, 2014. "Multifractality and long memory of a financial index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 226-234.
    6. Wei, Yu & Chen, Wang & Lin, Yu, 2013. "Measuring daily Value-at-Risk of SSEC index: A new approach based on multifractal analysis and extreme value theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2163-2174.
    7. Morales Martínez, Jorge Luis & Segovia-Domínguez, Ignacio & Rodríguez, Israel Quiros & Horta-Rangel, Francisco Antonio & Sosa-Gómez, Guillermo, 2021. "A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    8. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    9. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2011. "A copula–multifractal volatility hedging model for CSI 300 index futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4260-4272.
    10. Chen, Wang & Wei, Yu & Lang, Qiaoqi & Lin, Yu & Liu, Maojuan, 2014. "Financial market volatility and contagion effect: A copula–multifractal volatility approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 289-300.
    11. Pan, Zhiyuan & Liu, Li, 2018. "Forecasting stock return volatility: A comparison between the roles of short-term and long-term leverage effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 168-180.
    12. Zunino, Luciano & Figliola, Alejandra & Tabak, Benjamin M. & Pérez, Darío G. & Garavaglia, Mario & Rosso, Osvaldo A., 2009. "Multifractal structure in Latin-American market indices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2331-2340.
    13. R. P. Datta, 2023. "Analysis of Indian foreign exchange markets: A Multifractal Detrended Fluctuation Analysis (MFDFA) approach," Papers 2306.16162, arXiv.org.
    14. Deniz Erer & Elif Erer & Selim Güngör, 2023. "The aggregate and sectoral time-varying market efficiency during crisis periods in Turkey: a comparative analysis with COVID-19 outbreak and the global financial crisis," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-25, December.
    15. Zunino, L. & Tabak, B.M. & Figliola, A. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2008. "A multifractal approach for stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6558-6566.

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