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Flexible and robust modelling of volatility comovements: a comparison of two multifractal models

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  • Liu, Ruipeng
  • Lux, Thomas

Abstract

Long memory (long-term dependence) of volatility counts as one of the ubiquitous stylized facts of financial data. Inspired by the long memory property, multifractal processes have recently been introduced as a new tool for modeling financial time series. In this paper, we propose a parsimonious version of a bivariate multifractal model and estimate its parameters via both maximum likelihood and simulation based inference approaches. In order to explore its practical performance, we apply the model for computing value-at-risk and expected shortfall statistics for various portfolios and compare the results with those from an alternative bivariate multifractal model proposed by Calvet et al. (2006) and the bivariate CC-GARCH of Bollerslev (1990). As it turns out, the multifractal models provide much more reliable results than CC-GARCH, and our new model compares well with the one of Calvet et al. although it has an even smaller number of parameters.

Suggested Citation

  • Liu, Ruipeng & Lux, Thomas, 2010. "Flexible and robust modelling of volatility comovements: a comparison of two multifractal models," Kiel Working Papers 1594, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwkwp:1594
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    References listed on IDEAS

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    1. Lux, Thomas, 2008. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 194-210, April.
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    11. Lux, Thomas & Kaizoji, Taisei, 2007. "Forecasting volatility and volume in the Tokyo Stock Market: Long memory, fractality and regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1808-1843, June.
    12. Lux, Thomas & Morales-Arias, Leonardo, 2010. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2676-2692, November.
    13. Liu, Ruipeng & Di Matteo, Tiziana & Lux, Thomas, 2008. "Multifractality and long-range dependence of asset returns: The scaling behaviour of the Markov-switching multifractal model with lognormal volatility components," Kiel Working Papers 1427, Kiel Institute for the World Economy (IfW Kiel).
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    More about this item

    Keywords

    Long memory; multifractal models; simulation based inference; value-at-risk; expected shortfall;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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