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Portfolio value at risk based on independent components analysis

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  • Chen, Ying
  • Härdle, Wolfgang Karl
  • Spokoiny, Vladimir

Abstract

Risk management technology applied to high dimensional portfolios needs simple and fast methods for calculation of Value-at-Risk (VaR). The multivariate normal framework provides a simple off-the-shelf methodology but lacks the heavy tailed distributional properties that are observed in data. A principle component based method (tied closely to the elliptical structure of the distribution) is therefore expected to be unsatisfactory. Here we propose and analyze a technology that is based on Independent Component Analysis (ICA). We study the proposed ICVaR methodology in an extensive simulation study and apply it to a high dimensional portfolio situation. Our analysis yields very accurate VaRs.

Suggested Citation

  • Chen, Ying & Härdle, Wolfgang Karl & Spokoiny, Vladimir, 2005. "Portfolio value at risk based on independent components analysis," SFB 649 Discussion Papers 2005-060, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2005-060
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    References listed on IDEAS

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    1. Chen, Ying & Härdle, Wolfgang & Jeong, Seok-Oh, 2008. "Nonparametric Risk Management With Generalized Hyperbolic Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 910-923.
    2. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH," NBER Working Papers 8554, National Bureau of Economic Research, Inc.
    3. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
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    Cited by:

    1. Kritski, Oleg & Ulyanova, Marina, 2007. "Assessment of Multivariate Financial Risks of a Stock Share Portfolio," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 8(4), pages 3-17.

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    More about this item

    Keywords

    independent component analysis; Value-at-Risk;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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