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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. 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.
    2. 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.
    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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    Keywords

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    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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