Portfolio value at risk based on independent component analysis

  • Authors:
  • Ying Chen;Wolfgang Härdle;Vladimir Spokoiny

  • Affiliations:
  • CASE-Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, Spandauerstrasse 1, 10178 Berlin, Germany and Weierstraí-Ins ...;CASE-Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, Spandauerstrasse 1, 10178 Berlin, Germany;CASE-Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, Spandauerstrasse 1, 10178 Berlin, Germany and Weierstraí-Ins ...

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2007

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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.