Portfolio value at risk based on independent components analysis - Ying Chen; Wolfgang Karl Härdle; Vladimir Spokoiny (Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, 2005)
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.
Keywords: C14; C15; C32; C53; G20; 330; independent component analysis; Value-at-Risk