Portfolio value at risk based on independent component analysis

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.